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Lesson Warm Up 1 1 f. rational numbers; Sample: The value of the coins will have tenths and hundredths places. 1. Venn diagram − 2. 0.2 3. 4.375 g. C ∩ D = {20}; C ∪ D = {4, 5, 8, 10, 12, 15, 16, 20} 3 4. _ 5 3 5. 5 _ 4 h. C ∩ D = { } or ∅; C ∪ D = {6, 7, 12, 14, 18, 21, 24, 28} Lesson Practice 1 a. integers, rational numbers, real numbers i. true j. false; counterexample: 1 ÷ 2 = 0.5 b. rational numbers, real numbers c. irrational numbers, real numbers d. whole numbers; Sample: There can be no people or any number of people. e. irrational numbers; Sample: Area is equal to pi times the radius squared, so the answer will be irrational. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 1–1 Saxon Algebra 1 Lesson Practice 1 1. 160.515 67 11 _ or 1 2. _ 56 56 3. 1060 17 4. _ 20 5. 0.375 2 6. _ 3 7 7. 5_ 10 4 8. Sample: _ 10 9. Student B; Sample: Student A did not factor the 9 completely. 10. 2 · 2 · 2 · 2 · 3 · 3 11. 15% 1 18. false; Sample: A right angle and an obtuse angle have a sum of more than 180°. 3 inches 19. 4 _ 4 20. true; Sample: By definition, an acute triangle has only acute angles. 21. false; A trapezoid has only one pair of parallel sides. 22. rational numbers 23. true; Sample: By definition, a parallelogram has two pairs of parallel sides. 12. 720% 24. yes; The ones digit is even. 13. {1, 2, 3,…} 25. irrational numbers 14. whole numbers 26. a. 18 square feet b. rational numbers, integers, whole numbers, and natural numbers 15. K = {0, 2, 4, 6, 8, 10} 16. B 17. rational number © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 1–2 Saxon Algebra 1 Lesson 1 27. 36.96 miles 28. yes; The sum of digits is 2 + 0 + 7 = 9, which is divisible by 3. 3 4 _ > 29. _ 5 7 30. rational numbers © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 1–3 Saxon Algebra 1 Lesson 2 Warm Up 2 1. product 11 2. _ 15 3. 732.49 4. 1.035 1 5. _ 12 Lesson Practice 2 a. 65, 12; q, r, s, x b. 4, 71; g, h, y, z c. 17, d, e, f; 17 1 1 _ , u, v; d. _ 4 4 e. -3, s, t; -3 f. a, b, c; 1 63b g. 8v, 17yz, _ 4gh (4 + 2x) h. _ , 18s, 47jkl 38q i. 3 j. 6.50, 3.25, 0.75 k. h, b © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 2–1 Saxon Algebra 1 Lesson Practice 2 1. 8 2. 14 3. 36 4. 30 2 5. _ 5 2 12. false; Sample: By definition, the sets of rational and irrational numbers do not have any members in common. 13. a. 1 two; 3 threes; 3 fours; 1 five; 4 sixes; 1 seven 5 6. _ 9 b. 7. coefficients: 1, 12; variables: r, s, t, v Frequency of Numbers X X X X X X X X X X X X X 2 3 4 5 6 7 8 Numbers 8. coefficients: 2, 7; variables: x, y, w 2 ; 9. coefficients: 47, _ 5 variables: s, t 10. false; Sample: Zero is a whole number, but it is not a natural number. 11. true; Sample: The set of integers is a subset of real numbers. 14. whole numbers, integers, and rational numbers 17 meters; 15. 13 _ 24 rational numbers 16. 3 · 3 · 17 17. false; Sample: The sum of two obtuse angles is greater than 180º. 18. straight 19. no; The number formed by the last two digits is not divisible by 4. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 2–2 Saxon Algebra 1 Lesson 2 20. 0.3% 21. {0, 1, 2, 3,…} 21. natural numbers 23. D 24. constants: 2 and π; variables r and v; coefficient: 2π 25. c and a 26. Student B; Student A listed two terms. 27. a. 0.53, π b. r, h 28. C 29. 2 terms 30. whole numbers © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 2–3 Saxon Algebra 1 Lesson 3 Warm Up 3 1. variable 2. 0.84 3. 4.95 4. 5. (_47 ) (_38 ) Lesson Practice 3 a. 1296 b. 1.96 8 c. _ 125 d. 1,000,000 e. w12 f. y11z16 g. 1018 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 3–1 Saxon Algebra 1 Lesson Practice 3 3 12. true; Sample: By definition, the set of irrational numbers is a subset of the set of real numbers. 1. 5 2. 16 3. 24 13. > 4. 28 14. < 9 5. _ 20 21 15. 8 _ 40 1 6. _ 2 16. {…, -3, -2, -1, 0, 1, 2, 3,…}; temperature 7. coefficients: 6, 4; variables: m, n, b 17. 2 · 7 · 7 8. coefficients: 5, 9; variables: j, c, d 18. Student B; Sample: Student A multiplied the exponents instead of adding them. 4 ; 9. coefficients: 23, _ 7 variables: t, w 10. false; Sample: Fractions are real numbers, but they are not integers. 11. true; Sample: The set of whole numbers contains all the natural numbers and zero. 19. false; Sample: A rhombus does not always have 4 right angles to make it a square. 20. yes; The number is divisible by 2 and by 3. 21. a. 3 b. 6 c. 729 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 3–2 Saxon Algebra 1 Lesson 3 22. B 23. 4096 recipes 24. a. 1000 b. 109 dollars; $1,000,000,000 25. 675,000 people 26. A 27. 256 bacteria 1 28. _ 2 29. 27 ft3 30. a. 2 terms b. l and w © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 3–3 Saxon Algebra 1 Lesson 4 3 4. _ 8 Warm Up 4 1 5. 1 _ 5 1. exponent 2. 42.25 3. 82.2 Lesson Practice 4 a. 45 - (2 + 4) · 5 - 3 = 45 - 6 · 5 - 3 = 45 - 30 - 3 = 12 b. 9 · 23 - 9 ÷ 3 =9·8-9÷3 = 72 - 3 = 69 Simplify inside parentheses. Multiply. Subtract. Simplify the exponent. Multiply and divide from left to right. Subtract. 15 - 32 + 4 · 2 __ c. 7 15 - 9 + 4 · 2 =_ 7 Simplify exponents. 15 - 9 + 8 =_ 7 Multiply. 14 =_ 7 Add and subtract left to right in numerator. =2 Divide. d. > 3 9 π i n e. _ 2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 4–1 Saxon Algebra 1 Lesson Practice 4 3 1. 6 _ 4 3 2. 2_ 20 3 3. 3_ 8 4. 2 4 15. <; Sample: The value of the first expression is 64, and the value of the second expression is 96. 16. B 17. 5. 11.73 Frequency of Numbers X X X X X X X X X X X X X X 2 3 4 5 6 7 8 9 Numbers 6. 9.568 7. 3 8. 3 · 3 · 5 · 5 9. 124,302 is divisible by 3; Sample: The sum of the digits is 12, which is divisible by 3. 10. L = {-15, -8, 0, 1, 3, 6, 7, 12} 11. true; Sample: The set of whole numbers is a subset of the set of integers. 12. irrationals and reals 13. 16.7% 18. true; A square has 4 right angles and its opposite sides are parallel and congruent. 8 yards 19. 7 _ 15 20. Student B; Sample: Student A has an extra factor of 3, which results in a product of 324. 21. yes; The sum of the digits 1 + 1 + 1 + 6 = 9, which is divisible by 9. 22. a. n, x, y n , 3xy, 19 b. _ 6 14. 55.6% © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 4–2 Saxon Algebra 1 Lesson 4 23. (2300 - 1100) ÷ (2003 - 1976) = 1200 ÷ 27 ≈ 44 wolves 24. B 25. 353.2 cm 2 26. a. 12 · 5¢ + 2 · 10¢ + 4 · 25¢ = 60¢ + 20¢ + 100¢ = 180¢ b. 10 · 5¢ + 4 · 10¢ + 3 · 25¢ = 50¢ + 40¢ + 75¢ = 165¢ c. Ashley 27. 32 markers 28. Volume of cube = s 3 29. 42.8°C 30. $43.61 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 4–3 Saxon Algebra 1 Lesson 5 Warm Up 5 1. real numbers 2. 26.82 7 3. _ 8 4. 77.99 3 5. _ 8 Lesson Practice 5 a. 3.4 6 b. _ 7 c. 8 d. -23 e. -4.68 5 f. - _ 6 g. true h. true i. 22°F © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 5–1 Saxon Algebra 1 Lesson Practice 5 5 17. C 1 1. 4 _ 2 18. $1.30 1 2. 1_ 8 19. The distance from -5 to 0 is 5. 13 3. 3_ 24 1 4. 2_ 12 5. 7.53 20. true; The opposite sides of rectangles are congruent and parallel. 2 6. 3.468 7. 3 8. 2 · 3 · 5 · 5 9. yes; The ones digit is 0. 10. L = {-12, -8, -4, 0, 4, 8, 12} 11. true; All integers can be expressed as fractions. 12. Student B; Sample: 2 is irrational. The √ 21. No, a should be determined first. 22. 26°F. 1 1 _ = -5 23. 8 + -13 _ 2 2 yards ( 24. D 25. Airplane A 26. $500 + (-$34.65) = $465.35 27. a. $145.75 b. $153.04 13. 0.625; 62.5% 14. 3 feet, 1.25 yards, 1 yards 1_ 3 7 ; 0.07 15. _ 100 ) 28. -44.18 points 29. A 30. 16°F 16. |-11| = 11 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 5–2 Saxon Algebra 1 Lesson 6 Warm Up 6 1. absolute value 2. 67.96 7 3. _ 9 4. 124.76 5 5. _ 12 Lesson Practice 6 a. 36 b. -23 c. -42.12 1 d. -_ 2 e. false; Sample: counterexample: 5 - 12 = -7 f. true g. -24,000 feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 6–1 Saxon Algebra 1 Lesson Practice 6 6 15. 0.6; 60% 2 1. 2 _ 7 16. D 7 2. 18 _ 8 17. 71 1 3. 6 _ 3 18. B 4. 2 19. 10-yard line 5. 1.11 20. 36.3º 6. 4.05 21. -21°C 7. 2.48 22. -$65.49 8. 35.125 23. B 9. 2 · 2 · 2 · 2 · 37 24. no; Sample: After the rainfall, the lake level is 1 feet, which is at -2 _ 12 more than 2 feet below normal. 10. 2 · 2 · 2 · 3 · 7 11. Frequency of Numbers X X X X X X X X X X X X X X 4 5 6 7 8 9 10 25. 13.75 ≤ 23.25 Numbers 12. no; The sum of the digits is 2 + 3 + 2 + 6 = 13, which is not divisible by 3. 3 ; 0.06 13. _ 50 26. Student A; Sample: Student B added 11 floors instead of subtracting. 27. a. 23 b. 25 5 1 _ ; feet 14. 1_ 4 3 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. c. 28 LSN 6–2 Saxon Algebra 1 Lesson 6 28. a. 16, -4, 21 b. 4 8π + c. 16c - 4d + _ 15 21efg; Subtracting a number is the same as adding its inverse. 29. D 30. 1195 ft © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 6–3 Saxon Algebra 1 Lesson 7 Lesson Practice 7 Warm Up 7 1. variable a. 18 2. 9.5 b. 10 3. 11.7 c. 77 7 1 or 1 _ 4. _ 6 6 d. Sample: 8·3 4(1 + 2)2 ÷ 6 + _ 2 8·3 = 4 · 32 ÷ 6 + _ 2 Simplify inside parentheses. 24 = 4 · 32 ÷ 6 + _ 2 Simplify the numerator. = 4 · 32 ÷ 6 + 12 Simplify the fraction. = 4 · 9 ÷ 6 + 12 Simplify the exponent. = 6 + 12 Multiply and divide from left to right. = 18 Add. e. < f. Sample: Begin inside the parentheses. Square the height. Next, divide the weight by the new denominator. Then multiply the quotient by 703. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 7–1 Saxon Algebra 1 Lesson 7 7 ; 0.0007 16. _ 10,000 Practice 7 1. -1 1 17. 14_ 4 2. 47 18. > 1 3. -3 _ 12 19. Sample: The two formulas contain opposite operations. 3 4. 11_ 8 5. 0.172 20. Sample: Perimeter 1 (2π · 15) = (2 · 40) + _ 2 = 80 + 47.1 = 127.1 ft 6. 1.4 7. 120 21. B 8. 0.202 22. a. 6 · 122 = 864 in2 9. false; 0 is a whole number but not a counting number. b. (2 · 162) + 4(16 · 6.75) = 944 in2 10. integers 11. false; A triangle can only have one obtuse angle. c. 864 < 944; Box A 23. a. 12.8 feet, 6.4 feet, 3.2 feet 12. 3 · 3 · 23 b. no; Sample: The ball is bouncing back up halfway each time. 13. 1 · 37 14. yes; The number formed by the last three digits is divisible by 8. 15. 69 _ ; 200 34.5% © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 24. 61.464 units 25. 328 ft 26. -4 planes LSN 7–2 Saxon Algebra 1 Lesson 7 27. Student B; Student A should have subtracted 10. 28. 5 - (-2) = 7 feet 29. B 30. 120° © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 7–3 Saxon Algebra 1 Lesson 8 Warm Up 8 1. volume 3 2. _ 7 10 3. _ 27 9 4. _ 28 3 5. _ 16 Lesson Practice 8 a. 184,800 feet per hour b. 131.625 ft2 c. yes; Sample: 46,300 mm3 = 46.3 cm3 d. $32.26 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 8–1 Saxon Algebra 1 Lesson Practice 8 14. 8 75 7 1. 6 _ 12 15. 74 5 2. 1_ 24 16. 42 1 3. -2_ 4 17. C 1 4. 1 _ 3 18. 2 3 5. 0.185 6. 2.61 7. a. true b. false 19. B c. false 20. a. 7 376 d. true b. 43 74 8. <, -20 < 20 9. 21. a. A = 2 b · h Frequency of Numbers X X X X X X X X X X X X X X X X X b. · 10. 63 22. 11. 2 · 2 · · · c. 475 2 2 3 4 5 6 7 8 Numbers 7 2 2 2 A = 2b · h 2 2 63 23. 12. 5 13. 4 25 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 8–2 Saxon Algebra 1 Lesson 8 24. Student A; Sample: Student B needed to simplify inside the parentheses first. 25. a. 256 in3 b. Sample: I simplified the s2 first, because the order of operations tells us to simplify exponents before multiplying or adding. 26. profit of 5.5 million 27. Group B 28. Student A; Sample: Student B incorrectly used b as b0 and c as c0. 29. 168,960 feet per hour 30. a. 64 sq. in. b. 100 sq. in. c. 36 sq. in. d. 44 sq. in. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 8–3 Saxon Algebra 1 Lesson 9 Warm Up 9 1. quotient 6 5 2. 3x b 3. 57 4. 5 5. 16 Lesson Practice 9 a. 62 b. -10 c. < d. -128.92ºF © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 9–1 Saxon Algebra 1 Lesson Practice 9 9 17. 24 6 1. 1 _ 7 18. a. 80 ft/sec 5 2. 20_ 8 b. 48 ft/sec 1 3. 4 _ 2 19. $11.75 11 4. 1_ 21 20. Student B; Sample: Student A made an error in evaluating the negative number raised to a power. 5. 3.75 6. 5.8 7. 0.25 21. 2.5 8. 39.04 22. 106.5 total blocks 9. true; A square has 2 pairs of parallel sides and its sides are congruent. 23. no; The number is divisible by 2, but not divisible by 3. 44 ; 0.352 24. _ 125 10. 12 2 11. 1,860,000 m 25. a. 2112 cm2 b. 211,200 mm2 12. -156 13. 180° 14. 5 · 5 · 5 15. 2 c. 1:100 26. 1260.42 cm3 27. Divide n by 12. 28. 1 16. C © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 9–2 Saxon Algebra 1 Lesson 9 29. Student A; Sample: Student B did not follow the order of operations and did not work inside the parentheses first. 30. 525 words © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 9–3 Saxon Algebra 1 Lesson 10 Warm Up 10 1. irrational 2. 2 3. -19 4. 7.1 5. 12j6k9 Lesson Practice 10 1 a. _ 9 b. 7.39 5 _ , 6 , 0.85 c. -1, _ 8 8 d. < e. 35.69 seconds © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 10–1 Saxon Algebra 1 Lesson Practice 10 11 1 _ or 1 1. _ 10 10 8 2. 7 _ 15 1 3. 8_ 4 1 4. 2_ 25 17. Student A; Sample: Student B did not complete the operations in parentheses first. 11 hour or 55 minutes 18. _ 12 19. 7 5. 63_ 10 X X X X X X X X X X X X X X Numbers 20. a. Sample: 1000b b. 400 feet 8. 9.3 9. 24.846 Frequency of Numbers 9 10 11 12 13 14 15 11 6. 2_ 12 7. 32.13 10 21. A = 2z2; 288 cm2 12. acute 22. Student B; Sample: Student A only multiplied by the unit ratio once instead of twice. 13. 8.673 kg 23. +0.177 in. of mercury 10. 3.2 3 _ 4 _ , 1, _ , 6 11. -_ 3 7 5 7 14. 41.8 km 4 24. a. 9 · 6 + π _ 2 ( ) 15. true; Sample: The value of each expression is -5. b. 16 · 10 ⎡ 4 2⎤ ⎢9 · 6 + π _ 2 ⎦ ⎣ ( ) ≈ 93.44 yd2 16. A © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 2 LSN 10–2 Saxon Algebra 1 Lesson 10 25. Student B; Sample: Student A added the absolute values of the numbers rather than subtracting them. 26. $523.42 27. Rational and irrational numbers; Sample: By definition, the sets of rational and irrational numbers do not contain the same numbers. 28. -4.4 points 29. 12 yards 30. 68 feet 6 inches © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 10–3 Saxon Algebra 1 Lesson Warm Up 11 11 g. -21.3; Sample: Dividing two numbers with different signs results in a negative quotient. 1. opposites 2. -12 8 h. _ 9 3. -48 1 i. - _ 2 4. 625 j. −48°F 5. 32 Lesson Practice 11 a. -7.2; Sample: Multiplying two numbers with different signs results in a negative product. b. 30; Sample: Multiplying two numbers with like signs results in a positive product. c. -64 d. 4096 e. -625 f. 15; Sample: Dividing two numbers with like signs results in a positive quotient. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 11–1 Saxon Algebra 1 Lesson Practice 11 5 + 54 59 Multiply. Add. 1. true; Sample: 7 1 1 7 =_ ×_ =_ =1 7×_ 7 7 7 1 11. B 2. -16 12. a = 6.125 cm/s2 3. Student A; Sample: Student B did not find a common denominator. 13. $89.60 7 4. _ 8 15. 5.08 5. 14. -4000 m, -1600 m 3 1 _ = , 16. a. Sample: 1 - _ 4 4 3 _ about 4 m 4 Frequency 11 3 99 23 76 19 b. _ -_ =_ =_ 100 100 100 25 2 1 6. obtuse 17. Student B; Sample: Student A should have multiplied 4 and 17 together first. 7. 43 18. 169 cm 8. 358 19. Student B; Sample: Student A subtracted 282 instead of -282. 0 6 8 10 Number 9. B ⎤ 9⎡ _ 1 4 + 4 10. 5 + _ ⎢ 3⎣ 2 ⎦ ( ) 20. a. as likely as not 9 ⎤ 9⎡ _ 5+_ 4 ⎢ symbols of 3⎣ 2 ⎦ Inclusion 9 5+_ [18] symbols of 3 Inclusion ( ) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. b. impossible c. likely 21. -10 LSN 11–2 Saxon Algebra 1 Lesson 11 22. 15 23. -10 24. -180 25. 15 26. No, the perimeter of a rectangle cannot be a negative integer. 27. a. +4 0 2 +(-1) +6 +(-3) +2 4 6 8 10 b. 4 + 2 - 3 + 6 - 1 c. 8 spaces 28. yes; 2 yards is 72 inches. 29. 25°F 30. $40 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 11–3 Saxon Algebra 1 Lesson 12 Warm Up 12 1. algebraic 2. -4 9 3. _ 10 4. 1.7 Lesson Practice 12 a. Associative Property of Addition b. Identity Property of Addition c. Commutative Property of Multiplication d. Identity Property of Multiplication e. true; Associative Property of Multiplication f. false; Commutative Property does not work for subtraction g. true; Identity Property of Addition h. 18 + 7x + 4 = 7x + 18 + 4 = 7x + (18 + 4) = 7x + 22 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. Commutative Property of Addition Associative Property of Addition Add. LSN 12–1 Saxon Algebra 1 Lesson 12 1 i. _ d·3 3 1 ·3·d =_ 3 Commutative Property of Multiplication 1 ·3 ·d = _ 3 Associative Property of Multiplication =1·d =d Multiply. Identity Property of Multiplication ( ) j. $1.45 + $3.35 + $2.65 = $1.45 + ($3.35 + $2.65) Associative Property of Addition = $1.45 + $6.00 Add within the parentheses. = $7.45 Add. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 12–2 Saxon Algebra 1 Lesson 12 Practice 12 1. Identity Property of Multiplication 2. -6 3. 18 4. 48 5. false; The Associative Property only applies when the operations are all addition or all multiplication. 4 6. Sample: _ 6 7. true 8. B 49 9. _ 60 10. Student A; Sample: The quotient of a positive and a negative number is negative. 11. x + 5 + 15 = x + (5 + 15) = x + 20 or 5 + 15 + x = (5 + 15) + x = 20 + x Commutative Property of Addition Associative Property of Addition Add. Commutative Property of Addition Associative Property of Addition Add. 12. A 13. 1024 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 12–3 Saxon Algebra 1 Lesson 14. 36.75 lb 15. Sample: The Commutative Property of Multiplication says that the order of the factors does not change the product. 16. yes; Sample: The Commutative Property of Addition states that the order of the terms does not affect the sum. 17. Both are correct; Sample: The Commutative Property of Addition states that the order of the terms can be changed without changing the sum. 18. 10.58 sq. in. 19. -15; Sample: 5(28) + 3(-41) + 2(-16) = 140 - 123 - 32 = -15 12 22. Student B; Sample: Student A did not follow the order of operations. 23. Sample: First you have to work inside the parentheses and divide 9 by 3 to get 3. Next, take that 3 away from 8 to get 5. Then square 5 to get 25 and multiply by 4 to get 100. 24. k4x7y 25. Sample: Student A; Student B did not treat the constant and variable in the second term as factors. Instead of multiplying, Student B treated x as a digit in the ones place. 26. $473.75 27. 6.5 feet 28. between 150 and 157.5 miles 20. D 21. 4 yards © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 12–4 Saxon Algebra 1 Lesson 29. 22 + 24 - (3 - 12) = 22 + 24 - (-9) = 4 + 24 - (-9) = 37 12 symbols of inclusion powers algebraic addition 30. Sample: 7 + (-7) = 0 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 12–5 Saxon Algebra 1 Lesson d. √ 16 + √ 441 Warm Up 13 1. exponent √ 81 + √ 361 4 + 21 9 + 19 25 28 25 < 28 2. 1 3. 64 4. a7x12z4 5. 13 e. 13 feet; To find the side length, find the square root of the area: √ 169 = 13. 8 _ 9 Lesson Practice 13 2 a. yes; Sample: 15 = 225; The product of an integer and itself is a perfect square. b. no; Sample: There is no integer multiplied by itself that equals 350. 37 ≈ 6; c. Sample: √ 37 is between the perfect squares 36 and 36 = 6 and √ 49 49. √ = 7, so √ 37 is between 6 and 7, but closer to 6. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 13–1 Saxon Algebra 1 Lesson Practice 13 13 15. a. true b. false; (4 + 5) 2 is equal to 9 2, or 81, whereas 4 + 5 2 is equal to 4 + 25, or 29. 1. 8 5 2. _ 6 3. 0 4. 19 3 4 _ in., 8 in., 16. a. 8 _ 16 16 10 1 8_ in., and 8_ in. 16 16 3 1 in., 8 _ in., b. 8_ 5. 10 6. 12 16 16 10 4 _ 8_ in., and 8 in. 16 16 7. 6 and 7 8. B 17. 1.05, 1.09, 1.11, 1.5 9. b = 2 18. no; Sample: The first expression simplified is 5 5 900k v . 10. > 19. about 1300 meters 11. 1 8_ 3 yards per hour 9= 12. false; Sample: √ 3 and 3 is a rational number. 13. A 14. true; Commutative Property of Multiplication 20. 3.25 seconds 21. 1560 gal/min 22. yes; Sample: Divide 210 by 12 to convert it into feet. It is 17.5 feet in diameter. 23. 32.1775 in2 24. Sample: +$105 + (-$114) = -$9 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 13–2 Saxon Algebra 1 Lesson 13 25. 52 + (1 + 3) 2 · (16 - 14) 3 - 20 = 52 + 4 2 · 2 3 - 20 symbols of inclusion = 52 + 16 · 8 - 20 powers = 52 + 128 - 20 multiplication = 160 addition and subtraction 26. Student A; Sample: Student B incorrectly used the Associative Property when adding 2 + 3x. 27. 30 + 7x + (-12) = 30 + (-12) + 7x = [30 + (-12)] + 7x = 18 + 7x Commutative Property of Addition Associative Property of Addition Add. 28. D 29. 323,950,000 drachmae 30. a. impossible b. unlikely c. as likely as not © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 13–3 Saxon Algebra 1 Lesson 14 Warm Up 14 1. Probability 2. 38 3. -5 4. 83 5. -12 Lesson Practice 14 a. {1, 2, 3, 4} b. {2, 4, 6} c. {3, 4, 5, 6} 3 or 0.3 or 30% d. _ 10 7 or 0.7 or 70% e. _ 10 5 or 0.625 or 62.5%; f. _ 8 The chance of drawing 1 a 6 is _ , which is less 8 than the chance of 1 drawing a 7, which is _ . 4 1 g. _ 13 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 14–1 Saxon Algebra 1 Lesson Practice 14 14 2 16. _ 11 1 1. _ 3 17. C 5 2. _ 14 18. Student A; Sample: Student B found two different numbers that have a product of 16 instead of one number that, when multiplied by itself, equals 16. 3. 50.8 cm 4. 762 cm 5. 1 6. -20 7. 31 8. 33 9. 6 5 4 _ < 10. _ 5 6 11. 7 centimeters 12. A 13. Either x or y is positive and the other is negative; Either x or y is zero; Both x and y are positive or both x and y are negative. 14. Commutative Property of Multiplication 15. A © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 19. about 20 miles per hour 20. 200 kg · cm/s2 21. 37.6 oz; Sample: 2.35 rounds down to 2 and 2 · 16 = 32. The answer 37.6 oz is reasonable, as it is close to the estimate of 32 oz. 22. no; Sample: Since π is an irrational number and will never end, the program will never end. 23. real numbers 24. a. 1 5 , 32 b. _ 9 25. -17 LSN 14–2 Saxon Algebra 1 Lesson 14 26. Student B; Sample: The weight of each piece is the weight of the cakes divided by 16. The weight of the cakes is 3 + 5. Student B put parentheses around 3 + 5, grouping 3 and 5. Student A did not put parentheses around 3 + 5, and without these grouping symbols, 5 ÷ 16 is the operation performed first. 27. +6 people 28. 44; Sample: This is the same as 22 + 11 11 + 22. 29. Sample: If you don’t complete the problem in the correct order, you get the wrong answer. 30. 48 feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 14–3 Saxon Algebra 1 Lesson 15 Warm Up 15 1. term 2. 13 3. 0 4. 11.9 1 5. _ 5 Lesson Practice 15 a. 72 b. 16 c. -12 d. -28 e -10m - 40 f. 56 - 8y g. 4x5y4 - 20x2y3 h. -2x2m4 + 8x2m3 i. 15(4 + 8); $180 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 15–1 Saxon Algebra 1 Lesson Practice 15 11. Student A; Sample: Student B added the numbers instead of multiplying when using the Distributive Property. 1. 35 2. -45 3. 100 12. 48; Sample: I multiplied -8 by each number in parentheses and added the products. 4. c = 5 5. 64 eggs; Sample: b 2 _ =_ ; 25 800 25b = 1600; b = 64 13. 6(4 + 7); 6(4 + 7) = 6(4) + 6(7) = 24 + 42 = 66 lots 2 1 _ 6. _ = 5 10 7. 1; Sample: An event that is certain to happen has a probability of 1. All 10 of the balls have a number label less than 7, so the event is certain. 8. D 9. y = 22 10. 8 ft 15 14. true; Identity Property of Addition 15. 91.8 ft3 c 16. 14(_ 8) 17. 6(b + 7) = 6b + 42 2 1 or _ 18. _ 6 3 19. Student A; Sample: Student B incorrectly applied the square root. 20. Commutative Property of Multiplication © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 15–2 Saxon Algebra 1 Lesson 21. 7 · 8x Commutative Property of Multiplication Associative Property of Multiplication Multiply. (7 · 8)x 56x or x · 7 · 8 Commutative Property of Multiplication x(7 · 8) Associative Property of Multiplication x · 56 Multiply. 1 22. 15_ years 2 23. Sample: Substitute the value 3 for f and the value 5 for g. Evaluate exponents from left to right. Multiply from left to right. Subtract and add from left to right. 8 24. 14 12 10 15 26. Student A; Sample: Student B combined the two negative signs before taking the absolute value, but should have taken the absolute value first. 27. y = -8 28. Sample: It will be positive because every part is positive; the negative value in the absolute value symbols will become positive. 3 , 12% 29. a. _ 25 8 , 32% b. _ c. 25 17 _ , 25 68% 30. 44 in. 6 8 6 4 2 0 25. 2.51211 or about 25,131 times brighter © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 15–3 Saxon Algebra 1 Lesson Warm Up 16 16 Lesson Practice 16 1. integers a. 12 2. -adx5 + a6x3 b. -12 3. −1 c. 60 4. −2 1 d. _ 3 5. B e. Sample: -b(a - 3) + a, -ba + 3b + a, Distribute; -(-1)(2) + 3(-1) + 2, Substitute; 2 - 3 + 2 = 1, Simplify. f. Sample: -a(-b - a) - b, ab + a2 - b, Distribute; 2(-1) + (2) 2 - (-1), Substitute; -2 + 4 + 1 = 3, Simplify. g. 7 3 h. - _ 8 i. $1730.56 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 16–1 Saxon Algebra 1 Lesson Practice 16 16 13. Associative Property of Addition 1. 19 14. B 2. 25.5 15. a. 33.49 cm3 3. K = -5, -4, -3, -2, -1 b. 3.14 cm3 4. true; The product of any two whole numbers is contained within the set of whole numbers. c. 30.35 cm3 16. 0.5 atmosphere 17. $1641 5. false; Sample: -7 is an integer, but it is not a whole number. 18. C 19. a. 450 in2 6. -4yd - 4ycx b. 1350 in2 7. 2xa + 2xbc c. 3150 in2 8. -2 20. a. 15b + 3r 1 9. - _ 5 10. 16 11. -3714 12. 20x + 4; Sample: Since a square has four equal sides, 4(5x + 1) = 4(5x) + 4(1) = 20x + 4 would be used to find the perimeter. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. b. 2(15b + 3r) = 30b + 6r 21. Student A; Sample: Student B only considered numbers greater than 5. LSN 16–2 Saxon Algebra 1 Lesson 22. <; Sample: 36 + √ 40 6+6 12 12 < 23. 36 tiles 16 √ 25 + √ 80 5+9 14 14 24. ≈ -20,800 feet 25. Sample: The sign of the sum is negative because the number with the greater absolute value is negative. 26. Sample: France uses metric measures in their recipes, but the United States uses customary measures. 3 27. 10 · 2 + 4(7 + 2) = 10 · 2 3 + 4 · 9 = 10 · 8 + 4 · 9 = 80 + 36 = 116 Simplify grouping symbols. Simplify inside parentheses. Simplify exponents. Multiply. Add. 28. Student B; Sample: Student A added the two temperatures instead of subtracting to find the change. 29. 580 ft3 1 30. a. _ 50 b. 5 balls © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 16–3 Saxon Algebra 1 Lesson Warm Up 17 17 2. 6 i. Sample: the quotient of three less than x and 2; the difference of x and 3 divided by 2 3. 62 j. d - 15x 1. numeric 4. x5m2 + x2m7 5. B Lesson Practice 17 a. 8x b. 18 - y c. 5x + 7 d. x + 2 e. Sample: 10 divided by s; the quotient of 10 and s f. Sample: r less than 5; the difference of 5 and r g. Sample: 7 more than 3 times m; the sum of 3 times m and 7 h. Sample: three-fourths x plus 9; the sum of three-fourths of x and 9 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 17–1 Saxon Algebra 1 Lesson Practice 17 17 13. Sample: three times the sum of a number and 6 1. 4x + 2xy 14. B 2. -2x + 8y 15. 2p - 1 3. Sample: a part of an expression that is added to or subtracted from the other parts 16. 2(m - 7) 17. a. Sample: a is the number of apples and b is the number of bananas. 4. a. true b. false b. a + b c. true c. 0.2a + 0.1b d. false 6. 0.18x = 4.68 18. Student A; Student B should have found that (-2)2 = 4. 7. -6.4 19. 297 m2 8. = 20. 2 gallons 9. 3 and 4 10. false; Identity Property of Multiplication states that k · 1 = k 21. Student B; Student A multiplied the exponents of the like variables instead of adding. 11. 6 22. 30% 5. 3(-x + (-7)) 12. false; yx2m3 = (2)(-1)2 (-2)3 = (2)(1)(-8) = -16 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 17–2 Saxon Algebra 1 Lesson 17 23. Student B; Sample: Student A did not move the negative sign with the variable when the Commutative Property was used. 24. (_34 ); Sample: -_23 ÷(-_89 ) 18 3 9 2 _ _ _ = -_ · = = ) ( 24 4 3 8 25. no; Sample: The variables x and y can have many different values, so the expression does not have to represent just one value. 26. 38.64 kg 27. Sample: Simplify the fraction, raise base numbers to their exponents, and multiply. 28. -$11.63 29. Subtract 2 from 23. 30. 40(x + y) = 40x + 40y © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 17–3 Saxon Algebra 1 Lesson 18 Warm Up 18 1. variable 2. 0.00032 3. x9y6 4. 2x + 6 Lesson Practice 18 a. -6xy - 5x + 4 b. 24m c. 9acy - 2ac d. 6x4y e. 3x2y - 4xy f. 2m3n g. 2x2 + x + 2 feet; 12 feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 18–1 Saxon Algebra 1 Lesson Practice 18 15. a. 11 + 4x; 8x b. 12x + 11 1. 5x + (-8) 16. a. Sample: Marshall = 2j + 3; Hank = 2j; Jean = j 2. 2m - 2 - 3cm 3. -3xy + 2xy2 b. Hank is 24; Marshall is 27. 4. D 5. a. 12x + 15y and 9x + 7y b. 21x + 22y 6. no; Sample: Many addition problems with negative numbers have positive answers. For example, -2 + 3 = 1 or 6 + (-2) = 4. 7. -25 inches 8. about 274 in3 or 4487 cm3 greater 9. -2 10. -9 18 c. 7 17. 8x + 2x2 + 5x, Distributive Property; 2x2 + 8x + 5x, Commutative Property of Addition; 2x2 + 13x, Add. 1 18. _ 3 19. true; pm2 - z3 = (-5)02 - (-3)3 = 0 - (-27) = 27 20. Student A; Sample: Student B substituted the wrong values for y and z. 11. 14abc - 7ac 12. 15x3y 13. 36 1 14. _ 4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 18–2 Saxon Algebra 1 Lesson 21. Finding a common denominator shows you that the first fraction is greater than the second fraction, and that a greater positive number minus a lesser positive number results in a positive number. 18 30. Student B; Sample: Student A squared the sum instead of finding the sum of the squares. 22. a. x - 3 b. 10x + 12(x - 3); 22x - 36 23. a2 + b2 = c2 24. a. 2w + 2l b. 4w + 6l 25. B 26. -m2n2 + m3n; Sample: Using the Distributive Property, each term is multiplied by -m: -m(mn2) -m(-m2n). 3 27. _ 5 28. 12 feet 29. Sample: 24 ÷ 4 = 6, 1 1 , and 6 ≠ _ . 4 ÷ 24 = _ 6 6 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 18–3 Saxon Algebra 1 Lesson 19 Warm Up 19 1. opposites 2. 6.25 3. 13.8 4. 6(-3) + 3 = -15 and -2(-3) + 4 = 10, so 6x + 3 < -2x + 4 when x = -3 5. C Lesson Practice 19 a. not a solution, 12 - 14 = -2 b. solution, -11 = -7 - 4 c. x = 22, 22 - 5 = 17; 17 = 17 d. m = -18; -30 = -18 - 12; -30 = -30 e. p = 34 f. y = -22 1 g. d = -1 _ 3 h. 74 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 19–1 Saxon Algebra 1 Lesson Practice 19 1. -8mx2y + 23x 2. x = 2 19 13. 52.05°C 14. 3500 - x = 1278; 2222 tickets 3. x = -13 15. Add 2.5 to both sides of the equal sign. 4. x = 10 16. C 5. 7(x + (-5)) 17. Student B; Sample: Student A added unlike terms. 6. 3x + 12 7. m6x5 8. Commutative Property of Addition 9. false; Sample: The answers are opposites; -54 = -1 × 54 = -1 × 625 = -625; (-5)4 = (-5)(-5)(-5)(-5) = 625 10. -3 11. Student B; Student A should have 1 from both subtracted _ 3 sides of the equation to isolate x. 18. 2x - 5 19. a. 4t; 5t; 3t b. 12t c. 2 miles 20. Student B; Sample: Student A translated it into an expression using a quotient rather than the product. 21. 5.75 22. C 23. a. The resulting value is negative. 12. C © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. b. The resulting value is positive. LSN 19–2 Saxon Algebra 1 Lesson 19 1 24. a. _ 7 2 b. _ c. 7 3 _ 7 25. Sample: a number that is the square of an integer 26. $530.45 27. Sample: First I would divide π by 4. Then I would find b². Finally, I would multiply to find the solution. 28. -12; Sample: When a number is added with its additive inverse, the sum is 0; 12 + (-12) = 0 29. 5(a + c) + (14a + 8c); 19a + 13c 3 4 1 _ 1 _ _ = ; = 30. _ 52 13 51 17 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 19–3 Saxon Algebra 1 Lesson Warm Up 20 i. 1. absolute value x y 20 -3 -2 -1 -7 -5 -3 j. $0, $75, $150, $225 2. 5 y 3. 9 200 150 4. 37 + 4c 100 5. -2x4 50 O x 50 100 Lesson Practice 20 a-f. 6 d(-3, 4) 4 c(-2, 0) -6 -4 -2 y a(0, 5) 2 O -2 -4 x 2 4 6 e(5, -1) f(2, -4) b(-1, -6) g. The amount paid is dependent, and the number of toys purchased is independent. h. The number of hours worked is dependent, and the number of yards mowed is independent. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 20–1 Saxon Algebra 1 Lesson Practice 20 8 1. -11 -8 -4 20 y (4, 7) (3, 6) (2, 5) 4 (1, 4) x O 4 8 -4 2. 5xyz - 3yz -8 3. xyz 10. 4. x = 14 3 5. x = - _ 10 6. 8 y 4 -8 -4 x O 4 8 (3, -4) -4 -8 7. 8 4 -8 -4 O y x 4 y 55 70 100 160 11. Student B; Sample: Student A should have determined the product of 2 and 2 first. 12. (0, 5) x 15 20 30 50 8 x y 5 0 10 20 50 5 15 45 -4 a. Profit in Dollars -8 8. C 9. c 1 2 3 4 r 4 5 6 7 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 40 30 20 10 0 10 20 30 40 50 Number of Cups Sold b. Sample: Substitute x = 30 into the equation LSN 20–2 Saxon Algebra 1 Lesson 13. x = 6 cm 22. -9.6 deer 14. 155 steps 5 points 23. 76 _ 7 15. Student A; Sample: Student B added the exponents of x. 24. 300 mg 16. Sample: Mathematicians use symbols to express briefly and accurately what might take longer to express in words. 25. a. 9 b. 2 (3) 26. 14 - _ ; 13 3+6 27. a. false; Sample: The coefficient of x is 1. 17. D 18. a. 4, b. -4, c. -8, d. -8, and b. true 28. coefficients 1 and -4; variables b, a, and c; There are 2 terms. 29. a. p + e b. 10p + 5e e. 4 19. 0.06 30. The graph is linear. x y 20. 54 21. Sample: (3 · 2) · 4 = 3 · (2 · 4) 6·4=3·8 24 = 24 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 20 0 0 1 5 2 4 10 20 y 20 (4, 20) (2, 10) (1, 5) O (0, 0) 2 4 10 LSN 20–3 x 6 8 Saxon Algebra 1 Lesson 21 Warm Up 21 1. variable 2 2. _ 5 3 1 _ or 1 3. _ 2 2 4. 6 5. D Lesson Practice 21 a. k = 27 b. m = -100 c. y = 3 d. x = -5 44 e. y = _ 3 96 f. n = -_ 5 3 ft g. 8 _ 4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 21–1 Saxon Algebra 1 Lesson Practice 21 21 8. x = 15 x = 7; The ladder rises 1. _ 4 28 feet. 9. B 10. 395 snow cones 2. Sample: The term in an algebraic expression is the part to be added or subtracted. 3. Sample: Multiply both sides by the multiplicative inverse 3 2 _ , which is , in order of _ 3 2 to isolate x. 3 _ 3 2 _ _ · x = 8 · , x = 12. 2 3 2 11. Sample: 3z 2y and -z 2y can be combined. 2yz and 8yz can be combined. Each pair has the same variables and the same powers of variables. 2 -4y z cannot be combined with any other term because no other term has y 2z. 4 12. 10,638,000 lb 7 miles per second 5. 8 (-2, 6) -8 -4 y 13. w 4 O 2 4 6 8 x 4 8 -4 -8 3w 6. a. y w 64 b. 3w -5 -3 (6, 48) 32 16 x y (8, 64) 48 2 7. A 16 32 48 64 1 9 4 15 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. O LSN 21–2 (4, 32) (2, 16) x 2 4 6 8 Saxon Algebra 1 Lesson 14. -20 Method 1 3 2 _ _ 4 + 4 3 ( ) 3 2( ) 2 _ 4 +_ =_ 3 3 4 ( ) 20. a. 8 1 _ + =_ 3 2 = 19 _ 6 ( ) 19 2 _ =_ 3 4 ( ) 19 =_ 6 900 600 (1, 1050) (4, 600) 300 O (6, 300) 2 (8, 0) 4 6 8 Time (Min) x y 1050 600 300 0 b. Sample: It takes her 8 minutes to get from home to school. 5 17. _ 26 18. 10 feet; Sample: A square has equal 2 sides and A = s , so the length of one side = 10. is √100 y x 1 4 6 8 Method 2 3 2 _ _ 4 + 4 3 Distance from School (Yds) 19. yes; Sample: The Commutative Property of Addition allows the order of the addends to be changed without affecting the result. 15. A 16. 21 21. yes; Sample: Dividing by a number is the same as multiplying by its reciprocal. Dividing 3 by -_ is the same as 4 4 multiplying by -_ . 3 1 22. a. 64, _ 64 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 21–3 Saxon Algebra 1 Lesson 28. 1 = 64 · __ =1 64 23. Sample: no; A rational number can be expressed as a ratio of two integers. 24. Sample: metric units of measure, such as cm² to mm² or dm² to cm² Time 29. 0.21x = 7.98 30. Student A; Sample: Student B should have added 5 to both sides of the equation to isolate x. y Time Remaining (hr) 25. Tomato Plant Growth Height b. Sample: 1 _ 1 _ 1 4·4·4·_ · · 4 4 4 21 4 3 2 1 O x 4 8 12 16 Number of Holes x 4 8 12 16 y 3.5 2.5 1.5 0.5 26. -10 27. a. s + k and 2s + 4k b. 3s + 5k © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 21–4 Saxon Algebra 1 Lesson 22 Warm Up 22 1. rational, irrational 2. point A 3. point C 4. point B 5. 12,280,000 Lesson Practice 22 a. 2006 b. 5 c. 49 in. Height of Jackson Grandchildren (in inches) Stem 4 5 6 7 Leaf 0399 246 8 12 Key: 6|8 = 68 d. January e. $25,000,000 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 22–1 Saxon Algebra 1 Lesson Practice 22 10. Sample: The lap times have become faster since 1960. 1. False; stem-and-leaf plots help organize data. -1 -6 0 -9 1 -12 70 60 50 40 30 20 10 0 3. 2pxy - 6pk 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 x y Fastest Lap Times in the Indianapolis 500 Time (seconds) 2. Year 4. y = 5 11. 8 9 1 _ or 1 5. x = _ 8 8 6. x = -8 (-4, -1) O x 4 8 -4 -8 7. x = 7 8. line graph; Sample: Line graphs show changes in data over time. b. false; Sample: √ 3 ÷ √ 3 is a whole number. y 4 2 _ 3 9. a. false; Sample: 3 ÷ 4 is not an integer. 22 12. Student A; Sample: Student B graphed the point (3, -4) by first moving vertically, then horizontally. 13. B 14. a. x must be negative. b. x must be zero. c. true c. x must be positive. 15. D 16. 25 - d © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 22–2 Saxon Algebra 1 Lesson 17. a. Sample: True; 200 150 Crustaceans Insects 2 ( ) 1 2 = -4(_ 3) 1 4 = -4(_ = -_ 9) 9 Arachnids 0 Snails 50 Fish 2 = -4 _ 6 ) Clams ( 100 2 Reptiles 2 = -4 _ 2 - (-4) Amphibians ) United States Other Countries 250 2 Birds ( Threatened and Endangered Animals 300 Mammals y x _ y-x 22 20. Sample: The Commutative Property does not apply to subtraction. b. Sample: True; |(-1 - 2)3| = |(-3)3| = |-27| = 27 21. 26.35 ft 2 22. -11 4 c = 16; c = 36 inches. 23. _ 9 The circumference is 36 inches. 18. Sample: A sample space is the set of all possible outcomes. 19. Sample: There are more threatened and endangered mammals, birds, and reptiles in other countries, but the total number of threatened and endangered animals in the United States is greater than the total for other countries. 24. a. 15 · 20 b. 1200 + (15 · 20) c. 1500 ft 2 25. Sample: A man makes 2 bank deposits of d dollars and withdraws w dollars. 26. 8ab2 - 3ab 27. 0.32 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 22–3 Saxon Algebra 1 Lesson 22 6 4 28. x y 29. a. 6x = $31.92; x = $5.32 4 b. _ x = $5.32; 5 x = $6.65 30. a. _4 13 10 b. _ 13 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 22–4 Saxon Algebra 1 Lesson 23 Warm Up 23 1. coefficient 2. 3x - 12 3. 2x + 10 4. 1 5. D Lesson Practice 23 a. Sample: Use the order of operations and first multiply 9 by 2. b. Sample: Use the order of operations in reverse, and subtract to undo the addition. First subtract 6. c. w = 4; 8(4) - 4 = 32 - 4 = 28 d. x = 11; -2(11) + 12 = -22 + 12 = -10 4 e. m = -_ 3 f. about 14 months © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 23–1 Saxon Algebra 1 Lesson 10. Favorite Vacation Destinations Number of Students Practice 23 1. 0 23 9 8 7 6 5 4 3 2 1 0 2. Sample: Start at the origin. Go 2 units left and then 4 units up. Mark the point 4 11. _ meters 9 3. B 12. D 4. Student B; Sample: Student A divided both sides of the equation by 12 instead of -12. 13. a. 25x + 10y; 50h + 5z 5. 2850 meters Beach 14. 3x + 12 = 3(2) + 12 = 6 + 12 = 18; 12 + 3x = 12 + 3(2) = 12 + 6 = 18 15. < 3 ·5=3 7. Sample: _ 5 16. y = -2 b. 45 people c. 30 people 9. double-bar graph; Sample: Double-bar graphs can compare two different sets of data side by side. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. Mountains Museum b. 25x + 50h + 10y + 5z 6. false; 3(9) - 8 ≠ 22; x = 10; Check: 3(10) 8 = 22, 30 - 8 = 22 8. a. comedy Park 17. x = 4 2 18. x = 4_ 3 19. x = 3 20. 0.45 LSN 23–2 Saxon Algebra 1 Lesson 23 3 21. a. _ 43 8 b. _ c. 43 26 _ 43 22. 19 feet 23. ≈ -81.6°C 24. 17°F 25. $123.35 26. 16 27. a8b3c5; Sample: Use the Product Rule for Exponents by adding together the exponents of like bases. 28. 33,200 cm/sec 29. D 30. a. as likely as not b. certain c. impossible © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 23–3 Saxon Algebra 1 Lesson 24 Warm Up 24 1. C 5 2. -2.85, -0.8, 0.58, _ 8 3. -3x2 + 11x Lesson Practice 24 a. y = 4 b. q = 3 c. n = -15 d. 14.4 e. 35.2 km © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 24–1 Saxon Algebra 1 Lesson 9 , variable C, 8. coefficient _ 5 number of terms = 2 Practice 24 1. A 9. x = -1.7; Sample: 0.25x + 0.5 = 0.075 is equivalent to 3 x 1 _ +_ =_ . 4 40 2 2. a. 3(2x + 5x) = 3(7x) = 21x b. 3(2x + 5x) = 6x + 15x = 21x 10. Student B; Sample: The circle graph shows the number of students, not the percentages. Student A found the total number of students and wrote that number as a percent. 3. x = 18 4. The solution remains the same. Sample: The Multiplication Property of Equality states that you can multiply both sides of an equation by the same number and the statement will still be true. 11. 62.8 inches 12. Will spent $1.20 on apples, $4.80 on peanut butter, $2.40 on juice, and $3.60 on strawberries. 5. 125 shares of stock 6. A 7. Sample: Multiplying both sides by 1,000 and then subtracting 900 from both sides will result in 450x = 108, x = 0.24; Subtracting 0.9 from both sides, will result in 0.45x = 0.108, x = 0.24 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 24 13. LSN 24–2 y 8 4 -8 -4 O (2, 1) 4 8 x -4 -8 Saxon Algebra 1 Lesson 2 21. _ 7 5 14. a. _ 8 1 b. _ c. 2 1 _ 4 15. 0.50(6c + 2d) = 3c + d 16. Sample: Yes; Using the Product Rule of Exponents the left side simplified is the same as the right. 17. 50% 8 2 _ = 18. a. _ 100 25 17 b. _ 24 22. Sample: To simplify the expression, some of the bases would need to be the same in order to add the exponents. 23. 6ab + 6ef; Distributive Property 24. a. Sample: After the decimal place a 1 is followed by an increasing number of 2s each separated by a 1.; no 25 19. Yes; Sample: The Commutative Property of Addition allows the order of the addends to be changed without affecting the sum. 4 ; Sample 20. _ 7 explanation: A fraction multiplied by its reciprocal equals 1; 4 4 _ ÷1= _ 7 7 ( ) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. b. Sample: Irrational, no section of the decimal repeats nor does it terminate. 25. 38.44 in³ 26. 42°C, 11 a.m. 27. -3 LSN 24–3 Saxon Algebra 1 Lesson 24 28. a. about 230,871,756 people b. about 173,153,816 more people 29. 5 trees 99 30. a. _ 100 b. 19,800 hair dryers © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 24–4 Saxon Algebra 1 Lesson Warm Up 25 25 e. f(c) = $0.07c f. f(d) = 400 - 30d 1. ordered pair, x-value, y-value 2. 17 3. -6 4. -1.6 5. A Lesson Practice 25 a. domain: {1, 2, 3, 4, 7, 8}; range: {1, 2, 5, 6, 7, 10} b. 1 5 7 10 12 5 11 12 13 14 Function c. Function d. 8 y 4 x -8 -4 4 8 -4 -8 not a function © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 25–1 Saxon Algebra 1 Lesson Practice 25 5. 2.04 1. y = 7 6. A 2. a. Sample: 103 + x = 99 103 + (-4) = 99 103 - 4 = 99 99 = 99 7. f(s) = 4s 8. Sample: Yes, because all functions also meet the criteria for a relation. 9. Relation. Sample: If you draw a vertical line through the circle it will show that several domain values have more than one range value. So a graph of a circle does not represent a function. b. Sample: 3 1 _ -x=_ 2 1 1 _ - (- _ )= 2 4 1 1 _ +_ = 2 2 _ 4 25 + 4 1 _ 4 3 _ 4 = = 4 3 _ 4 3 _ 4 3 _ 4 3 _ 4 3. Sample: This equation is a function. Domain (x) −2 0 2 4 5 Range (y) 0 2 4 6 7 4. f(m) = 15m © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 10. C = πd = 3.14(0.45) = 1.413 The circumference is 1.41 mm. 11. about 483,600,000 miles 12. Sample: A subway train can hold up to 6 cars. Each car can hold 40 passengers. LSN 25–2 Saxon Algebra 1 Lesson 13. $39.95 + $0.99x = $55.79; 16 DVDs. 19. 10 y (4, 10) 8 6 (3, 7.5) (2, 5) 4 2 (1, 2.5) x O 2 4 Batches of Fruit Drink 15. B 16. Sample: A double-bar graph would compare the amounts of each beverage sold each month. A double-line graph would show the changes in the amounts of each beverage sold. A stem-and-leaf plot can help to quickly organize the data and show the middle of the data. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. Cups of Orange Juice 18. -4 14. Student A: Student B did not use inverse operations to “undo” +4. Student B should have subtracted 4 from both sides instead of adding 4 to both sides. 17. circle graph; Sample: Circle graphs best compare parts to a whole. 25 20. no, Sample: Subtraction is not commutative. The correct expression is x - 3. 21. 2160 22. 2.4 million ft2 23. false; Sample: The Associative Property applies only to multiplication and addition. 1 24. y = 4_ 2 25. m = 8 LSN 25–3 Saxon Algebra 1 Lesson 25 26. a. true b. false; Sample: The value of the first 5 and expression is _ 3 the value of the second expression 38 is _ . 27 27. 120.88 miles 28. 29 or 512 bits 29. 4x2y - xy2; Sample: The area of the rectangle would be found using A = lw = xy(4x - y) = 4x2y - xy2. 30. -7 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 25–4 Saxon Algebra 1 Lesson 26 Warm Up 26 1. reciprocal 2. 5x + 3y 3. 3.5 4. B Lesson Practice 26 a. 3.5; 3x + 2 - x + 7 = 16 2x + 9 = 16 -9 = __ -9 __ 2x = 7 1 x = 3_ 2 b. 7; 6(x - 1) = 36 6x - 6 = 36 +6 = __ +6 __ 6x = 42 x=7 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. Collect like terms. Subtraction Property of Equality Simplify. Division Property of Equality Distributive Property Addition Property of Equality Simplify. Divide both sides by 6. LSN 26–1 Saxon Algebra 1 Lesson c. 5; 5x - 3(x - 4) = 22 5x - 3x + 12 = 22 2x + 12 = 22 -12 = __ -12 __ 2x = 10 x=5 26 Distributive Property Combine like terms. Subtraction Property of Equality Simplify. Division Property of Equality d. 45°, 45°, 90° © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 26–2 Saxon Algebra 1 Lesson 26 Practice 26 1 1. x = -5_ 2 2. D 3. B 4. a. Sample: A circle graph is used to show percentages of a whole. b. Sample: A line graph would best represent the change in temperature over a period of time. 5. about 370 mp3 songs 6. Sample: You can either divide both sides of the equation by 12 or use the Distributive Property and then solve. 7. -15x + 35 + 11 = 1 -15x + 46 = 1 -15x = -45 x=3 Distributive Property. Combine like terms. Subtraction Property of Equality Division Property of Equality 8. See student work. Students should draw vertical lines across their graphs to check that the lines do not intersect the graph in more than one place. 9. no 10. m = 21 11. Student B; Sample: Student A did not multiply each term by the correct power of ten, 100. 12. true; 7(8) - 12 = 44; 56 - 12 = 44 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 26–3 Saxon Algebra 1 Lesson 26 21. 105 13. a. 5h + 4 = 64 b. h = 12; 12 hot dogs in each package.; 5(12) + 4 = 64 22. 2 -8 14. 15x = 5,280; 352 hops 23. 113 15. Sample: The point is (-2, 5). Substitute x = -2 into the equation, and the result should be 5; y = 2(-2) + 9 = -4 + 9 = 5 1 24. - _ 12 25. -(-6) -(-4) -6 -8 -4 -2 0 2 (_16 ) 5 26. a. 1 b. 3 c. 4 16. Sample: Yes, they can be combined. When the second one is simplified, they are like terms. 1 , variables 27. coefficient _ 3 B and h, 1 term 28. a. 31,820,488,040 yd2 b. 10,272.62656 mi2 17. P(rain on Tues.) = 2a 18. about 33.5 micrometers3 1 19. _ 4 20. >; Sample: √ 324 - √ 144 √ 400 √289 18 - 12 20 - 17 6>3 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 29. yes; Sample: The Commutative Property of Multiplication allows the terms to be multiplied in a different order without changing the product. 30. See student work. LSN 26–4 Saxon Algebra 1 Lesson Warm Up 27 c. Sample: The title does not specify that these were the only dogs the pet shop sold and may not represent all breeds sold. 1. horizontal or vertical bars Height of Flag 2. False 3. Sample: 27 d. Sample: The vertical axis has a broken scale, so it appears that the number of products sold throughout the year changed more than it actually did. Time 4. 4.5 Lesson Practice 27 e. Sample: The salesman may want it to appear that his sales increased a large amount from the beginning of the year to the end. a. The vertical scale does not begin at 0. The title does not specify whether the car or the driver traveled all the miles. f. b. Sample: The large increments make the temperatures appear to be closer than they actually are. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. Sales 400 300 200 LSN 27–1 Jul Jun Apr May Mar Jan 0 Feb 100 Saxon Algebra 1 Lesson Practice 27 1 1. _ 2 2. x = 0.7 5 3. x = _ 2 4. A 5. no 6. Associative Property of Multiplication 7. Sample: d(s) = s2 or f(s) = s2 8. Sample: The title does not specify that the animals listed are only 5 of the 10 species in the petting zoo. 9. yes; 5(4) + 8 - 3(4) + 4 = 20 is true 10. false 11. Sample: The student could use a scale of 0 to 200 and state that the data is in thousands. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 27 12. Sample: Machine 4 appears to produce about 3 times more parts than Machine 2 each day. Machine 2 appears to be less efficient. 13. true 14. 4 hours 15. h = 12.5 m 16. Sample: Work in reverse order of operations, subtracting 0.35 from both sides of the equation. 17. 2 18. Sample: Solve Equation 1 3 x = 12 -_ 4 x = -16 Substitute 5 1 _ (-16) = -2_ 32 1 = -2_ 2 LSN 27–2 2 1 -2 _ 2 Saxon Algebra 1 Lesson 19. 8 27 y 4 (-1, 0) -8 -4 x 4 8 -4 -8 20. 7 millimeters 21. 1480 Indian rupees 22. For 8, the absolute deviation is 3. For 9, the absolute deviation is 2. For 11, the absolute deviation is 0. For 12, the absolute deviation is 1. 23. Sample: 3(x + y) = 3x + 3y 1 ; Sample: The probability that the results will be heads 24. _ 2 will remain the same. 25. 40 26. a. Sample: q · $0.25 + d · $0.10 b. $6.55 27. > 28. Sample: The number of stairs he ran up minus the number of stairs he ran down describes his position at the end of his run. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 27–3 Saxon Algebra 1 Lesson 29. 10 · 42 + 72 ÷ 23 10 · 16 + 72 ÷ 8 160 + 9 169 27 Simplify the exponents. Multiply and divide from left to right. Add. 30. Sample: rational numbers, because irrational numbers cannot be shown as fractions or ratios. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 27–4 Saxon Algebra 1 Lesson 28 Warm Up 28 1. like 2. -14 3. -2 4. -7 5. D Lesson Practice 28 a. 9; 6x = 3x + 27 -3x = __ -3x __ 3x = 27 Subtraction Property of Equality Simplify. 3x 27 _ =_ Division Property of Equality 3 3 x=9 Simplify. Check 6(9) 3(9) + 27 54 = 54 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 28–1 Saxon Algebra 1 Lesson b. 4; 2 + 3(3x - 6) = 5(x - 3) + 15 2 + 9x - 18 = 5x - 15 + 15 9x - 16 = 5x -9x = ___ -9x __ -16 = -4x -16 -4x _ =_ -4 -4 4=x 28 Distributive Property Simplify. Subtraction Property of Equality Simplify. Division Property of Equality Simplify. Check 2 + 3[3(4) - 6] 5[(4) - 3] + 15 2 + 3[12 - 6] 5[1] + 15 2 + 18 5 + 15 20 = 20 c. identity; 2(x + 3) = 3(2x + 2) - 4x 2x + 6 = 6x + 6 - 4x 2x + 6 = 2x + 6 -2x = ___ -2x __ 6=6 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. Distributive Property Simplify. Subtraction Property of Equality Simplify. Always true! LSN 28–2 Saxon Algebra 1 Lesson d. no solution; 3(x + 4) = 2(x + 5) + x 3x + 12 = 2x + 10 + x 3x + 12 = 3x + 10 -3x = ___ -3x __ 12 = 10 28 Distributive Property Simplify. Subtraction Property of Equality Simplify. Never true! e. 25 days © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 28–3 Saxon Algebra 1 Lesson 11. a. Sample: Average Home Prices 5. 400 lb $320 $280 $240 0 York $200 b. Sample: The average home price in Dunston is much greater than most others. On average a house in Dunston would cost about 4 times more than one in Reefville. 6. A 7. Student B is correct. Sample: Student A didn’t distribute properly. 8. Sample: zx must be positive; therefore, x must be a negative number. c. Sample: The clients are likely to conclude that home prices in Reefville are much less than in the other cities. 9. a. about 4 b. about 2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. $360 Dunston 4. Student B; Sample: Student A incorrectly distributed in step 1. $400 Boynton 3. 3 + 0.05n = 2 + 0.10n, n = 20; 20 dimes and 20 nickels Reefville 2. p = 0 Woodside 1 1. y = 6_ 2 10. false; Sample: A broken scale makes data changes appear greater than they are. Price (in thousands) Practice 28 28 LSN 28–4 Saxon Algebra 1 Lesson 12. a. D: {0 ≤ x ≤ 4}; 22. R: {0 ≤ y ≤ 4} b. The relation is a function. Sample: Each domain value is paired with exactly one range value. 14. 65 b. from $8.50 to $10.00 16. true 23. 23 24. true; Associative Property of Addition 25. 511 17. Sample: (3, -1) 18. $247 + x = $472; $225 19. a. 6m + 1 and 4m + 16 b. 10m + 17 Method 1 8(10 - 4) = 8(10) - 8(4) = 80 - 32 = 48 Method 2 8(10 - 4) = 8(6) = 48 13. B 15. a. Sample: C = $0.05m + $3.95 28 26. Any irrational number subtracted from itself will equal 0, which is not an irrational number; =0 Sample: √ 3 - √3 20. g + 13 27. 17x + 13 21. about 0.75 N 28. a. rational numbers b. Sample: yes; 0 and 1 can be a probability. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 28–5 Saxon Algebra 1 Lesson 28 29. Sample: 1 mi = 5280 ft, so the student will multiply because the conversion is from a larger unit of measure to a smaller unit of measure. 30. Sample: A graph that shows changes over time. For example: The salaries of women from 1990 to 2010. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 28–6 Saxon Algebra 1 Lesson 29 Warm Up 29 1. variable 2. 28 3. 10 4. 3 11 5. - _ 3 Lesson Practice 29 3 m+4 a. n = -_ 2 b. x = -y + 4 5 (F - 32), 30°C c. C = _ 9 V = h, 36 in. d. _ lw m , 12.5 gallons e. g = _ F © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 29–1 Saxon Algebra 1 Lesson Practice 29 29 11. x must be negative. 5 1. y = -x + _ 3 12. Sample: All categories of the data set should be represented. 1 x+1 2. y = _ 4 3. $28.50 13. 5 4. C 14. Each has an area of 40 square units 5. domain: {6, 7, 8, 9}; range: {0, 1, 2, 3, 4} 15. a. 10c 6. B b. 5c + 15 7. Sample: Add or subtract terms so that the terms with an x-variable are isolated on one side of the equation. Simplify the equation by collecting like terms. Multiply or divide so that the x-variable has a coefficient of 1. c. 10c = 5c + 15; c = 3 16. true; Sample: 6x + 8 = 74 6x = 66 x = 11 17. stem-and-leaf plot; Sample: Stem-andleaf plots are best for ordering data. 8. 22(3t + 2s) 9. Triangle B 10. Student A: Sample: Student B in using larger increments does not emphasize the differences. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 29–2 Saxon Algebra 1 Lesson 18. 120 y (10, 120) 100 (5, 60) 40 (3, 36) 20 O 2 4 f 3 5 8 10 6 8 4 24. k = - _ 7 25. Sample: The number represented by z is odd, and it is an integer. (8, 96) 80 60 29 x 10 i 36 60 96 120 19. false; Sample: Repeating decimals are rational numbers because they can be expressed as fractions. −− For example, 0.33 can 1 . be expressed as _ 3 A repeating number multiplied by a variable could be a rational number. 1 -1 26. _ 2 27. 8 - 23 8-8 0 Parenthesis first. Simplify Exponents. Subtract. 28. y = 0 29. about 341,327,254 1 30. a. _ 4 b. 35 families 20. -125°F 21. 1 + 2s 22. x2 + 2x2y - 4xy 1 23. y = - _ 14 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 29–3 Saxon Algebra 1 Lesson Warm Up 30 8 30 y 4 1. relation x -8 -4 4 8 -4 2. (3, 4) -8 3. (-3, 4) The graph is a function and it is not linear. 4. (-3, -3) 5. 11 c. Graph 2 d. Graph 2 Lesson Practice 30 e. Graph 1 a. x y 0 5 8 2 9 -2 1 f. The domain is x ≥ 0 and the range is y ≥ -1. y x O -8 g. The domain is all real numbers and the range is y ≥ 1. 4 8 -4 h. f(x) = 30x -8 400 The graph is a function and it is linear. y 320 240 b. x y 0 1 -1 2 1 2 160 80 x O -2 2 4 6 8 -80 8 classes send 240 emails; f(x) = 30x; 240 = 30(8) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 30–1 Saxon Algebra 1 Lesson Practice 30 b. yes; A vertical line will cross the graph at one point only. 7 1. x = 1_ 10 2. x = 0.4 c. no; This is not a linear function. 3. x = 20 10. 5 4. x = -_ 2 x -4 4 8 -4 ) yes; It is linear because the graph is a line. 9 3 1 _ _ _ 4 + 7 6 2 2 2 ( ) y 4 ) ( 12 8 9 ; 5. x = _ 2 9 9 _ _ -4 -3 +762 2 9 _ -4 (2 30 ( ) 9 1 _ _ 6 + 7 6 2 2 11. Student A Sample: Student B did not subtract 6 on both sides. 11 11 _ =_ 2 2 6. false; A vertical line crosses the circle at two points so the equation is not a function. 12. area of the shaded part: 14x - 24 8. D i 14. r = _ pt 9. a. Number of Shrubs 7. Graph 1 3 1 x + 6; y = 1 _ 13. y = -_ 2 2 15. 18 Shrubs Planted 10 8 6 4 2 0 0 0.5 1 1.5 2 Time (hours) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 2.5 3 LSN 30–2 Saxon Algebra 1 Lesson 22. 16. Student B is correct; Sample: Student A did not distribute the -4 and -6 over both terms. 4 4 m 4 6 10 20 19. Sample: Changes in data appear less than they actually are. 5 6 7 8 Leaves 1, 3, 3 1, 2, 3, 3, 5 2, 4, 8 0 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 8 12 16 h 4 5 7 12 23. 10% 20. Sample: The circle graph may make it appear that orange juice and fruit punch are the only drinks sold at the store and that fruit punch is the drink most sold by the store. A bar graph would be a more appropriate graph, as it does not represent parts of a whole. Stem x O 18. D Woodmont Temperatures (°F) y 8 17. 13.5 cm 21. 30 24. Sample: 1 18 · _ x Commutative 6 Property of Multiplication 1 = 18 · _ x Associative 6 Property of Multiplication = 3x ( ) 25. 3.6 + 4.08 + 8 Subtract from left to right. = 7.68 + 8 Add from left to right. = 15.68 Add from left to right. LSN 30–3 Saxon Algebra 1 Lesson 30 26. Sample: When I use a unit as a factor n times, I need to apply a unit ratio for converting that unit n times. 27. Sample: 2 3 + 2 3+ _ 4 ) ( 3 +4 =3+ _ 4 ( 3 = 3 + 4_ 4 3 = 7_ 4 symbol of inclusion ) powers symbols of inclusion addition 28. $34 29. Sample: b, because any number less than one multiplied by itself will decrease 30. Samples: An airplane descends at a steady rate. An item loses value steadily over time. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 30–4 Saxon Algebra 1 Lesson 31 Warm Up 31 1. simplify 2. -0.3 3. -4 4. 14 5. 25 Lesson Practice 31 a. 0.62 < 0.65; 8 boxes for $4.96 is the better buy. 3 °F/s b. _ 4 1 of a page per min c. _ 6 d. 1 e. 6 f. 25 blue chips and 35 red chips g. 925 miles h. 6 miles © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 31–1 Saxon Algebra 1 Lesson Practice 31 15. $4200 1. 6 16. 2 out of 5 2. -6 17. a. f(x) Miles Traveled 3. n = 1.2 4. no solution 120 90 60 30 0 5. D x 1 2 3 4 Number of Gallons 6. -x + 2 b. f(x) = 33x 7. 8ck - 4ak + 12km c. 330 miles 18. a. 3d + 6g, 5d + g 8. 22 b. 8d + 7g 9. -64 c. $68 10. $4.25 per box 19. 90°, 60°, 30° 11. 6 20. domain: {11, 12, 13, 18, 19}; range: {0, 1, 2, 4, 10} 3 21 _ 12. _ x = 13 , 91 foxes 13. ≈ 15 ft/sec 14. 31 x -3 -1 0 y 11 3 2 1 3 3 11 y 12 8 x -4 O 4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 31–2 Saxon Algebra 1 Lesson 21. x y 19 5 1 _ 2 _ _ + = 28. false, _ 3 3 18 6 11 2 ≠ _; m = -_; ( ) -2 -1 0 1 2 3 0 -1 0 3 18 Domain: all real numbers Range: y ≥ -1 4 3 Check: 5 1 _ -2 11 _ _ _ + = 3 3 6 18 ( ) 29. 20 · $9 + 10 · $13 $180 + $130 Multiply from left to right. $310 Add. y 2 x -2 31 2 22. In the equation x = x, x can have any value. 30. 4s = 916; s = 229 m 23. a. Sample: m - 10) 65 + (_ 5 b. Sample: m - 10) 65 + n(_ 5 c. Divide m by 5. 24. B 25. Student B; Sample: Student A did not multiply both sides by 6. 26. $2562.22 27. 4x = 300; Divide by 4 to get 75. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 31–3 Saxon Algebra 1 Lesson 32 Warm Up 32 1. base 2. 81 3. x11 4. 8 5. -53 Lesson Practice 32 1 a. _ 5 x 1 b. _ 8 4 p q c. d8 d. 54 1 e. _ 4 f. x6 g. x11 z4 h. _ 5 xy i. 106 or 1,000,000 times more intense © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 32–1 Saxon Algebra 1 Lesson Practice 32 11. Sample: By combining like terms, the equation becomes simpler and easier to deal with. Combining contributes to the process of isolating the variable. 1. y 5 16 m q 2. _ 2 p 3. x = 2 17 4. y = _ 6 12. true, -28 = -4(9) + 8; -28 = -36 + 8; -28 = -28 5. y = -18 6. r = -3 13. no; Sample: For the input, 1, there are two outputs, 5 and 8. For the relation to be a function, each input would only have one output. π 7. _ 4 8. 19 9. Student B; Sample: Student A did not find the cross products of the proportion. 10. Sample: The title of the graph does not specify that the data only apply to those who suffer from allergies. Someone may conclude that 75% of people suffer from indoor and outdoor allergies. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 32 14. 5 dozen pencils 15. 86,400 LSN 32–2 Saxon Algebra 1 Lesson 16. Sample: The bar graph will show the exact number of roller coasters in each country and will compare the number of roller coasters in each country. The circle graph will show the relative number of coasters in each country to the total number of coasters. 17. 100 dozen 32 21. C 22. 104 = 10,000 times greater 23. a. x + 4 b. 12 ft, 16 ft 24. 28°F 25. 14 years old 26. a. Sample: ($3.25 - 0.32)x = 73.25 b. 25 gallons of gas 18. 100,000 cm 27. 20pxy - 8cxy 19. 62.5 miles 28. x = 3.5 20. yes 29. x = -0.5 x -3 -2 -1 0 1 2 y 13 12 11 10 11 12 20 18 16 14 12 10 8 6 4 2 -10 -8-6-4-2 -2 x 2 4 6 8 10 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 32–3 Saxon Algebra 1 Lesson 32 30. a. x 1 2 3 4 5 y 25 50 75 100 125 b. They all lie on the same line. c. 3.2 hr or 3 hr and 12 min 140 120 100 80 60 40 20 0 y x 2 4 6 8 10 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 32–4 Saxon Algebra 1 Lesson 33 2 f. _ 7 Warm Up 33 1. sample space 2 g. _ 7 2. 1, 2, 3, 4, 5, 6 h. 2:6 or 1:3 3 1 _ or 3. _ 6 2 i. 5:3 6 4. _ 11 1 j. _ 40 1 5. -_ 5 1 k. _ 35 Lesson Practice 33 a. independent b. dependent c. independent d. independent 1 e. _ 4 First H T Second Outcomes 1 H 1 2 H 2 3 H 3 4 H 4 5 H 5 6 H 6 1 T 1 2 T 2 3 T 3 4 T 4 5 T 5 6 T 6 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 33–1 Saxon Algebra 1 Lesson Practice 33 13. 3 - 7 = -4 and -4 is not a whole number. 1 1. v = -_ 2 14. B 2. b = -7 1 points 15. -5 _ 4 3. p = 10 16. 4. m = 3 6. x = 10 y 7. _2 x 1 8. _ 2 5 w z 2 _ xz 10. Sample: 1 _ 36 17. Sample: A student who wants to make it appear that test grades have not dropped dramatically could use large intervals on the graph to persuade people to make this conclusion. 5. x = -0.4 9. 33 After draw 18. 1; They are reciprocals. 19. 103 = 1000 times faster 20. 7.5 gal/mi 11. Sample: Probability is the ratio of favorable outcomes to total outcomes (or sample space). Odds is the ratio of favorable to unfavorable outcomes. 21. Student A; Student B multiplied 9 by 225 instead of dividing 225 by 9. 22. 170 mi 12. true © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 33–2 Saxon Algebra 1 Lesson 23. Sample: No, the set cannot be a function because all functions are also relations. 2 28. a. _ 3 24. Sample: First multiply each term by 100. Then add –20 to both sides of the equation. Finally divide both sides by 9 to get the answer n = 30. 30. false 33 b. x = 9 29. 12 ft 25. 32.5 m2 26. x 2 3 4 5 a. y 185 215 245 275 285 270 255 240 225 210 195 180 y x 1 2 3 4 5 b. after 6 more games 27. yes; Sample: The qualifying average speed is about 7.15 miles per hour. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 33–3 Saxon Algebra 1 Lesson 34 Warm Up 34 1. constant 2. 16.4 3. -29.92 4. -15 5. 63 Lesson Practice 34 a. yes; common difference = -1; 3, 2 b. no c. -3, 1, 5, 9 d. 4th term: 5; 11th term: -16 e. a10 = 82 f. a11 = 4 g. an = 12 + (n - 1)6 h. 96 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 34–1 Saxon Algebra 1 Lesson Practice 34 10. Sample: The first two terms have a difference of 2 while all of the other terms have a difference of 4. 1. x = -4 2. x = 20 3. 52 seats 4. 11. D x y -2 3 -1 -3 0 -5 1 -3 2 3 8 12. yes; 7; 35, 42 33 13. _ 200 1 14. _ 36 15. a. a n = 10 + (n - 1)6 b. 76 y 4 -8 -4 34 O x 4 8 1 16. a. _ 4 4 b. _ 21 -8 5. z = 3(y - x) 17. 24 1 1 _ m to m 18. _ 3 10 10 6. x = -48 19. D 7. all real numbers 20. yes; Sample: For every value of x, there is only one value of y. A vertical line drawn through the graph of the equation also strikes the graph only once. 8. dependent 9. yes; The sequence has a common difference of -0.8. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 34–2 Saxon Algebra 1 Lesson 21. 300 feet b 22. a = _ 2 23. Sample: The increments are large, making the increase in tuition costs seem less than they actually are. 34 30. Student A; Sample: Student B confused the dependent and independent variables. 24. Sample: The resulting equation 5 = -5 is a false statement. 25. x = 3.5; 16(3.5) + 4(2(3.5) - 6) = 56 + 4(7 - 6) = 56 + 4 = 60 26. false; Sample: √5 ÷ √ 5 = 1; Any number divided by itself, even an irrational number, will equal 1. 27. 612.50x - 250x + 400 = 5500; It will take about 4 months. 28. 8t = 50: It will take him 1 hours. about 6_ 4 29. 350 miles © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 34–3 Saxon Algebra 1 Lesson Warm Up 35 35 d. -12x + 4y = -12 y 1. ordered pair O -2 2. -13 3. 28.2 (1, 0) 2 x 4 6 (0, -3) -6 4. -8 e. The x-intercept is 4 and the y-intercept is 2. They mean that to go 24 miles by one mode, she could run for 4 hours or bike for 2 hours. 5. -7 Lesson Practice 35 a. The x-intercept is -6 and the y-intercept is 4. b. y 6 4 2 O x 2 4 6 c. The x-intercept is -8 and the y-intercept is -9. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 35–1 Saxon Algebra 1 Lesson Practice 35 Distance (mi) 14. 1. x = -1.5 3 2. y = _ 4 3. all real numbers 40 35 30 25 20 15 10 5 0 35 ; 1 2 3 4 5 6 7 8 9 10 Time (h) 20 miles 4. x = -1 15. yes; -5; 14, 9 5. -5 16. Student B; Student A subtracted the second term from the first term instead of the first term from the second term. 6. -48 7. 6y3 + 5y 8. 13xy2 - 5x2y 17. 16 square units 9. real numbers, irrational numbers 18. a. a1 = 9, a n = a n-1 + 1.5 10. The x-intercept is -4 and the y-intercept is -2. b. 18 lb 19. a. -65 11. The x-intercept is -5 and the y-intercept is 2. b. -7 c. a n = -65 + (n - 1)(-7) 12. Sample: They give you 2 points that are easy to find and graph because they lie on the x- and y-axis. 20. independent 13. B 1 22. _ 15 21. $115 23. D © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 35–2 Saxon Algebra 1 Lesson 35 24. no; The base of 4 was correctly raised to the second power, but the rule for negative exponents was not correctly followed. The correct solution is 4 -2 1 =_ . 16 25. 0.75 mi/min 26. Sample: Do you prefer SUVs or passenger cars? 27. The money earned is dependent, and the hours worked is independent. 28. 10.4°F 29. f (d) = 1440 - 32d 30. Sample: f = 8h; The relation is a function. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 35–3 Saxon Algebra 1 Lesson 36 Warm Up 36 1. ratio 2. 9 3. 84 4. 12 5. -14 Lesson Practice 36 a. 25°; 20° 5 _ 25 ; b. _ 3 3 c. 26.25 meters d. 90 in. by 45 in. e. 1 sq. in. : 4096 sq. in. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 36–1 Saxon Algebra 1 Lesson Practice 36 36 17. a. 7x + 10y = 280 b. 28; Sample: To earn $280 by only washing SUVs, 28 SUVs would have to be washed. 1. x = 75 2. x = 44 3. 13 4. 30 c. 40; To earn $280 by washing only cars, 40 cars would have to be washed. 5. -2 6. first 7. true 18. yes; -0.3; -0.8, -1.1 8. 6.75 19. Student A; Student B’s sequence does not have a common difference. 9. B 10. a. See student work. b. 15 feet 11. 0.25 sq. ft:100 sq. ft 12. The x-intercept is 12 and the y-intercept is 8. 13. 20 _ 8 = x _ , 14 8x = 280, x = 35 14. 9 20. Sample: There are 4 students left and 2 prizes, 1 of which is a book. P(student and 1 _ 1 1 _ · = book) = _ 4 2 8 1 pounds 21. about 33_ 3 22. C 23. a. 300 - 10w, 100 + 5w 15. -7 b. 400 - 5w 16. 5.5 square units c. $370 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 36–2 Saxon Algebra 1 Lesson 36 24. The number of firefighters is dependent, and the size of the fire is independent. 25. 3(x + 2) + (x + 2) = 128, x = 30 26. 16 lessons 2 27. _ xz 28. r = 0.015 29. Sample: The samples are measured precisely. Smaller intervals would better show the differences. 30. 34 - 2(x + 17) = 23x - 15 - 3x 34 - 2x - 34 = 23x - 15 - 3x Distributive Property -2x = 20x - 15 Combine like terms. 20x = -__ 20x Subtraction Property of -__ Equality -22x = -15 1 1 _ -_ · -22x = -15 · Multiplication Property 22 22 of Equality 15 Multiply. x=_ 22 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 36–3 Saxon Algebra 1 Lesson 37 Warm Up 37 1. exponent 2. 2401 3. -3336 1 4. _ 3125 5 3y 5. _4 5x Lesson Practice 37 a. 1.234 × 106 b. 3.06 × 10-2 14 c. 35.6766 × 10 ; 3.56766 × 1015 d. 9 × 10 3 e. > f. 7.5 × 102 seconds © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 37–1 Saxon Algebra 1 Lesson Practice 37 13. 8 37 y 4 1. -1 x -8 (6, 0) -4 8 (0, -3) 2. 68 -8 3. 30 4. 12b2 + 5b 14. a. 1 to 2 5. -21x - 24 b. smaller: 12 cm; larger: 24 cm 6. 0.0000000074 c. 1 to 2 7. Sample: It has to be of b the form a × 10 , and a has to be greater than or equal to 1 and less than 10. d. smaller: 9 sq. cm; larger: 36 sq. cm 8. Sample: It quickly shows how large or small a number is without having to count zeros. 9. B 10. 0.00004 1 11. 13_ 3 12. x = 99 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. e. 1 to 4 15. Student B; Sample: Corresponding angles of similar triangles are congruent. They are not in proportion. 16. 5 inches by 6 inches 4 17. _ 9 2 4 _ 4 = 18. 2 _ 3 3 1 2 4 _ _ 1_ 2 = and 3 3 3 1 4 = -_ 0 - 1_ 3 LSN 37–2 3 Saxon Algebra 1 Lesson The sequence is arithmetic with a common difference 4 of -_ . 3 19. dependent 3 21 _ 20. Sample: _ x = 13 21. B 1 1 m to _ m 22. _ 7 9 10 10 23. 9 and 10 24. Sample: The data could be displayed in a circle graph even though the given breeds do not represent the entire data set, which could lead to incorrect conclusions. 25. bar graph; Sample: Bar graphs can clearly display information gathered in surveys to compare different categories of data. 37 28. 7x + 9 = 2(4x + 2) 7x + 9 = 8x + 4 Distributive Property -7x -7x Subtraction Property of Equality 9=x+4 -4 ___ -4 __ Subtraction Property of Equality 5=x 29. a. f = 3y b. 82.5 ft c. N = 36y 30. a. 2x + 2(3x - 2) = 38 + x b. x = 6 c. length = 3(6) - 2 = 16 cm 26. f(w) = 2w + 20 27. (105) × (107) = 1012 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 37–3 Saxon Algebra 1 Lesson 38 Warm Up 38 1. factor 2. 6x2 - 10x 3. -12x4y + 21x3y2 4. x8 1 5. _ 64 Lesson Practice 38 a. 2 · 2 · 5 · 5 b. 3 · 17 c. 8mn4 d. 5pq2r 2 e. 4d 2e2(2e + 3d) f. 6x3y2z(2x - 7yz) g. x + 3 h. 2 + 5x2 i. h = -4(4t2 -15t - 1) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 38–1 Saxon Algebra 1 Lesson 12. h = 8(5 - 2t2) Practice 38 6-k 1. j = _ h Plant Height 2. a = bc - 3 3. Plant Height Time 4. 13. Sample: They use opposite operations. The Distributive Property uses multiplication to rewrite a product as a polynomial. Factoring divides out the GCF to write a polynomial as a product of its factors. 14. Sample: The fraction 6(x - 1) _ can be 6 Time reduced because the division of 6 undoes the multiplication of 6 in the numerator. The numerator of the 6x - 1 fraction _ cannot be 6 factored and therefore cannot be reduced because division does not undo subtraction. Plant Height 5. 38 Time 6. 4.8 lb/book 7. $7.90/hour 8. 2,000,000 18 or ≈ 2.57 9. _ 7 10. 2 · 2 · 5 · 7 15. 2 × 10-9 16. 1 × 10-9 17. 7.8 × 107 11. B © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 38–2 Saxon Algebra 1 Lesson 18. 3.64816 × 10-9 square meters 38 28. 22 visits 29. $16 30. a. 20. a. 1 × 1011 b. 3 × 10 -11 lb 21. Sample: When y = 0, 0 = 12x, so 0 = x. When x = 0, y = 12(0), so y = 0. The x-intercept and the y-intercept are the same, the origin. 22. 11:9 Shrubs Planted Number of Shrubs 19. 16 10 8 6 4 2 0 0.5 1 1.5 Time (hr) b. yes; A vertical line will cross the graph at one point only. c. no; This is not a linear function. 23. The base of 3 and the exponent of -2 were multiplied; the rule for negative exponents was not used. The correct -2 1 . solution is 3 = _ 9 24. Sample: The break in the graph is distorting the number of books sold. 3 _ 17 ; ,5 25. yes; _ 4 4 26. D 27. 3|0 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 38–3 Saxon Algebra 1 Lesson 39 Warm Up 39 1. real 2. -12x4 + 3x3y2 3. 2mnx - 3m2ny + 5mn2y 4. 1 - 5x 5. 3ab(ab2 - 2a3 + 4) Lesson Practice 39 2 2 7q r r4 +_ a. _ w , q ≠ 0, w ≠ 0 4 q 4 2 uay 2t y _ b. _ zq - z , q ≠ 0, t ≠ 0, z≠0 9m2 m _ _ c. 5 + 2 , j ≠ 0, k ≠ 0, j kj m≠0 cb 4n3 _ , b ≠ 0, n ≠ 0, d. _ 3 3 n zv zb v ≠ 0, z ≠ 0 f 2hs2 2fs2k 7fs _ + -_ , e. _ 5 4 10 d d d d≠0 z2 x2 w f. _ + 5tz2xw2 2 d 2zxw6, d ≠ 0, w ≠ 0 3 y t _ + g. _ 4 5 tz y z © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 39–1 Saxon Algebra 1 Lesson Practice 39 39 5. k + 2.5 1. y = -6 6. x - 3 2. x = 6 7. 3y + 2 8. 3. false; Sample: 2 ÷ 3 is not an integer. 9d2s , h ≠ 0, s ≠ 0 d4 + _ _ s3 h 4. a + 3 9. Sample: Division by zero is undefined. A number cannot be divided into groups of zero and zero has no reciprocal. 10. Sample: x -2 _ (2x-4 + n-3) n -1 2x-4 · x-2 =_ n-1 x-2n-3 +_ -1 n Distributive Property 2x-6 + n-2x-2 =_ -1 Rules of Exponents 1 +_ 2 2 Rules of Exponents = n 2n _ x6 n x n ≠ 0, x ≠ 0 11. D 4p w2t 12. _2 - _ , p ≠ 0, t ≠ 0, w ≠ 0 4 tw p 13. 2 · 3 · 3 · 3 · 17 14. Student B; Sample: The third term of the polynomial is the same as the GCF, and factoring results in a monomial divided by itself, which is 1. Student A represented the third term with 0, not 1. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 39–2 Saxon Algebra 1 Lesson 15. 3ab(2a + 5); Sample: 3ab and 2a + 5 1 4 _ _ 3 _ 15 25. 44 - 1 3 4 4_ - 1 15(1) 4 ( 16. C b. 6xy(4xy2 + 3y + 1) 6(x + 4) 2(x + 4) 6(x + 4) _ _ = = 18. _ 9 · 15 135 45 19. no; Sample: Double only one of the dimensions to double the volume. 20. y (0, 6) 4 O -4 (2, 0) 4 x 8 -4 -8 21. The x-intercept is 96 and the y-intercept is 60. 22. $4000 23. 6.08 × 10 -3 24. Student B; Sample: Student A wrote 5 zeros and moved the decimal point 6 places instead of 5. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. ) 19 - 4 15 15 = 15 17. a. 6xy -8 39 9 26. _ 64 27. Sample: Odds are the ratio of favorable to unfavorable outcomes, so added together they equal the total number of outcomes (3 + 7 = 10). If the odds of winning a CD are 3:7, then there are 7 outcomes for not winnning a CD. So the probability of not 7 . winning a CD is _ 10 28. Sample: The ordered pairs will form a relation but not a function because a given stamp will have more than one possible value. LSN 39–3 Saxon Algebra 1 Lesson 39 29. Sample: The vertical axis has a broken scale, making the data appear to increase dramatically. The employer may want the candidate to feel the employer gives large raises. 30. f(g) = 0.5g + 0.5 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 39–4 Saxon Algebra 1 Lesson 40 Warm Up 40 1. exponent 6 7 2. 20x y 3 2y 3. _2 3x 4. 0 5. > Lesson Practice 40 4 a. 5 = 625 b. b 28 c. 9n 8 d. 162a 4 12 27y e. _ 64 x2 f. _ 10 49y 3 g. 27x cubic inches © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 40–1 Saxon Algebra 1 Lesson 40 2 x 12. _ 2 a dx d Practice 40 1. m = -96 13. g3w3x2 + g6y2 2. x = 0.6 r t y 2rt y 8rt _ 14. _ + -_ 5 4 3 2 2 2 w w w 2 3. k = 3 15. 2xy z 4. true 16. Student A; Sample: Student B canceled without first writing the numerator as a product. The factor that is canceled in the denominator must be the same factor that is canceled in the numerator and, therefore, must be a common factor. 5. 420 6. C 5 3 4 e e r _ + , k ≠ 0, r ≠ 0 7. _ 6 k 4r 8. The area of the pizza will be quadrupled; A = π(12) 2 = 144π 9. no; Sample: Let a = 3, b = 4, and n = 2. 2 (3 + 4) 2 = 7 = 49, but 3 2 + 4 2 = 9 + 16 = 25. 17. a. 2 · 5x(10x + 15) b. 50x(2x + 3) 10. Sample: You add exponents when you are multiplying two powers with the same base. You multiply exponents when you are raising a power to a power. 18. 195 19. domain: {2, 4, 5, 9}, range: {4, 7, 9, 12} w5 1 +_ 11. _ 2 3 4 d c c d © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 40–2 Saxon Algebra 1 Lesson 23. 3.48 × 10 20. a. 40 6 Tree Heights 24. 80 270 Feet 250 230 25. 210 190 -20 170 x 16 (10, 0) -40 Tree 8 Tree 7 Tree 6 Tree 5 Tree 4 Tree 3 Tree 2 Tree 1 150 0 y (0, -55) b. 26. no; The sequence does not have a common difference. 2 - 0.2 = 1.8 but 20 - 2 = 18. Tree Heights Feet 200 100 Yellow Yellow Purple Purple Purple Purple Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Purple* Purple* Purple* Purple Yellow Yellow Purple* Purple* Purple* Purple Yellow Yellow Purple* Purple* Purple* Purple Yellow Yellow Purple* Purple* Purple* Tree 8 Tree 7 Tree 6 Tree 5 Tree 4 Tree 3 Tree 2 0 Tree 1 27. c. Sample: The heights appear to vary greatly in the graph with the broken scale. The heights appear very close to each other in the graph with large increments. -4 21. Sample: 1 × 10 is a small number, but it is greater than 0, so it is greater than -10. 22. A © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 12 ways LSN 40–3 Saxon Algebra 1 Lesson 40 28. 5 29. 648 inches 30. Sample: If x is zero, then the rule would be -n 1 , but 0 n = 0 0 =_ 0 n since zero multiplied any number of times is zero. This would mean dividing by zero, which is undefined. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 40–4 Saxon Algebra 1 Lesson 41 Warm Up 41 1. linear 2. 3, 5, 7 3. quadrant IV 4. quadrant III 5. quadrant II Lesson Practice 41 a. 4 kicks/measure b. 5280 ft/mi c. 3 2 d. - _ 5 0 ;0 e. _ 3 5 ; undefined f. _ 0 g. 4 h. During each measure, Iliana kicked the drum 4 times. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 41–1 Saxon Algebra 1 Lesson Practice 41 1. b = -2 2. y = -3 41 14. Student B; (-2)5 = -32, not -10. Student A multiplied the coefficient by the exponent, which is incorrect. 1 3. m = _ 8 1 4. 1 _ 4 1 5. -_ 3 6. 0 7. undefined 8. 1.104 × 105 9. A 10. no; The terms 5x3, 6x2, and 3x all have a common factor of x; 2x2(5x2 + 6x - 3) 11. $66.67 per year 12. Sample: Mindy is descending the mountain. 15. A = 16x2y2 16. a. 106 b. 109 17. 125a3b3 cubic inches f 2sr 2 3f 2rs 8fr _ + -_ 18. _ 5 3 4 d d 7 6 5 d g h r g _ 19. _ 2 2 tr t 20. 3 inches 21. The x-intercept is 2. The y-intercept is 5. 22. 5F - 9C = 160 or -9C + 5F = 160 23. a1 = 8, an = an-1 + 11; 52, 63 13. b15 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 41–2 Saxon Algebra 1 Lesson 41 24. Sample: When looking at two events, if they are dependent, the first will affect the probability of the second. If they are independent, the first does not affect the second. 1 cups 25. 2 _ 4 26. f(x) = $2.50x 27. Parabola A is a function; Parabola B is not a function. 28. v = 2.32 m/s, Ek = 6.728 kg · m2/s2 29. a. 65x b. 50(x + 1) c. 65x = 50(x + 1); 1 x = 3_ 3 d. 216.7 miles 30. length = 4 in., width = 3 in. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 41–3 Saxon Algebra 1 Lesson 42 Warm Up 42 1. proportion 2. 8 3. -6 4. 20 games 5. 56 white marbles Lesson Practice 42 a. 24.5 b. 36 315 x =_ ; x = 66.15 c. _ 100 21 p 59.5 _ = ; 350% d. _ 17 100 e. (0.33)(32) = 10.56 miles per gallon; 32 - 10.56 = 21.44 miles per gallon 45 t _ = ; $6944.40 f. _ 15,432 100 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 42–1 Saxon Algebra 1 Lesson Practice 42 42 15. incorrect; y = 176 - 24x 11 1. d = -_ 2 16. $35 a. 2. t = -2 x (Number 2 4 6 of Pies) y (Total $5 $10 $15 Cost) 3V 3. w = _ lh d 4. t = _ r 5. between 6 and 7 b. yes 6. 61.2 y Price ($) 12 7. 251.1 8. 36m2n6 8 4 x 4 Number of Pies 9. C c. y = 2.50x 10. $3.05 per gallon d. $35.00 11. All of them are used to express a part of a whole. 17. Sample: They could draw the graph with a broken axis. 12. a. 1 18. a. _ 6 1 b. _ Numbers of Pitches Thrown per Inning Stem 1 2 3 Leaves 9, 9 0, 1, 2, 3, 5 0, 8 2 Key: 1 9 means 19 b. greatest: 38; least: 19 19. a. a1 = 52, an = an-1 + 3 b. 64 in. 13. 14 hours 14. 106 = 1,000,000 times more information © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 42–2 Saxon Algebra 1 Lesson c. no; Sample: Humans eventually stop growing. 20. The x-intercept is -8 and the y-intercept is -7. 42 29. a. $22 per 1 day b. $537 3 4 _ ; 30. _ 3 4 21. The volume will increase by 8 times. 22. 14p2qr2 23. Sample: ( ) _ ) rs-2 - _ s-3r-1 r -2 _ _ s-3 sr-1 = ( r-3 r-1s-2 - s-3r-3 _ s-2r-1 s-3r-3 =1-1=0 24. 2 × 10-3 25. C 26. 25 miles per gallon 27. Student A; Sample: Student B raised the base to the second power. 1 mile/inch 28. _ 4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 42–3 Saxon Algebra 1 Lesson 43 Warm Up 43 1. greatest common factor 3 2. _ 4 2 3. _ 2 3x 4. 1 - 7x 5. 3x2(1 + 2x) Lesson Practice 43 a. x = 0 b. x = -8 c. x = 7 7x - 27 ,x≠0 d. _ 5x x-1 5; x ≠ 0 , x ≠ -_ e. _ 3x + 5 3 4 , x ≠ 0; x ≠ -7 f. _ 3x 2(h + r) ; h ≠ 0, r ≠ 0 g. _ rh © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 43–1 Saxon Algebra 1 Lesson Practice 43 43 3. 9 12. Sample: Use a vertical line test. If a vertical line passes through more than one point on the graph, the relation is not a function. 4. 190 13. 62.5 miles 5. x = -10 14. A 6. x = 5 3z , z ≠ 0.9 15. _ (z - 0.9) 7. 16.8 16. undefined at x = 0 8. 45 1 17. _ 90 1. 10 2. 20 9. $900; x + 2x = $2700, x = $900 10. a. 1.8 + 0.05n = 2.55 b. 15 nickels 11. Student B; Sample: Student A confused the dependent and independent variables. If any of the x-values were the same, the relation would not be a function. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 18. a. an = 17 + (n - 1)10 b. 47; 117 19. Sample: Multiply both sides by 6 to get 6y = -5x - 12 and then add 5x to both sides; 5x + 6y = -12. −−− −− −−− −− 20. MN and KL; MP and KJ; −− −− NP and LJ; ∠M and ∠K; ∠N and ∠L; ∠P and ∠J 21. 3.52 × 10-2 LSN 43–2 Saxon Algebra 1 Lesson 43 22. a. 8x(6x + 4) b. 16x(3x + 2) 23. A 24. They are multiplicative inverses of each other. 5k3w6 rtw _ 25. _ ng g rs2 r2 _ 26. _ + s 2 t 27. 12 guests/table 134.4 x _ = 28. a. Sample: _ 100 42 b. 320% c. Sample: 320% = 3.2 times a number; 42 · 3.2 = 134.4 29. about 13 ft 30. 15.6 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 43–3 Saxon Algebra 1 Lesson 44 Warm Up 44 1. slope 2. (-6, -4) 3. (4, -5) 4. (5, 3) 4 5. _ 1 Lesson Practice 44 2 a. _ 3 1 b. - _ 5 c. 6 d. –4 e. 7 7 f. - _ 11 9 g. _ 11 h. 0 i. undefined slope j. 58.7 ft/s © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 44–1 Saxon Algebra 1 Lesson Practice 44 1. 0.0000000082 18. 89.5 ft 19. a. 20x + 2y = 500 b. 250; Sample: To earn all profits with just pencil sales, 250 boxes of pencils would have to be sold. 2. 230,000 3. 1.125 × 105 4. 5.8 × 10-4 5. domain: {1, 3, 5, 7}; range: {2, 4, 6, 8} c. 25; Sample: To earn all profits with just T-shirt sales, 25 T-shirts would have to be sold. 6. domain: {3, 4}; range: {4, 5} 7. f(x) = 20x + 180 8. 5% 9. 121.50 20. a. Sample: 0.75x = 10.5 b. Sample: To get rid of the decimal, multiply both sides by 100 and then solve 100 · 0.75x = 10.5 · 100. Isolate the variable by dividing by 0.75, x = 14 laps 10. x = -2 3 11. m = _ 5 1 12. m = -_ 3 13. undefined 14. 2 inches per month 15. −4 16. 882 trees 17. $52.65 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 44 21. 1.3188 × 109 22. 3xy2(x + y - 2x2y4) 23. −29 LSN 44–2 Saxon Algebra 1 Lesson 44 24. a. 32,768 ways 1 b. _ 32,768 25. B 26. Sample: number of ice cream cones sold from August to November 0.75m 3m _ = 27. _ 2.50 + 0.50m 10 + 2m 28. Student A; Sample: Student B did not add the inverse of 3 when solving for the undefined value. 29. a. 4x² + 24x units x2 b. _ 30. 4x2 + 24x x c. _ 4(x + 6) r_ +2 r © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 44–3 Saxon Algebra 1 Lesson Warm Up 45 45 h. A number divided by 7 is at most 8. 1. algebraic expression 9 °C + 32 ≥ 140 i. _ 5 2. 0 3. 16 x2 _ 4. 2 y x 5. _ 4 4 y z Lesson Practice 45 x > -9 a. _ -2 b. 0 ≤ 2n - 8 1 n + 3 ≠ 15 c. _ 2 d. 11n < 121 e. Sample: The product of 12 and an unknown is at least -8. f. Sample: The sum of the product of 1.5 and a number and 2.5 is less than 11.5. g. 9 is greater than the difference of one-third of a number and 8. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 45–1 Saxon Algebra 1 Lesson Practice 45 11. Sample: “4 more” means to add 4. “The quotient of an unknown and 9” can be represented as a fraction with a variable over 9. “No less” can be translated to greater than or equal to. The correct inequality is n _ + 4 ≥ 15. 9 1. 1280.16 cm 2. 126,720 in. 3. -61 4. 2 5. 6x ≤ 15 6. x > 7 12. s + 45.7 ≥ 83.2, where s is the score of the third round. 7. Sample: The product of -4 and b is at least 7. 8. Sample: Four less than the quotient of t and 7 is less than 8. 13. C 3 1 2 _ _ , , -2, 9. -_ 2 2 3 15. a. $1.78 per day 4 14. m = 1 b. $1.00 per day y 1 _ 2 2 -2 c. Sample: Stock A is the better buy. Its graph shows a larger rate of increase in value over the 9 days. 3 _ 2 2 -2 45 x 2 _ 3 10. B 16. 0.71 parts per million per year 6 17. m = _ 5 18. 5m2n(n3 + 2m) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 45–2 Saxon Algebra 1 Lesson 4 1 19. _ -_ 3 3 4 xw j wx 28. a. 105 = 100,000 times longer 20. (0, 12), (-3, 0) b. 102 times longer; 102 · 103 = 105 = 100,000 times longer; yes 21. a. 80 miles b. 280 miles c. 40 miles d. no; Sample: The shorter route may have more traffic or a slower speed limit for driving. 22. 1.225π × 107 square kilometers 45 1 29. _ 30 30. For 8,000,000, the number of zeros equals the exponent, but that does not hold true for the other examples. The pattern only exists if there is one digit followed by zeros. 23. $6.75/hour 24. Sample: V = 803 + (803 · 25%) = 1003.75 in3; See student work. 25. 24 + 9x _ ; x x≠0 26. Student B; Sample: Student A did not factor the GCF from the numerator correctly. 27. x 0 1 -1 2 4 y 1 0.5 1.5 0 -1 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 45–3 Saxon Algebra 1 Lesson Warm Up 46 j. 5 1. perfect square k. -2 25 = 5 2. yes; √ l. 3 3. no; Sample: There is not a whole number squared that equals 12. 46 m. no real solution n. 12 ft 49 = 7 4. yes: √ 5. 125 6. 81 Lesson Practice 46 a. 14 b. -8 c. 1 d. no real solution 9 3 _ , or e. _ 12 4 f. 12 g. -7 h. 20 i. no real solution © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 46–1 Saxon Algebra 1 Lesson 1. 63 5 13. a. _ 24 2 b. _ 2. 20 14. a. 10y ≥ 180 Practice 46 46 7 b. y ≥ 18 3. no real solution 2 2 2 2 g t h gt 3gt h _ _ + 15. _ 3 2 2 4. -10 d d 5d 5. -3m2xy + 8mxy2 64x8 16. _ 9 6. C 5 17. d > _ π , where d is the diameter. 7. -2 ≤ x - 7 8. a ≥ 35 18. 90 inches by 150 inches or 7.5 feet by 12.5 feet 9. 11 and 12 19. a. 4.9 × 1012; 3 × 10 10. independent variable: number of cattle as a multiple of 15; dependent variable: number of mineral blocks 11. y 12 8 4 -4 -2 O x 2 4 12. 35 8 b. about $1.63 × 104 per person 20. 27x2y3z = 3 · 3 · 3 · x · x · y · y · y · z and 12xy2z = 2 · 2 · 3 · x · y · y · z, so both terms have 3 · x · y · y · z in common and the GCF is 3xy2z; 3xy2z(9xy + 4) 21. 4.85 gallons per minute 21. 300 23. B © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 46–2 Saxon Algebra 1 Lesson 46 2 24. _ ; Sample: I factored out 3 a 6 in the numerator and a 9 in the denominator. Then I canceled the 1 - x binomial and simplified the remaining fraction. 1 25. m = -_ 4 1 26. m = _ 4 27. Student A; Sample: Student B incorrectly translated “at most” as greater than or equal to instead of less than or equal to. 28. 6w ≤ 45 29. about 18 pages 2 inches 30. 2 _ 3 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 46–3 Saxon Algebra 1 Lesson 47 Warm Up 47 1. percent 2. 75% 3. 8 4. 140 5. 31.25% Lesson Practice 47 a. % of increase: 5% b. % of decrease: 25% c. $19.80; $63.80 d. $75,680; $268,320 e. 39% f. 22% © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 47–1 Saxon Algebra 1 Lesson Practice 47 4 1. x = _ 3 2. p = 4 4 3. k = -_ 7 4. 3.6x > 18 5. 46 6. $4.50 per box 7. -8 8. 40% increase 9. C 10. Sample: It is possible to have a percent of increase more than 100%; this could be when a price more than doubles. However, it is not possible to have a percent of decrease more than 100%. 11. Sample: Each number after the first is 40% of the preceding number; 1920, 768 47 13. Sample: Rise over run refers to a change in the vertical position of a line divided by the corresponding change in the horizontal position. 14. not correct Sample: discounted price: $500 - $125 = $375; new price: $375 + $93.75 = $468.75; The original price is higher. 15. Student A; Sample: The expression is equal to the fourth root of 16, which is 2. 16. 18π inches 17. 10 18. 21 sparrows and 24 doves 19. 27 20. a. a1 = 9, an = an-1 + 13 b. 9, 22, 35, 48 12. D © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 47–2 Saxon Algebra 1 Lesson b. no; Sample: The polynomial in parentheses, 2a + 2ab + 2bc, still has a common factor of 2. The complete factorization would be 4(a + ab + bc). 21. Student B; Sample: Twice a number means 2 times a number; Student A added instead of multiplying 3 22. m = ±_ 2 23. The expression is defined for all values of x. 47 30. $158.17 24. $313.56 25. -4 eggs/omelet 26. -64a3b6c6 27. Sample: Because if x = 0, then x2 = 0, and you can not have a zero denominator. 28. 0.000000000000002817939 29. a. yes; Sample: Using the Distributive Property, 2(2a + 2ab + 2bc) = 4a + 4ab + 4bc, which is the original polynomial. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 47–3 Saxon Algebra 1 Lesson 48 Warm Up 48 1. outcome 3 _ 2 _ 4 2 4 _ _ , , , 1 , 1 2. _ 5 8 5 9 3 3. 2.337, 2.5, 2.59, 2.75 4. 1 5. -2 Lesson Practice 48 a. mean: 29; median: 28; mode: 25 b. trucks c. 59 and 64 d. Sample: the outliers raise the mean age of the graduating students by 3.8 years and the median by 0.5 year. e. $2.31; Sample: no; If I lived in 1 of the 10 cities, I would use the mean, $2.33, since it might be better to use the higher price when budgeting. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 48–1 Saxon Algebra 1 Lesson Practice 48 9. true when n is even and false when n is odd; Sample: Multiplying a negative number an even number of times results in a positive number, while multiplying a negative number an odd number of times results in a negative number. 1. 2ab2c 2. 5m2xy2 3. 4ax3 - 8x2 6 4. _ 4 ac 15 5. _ 28 6. mean: 4; median: 4; mode: 6 7. 21.25 216 , so 10. a. 9 = _ x + 12 9(x + 12) = 216. 8. a. (_xy - _xr )( _xy - _xr ) b. x = 12 x2 r2 _r - _r + _ or b. _ y y 2 2 y x2 _ y2 c. 24 x xr rx r2 _ _ -_ + yx xy 2 11. B x x2 2r r2 _ _ _ c. 2 - y + 2 y 48 x 12. yes; Sample: It is possible for the mode to be the highest or lowest value in the data set. 13. a. $198.38 b. increase by 32% 14. percent increase of 106% © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 48–2 Saxon Algebra 1 Lesson 15. Sample: The sum of 8 and 7 is 15, which is odd. 16. Sample: The mode of the data set is 0, but this is not representative of Juan’s average score. He may have missed the last three games, so the median or mean would better describe the set. 17. 12; Sample: The outlier represents a goalie who performed very well for the season. 18. a. -3x + 10y = 360 b. 36; Sample; If 0 minutes are used, the bill is $36. In other words, even if the phone has not been used, the person will still be charged $36. 48 c. -120; Sample: In order to have a $0 bill, -120 minutes would have to be used. This is impossible. 19. h = -2(8t2 - 6t - 1) 20. 22.32 2 21. _ x+4 22. m = -8 1 x + (-4) < 6 23. _ 2 24. A 1 _ 25. m 6 26. B 27. 20% decrease 28. Student A; Sample: Student B calculated a percent decrease. 29. Square with side length 3.5 inches 30. inductive reasoning; The conclusion is based on an observed pattern. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 48–3 Saxon Algebra 1 Lesson Warm Up 49 49 g. y = 0.5x + 50; Car Rental Rates Amount in Dollars ($) 1. B 4 1 _ x + 2. - _ 3 3 3 7 _ x 3. _ 2 2 4. 18 90 80 70 60 50 40 30 20 10 0 5 10 15 20 25 30 35 40 45 Number of Miles 5. 81 Lesson Practice 49 a. m = 0.7; b = -4.9 b. m = 3; b = 4 c. 4 y 2 -4 -2 x O 2 4 4 8 -2 -4 d. 8 y 4 -8 -4 O -4 -8 x _x - 5 y=1 4 e. y = x + 4 1 x-2 f. y = -_ 3 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 49–1 Saxon Algebra 1 Lesson Practice 49 10. a. 1. 3x3y4 - 5x2y4 3. -288 4. -1 10 , 0) (_ 3 6 2 _ ; b = 6. m = _ 5 5 7. B 8. a. y = 15x + 75; y represents the total cooking time and x represents the number of biscuits. b. 75; no; Sample: You would not cook 0 biscuits for 75 seconds 9 ; y-intercept: 32 9. slope: _ 5 40 y 1 1 _ y=_ x 6 4 b. no; Sample: According to the x-intercept, a cat 1 lb that weighs 1_ 2 should get zero cups of food a day. 2. -8x5y4 + 6x4y4 5. 49 11. mean: 3; median: 3.5; mode: 4 12. Student B; Sample: Student A failed to list the data in numeric order before finding the median. 13. no; Sample: The data centers around the values 2 (mean and median) and 1 (mode). It is more likely that the next person surveyed will have 1 or 2 pets. x - 12 14. _ 2x - 1 15. 17.6 20 16. Sample: -6 10 -8 -4 O x 4 8 17. 20 blocks 18. 5:10 or 1:2; 10:5 or 2:1 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 49–2 Saxon Algebra 1 Lesson 19. a1 = -3, an = an-1 + 9; -3, 6, 15, 24 20. a. ∠Q b. 110° 49 29. inductive reasoning; The conclusion is based on an observed pattern. 30. a. (2x)2 or 4x2 square inches c. 3:2 or 2:3 20 d. _ b. 5(4x2) or 20x2 square inches 3 21. 28.4 million 22. 4 cm 23. Student B; Sample: Since the price decreased by 15%, 85% of the original price would be the current price. 24. a. 46 inches b. 2704 square inches c. 588 square inches 25. = 26. 15% increase 2 1 < 1_ 27. 2x + _ 3 3 28. -1.375 km/yr © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 49–3 Saxon Algebra 1 Lesson 50 Warm Up 50 1. inequality 2. 137 ≥ 2x - 13 9 3. _ 4 3 4. _ 5 Lesson Practice 50 a. -2 and 0 b. c. d. e. -2 0 1 2 -1 0 -4 2 3 1 -2 4 3 2 0 4 2 f. m > 0.5 g. n ≥ 12 h. g < 45 2 i. p ≤ _ 5 j. 70 100 110 120 130 t ≥ 100 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 50–1 Saxon Algebra 1 Lesson Practice 50 15. Sample: Draw a number line and label several numbers, including 12. Draw a circle at the location of 12 and fill it in. Then shade the section of the number line to the right of the circle. 1. km(6k4m - 2k2 - 1) 2. mx3 y2(x - my + 5mx3) 8x3 3. _ 12 27y 4. 16x12y8 5. false; 3 - 5 = -2, and -2 is not a whole number. 16. x < -2, x > -2, or the graph of x ≠ -2 is all values except -2 9 6. m = _ 14 17. a. 1.2756 × 107; 6.959 × 108 7. 5x - 6y = 2 1 _ 8. y 4 b. approximately 5.5 × 101, or about 55 times 1 9. _ 21 10. 1:499 18. 1.8 × 1017 joules 11. an = 32 + (n - 1)(-6); 8; -34 19. a. 0.8 page/min 12. Student A; Sample: Student B solved the equation for x instead of for y. 13. 6 14. A © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 50 b. 0.9 page/min 20. yes; Sample: Because of the Distributive Property of Multiplication, she can break the problem apart. x+5 1 _ , x ≠ 21. _ 6x + 1 6 LSN 50–2 Saxon Algebra 1 Lesson 22. 5h + 135 ≥ 280, where h is the number of hours 50 29. a. y = 7.5x - 185 b. 23. B 24. Sample: Kwami’s collection increased by 3 which is a 50% increase. Lisa’s collection increased by 8 which is a 40% increase. c. 25 candles 30. t ≤ 32; 30 35 25. mean: 27; median: 25; mode: 15 26. 412 27. Sample: If he creates a table of values using the equation, he can make sure that those ordered pairs are on the line in the original graph. 28. y = 4x; Sample: (0, 0), (1, 4), (2, 8) 16 12 8 4 0 4 8 12 16 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 50–3 Saxon Algebra 1 Lesson 51 Warm Up 51 1. rational 2. 6n - k 3. x(4x + 1) 4. w(w - 1) 5. D Lesson Practice 51 a. h ≠ 0 b. p ≠ -4 c. g ≠ 5 d. a ≠ 0, 2a e. d ≠ 0, cannot be simplified 3z f. z ≠ 2, _ 5 5(y - 2) g. x ≠ 0, y ≠ 0, _ 2 xy 2f h. _ 2 r i. 9m -2 4 n x + 11 in. j. _ 2y © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 51–1 Saxon Algebra 1 Lesson Practice 51 51 15. 60° 1. 3 16. $1.60/lb 2. -3 17. a. 285% · $158 + $158 =s 3. 4 b. $608.30 4. -4 5. 3x - 56y = 8 3x - 4 6. _ 4y 16d 7. _ 2 8. 3m 9 _ 6 2 h y 9. D 10. 1040 feet 11. p ≠ 6; Sample: A value of 6 would make the denominator equal to zero, and division by zero is undefined. 18. no; Sample: A rational expression is undefined only when the denominator is zero because division by zero is undefined. If the numerator is zero and the denominator is a nonzero number, then the value of the rational expression is zero because zero divided by any nonzero number is zero. 9 19. m = - _ 7 12. 153 20. 46% increase 13. If a number is a natural number, then the number is a whole number; true 21. deductive reasoning; The conclusion is based on the definition of a triangle. 14. B 22. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 51–2 5780 5880 Saxon Algebra 1 Lesson 23. s ≤ 900; 850 51 29. a. f ≥ -15 900 b. Sample: The temperature is greater than or equal to negative fifteen. 24. a. Sample: First I would list the data in numeric order. Then I would count the number of data values (20). Because the number is even, I would find the average of the tenth and eleventh data values to determine the median. 1 ; 30. l ≥ 1 _ 2 0 1 2 b. 156 5 x+3 25. y = -_ 3 26. C 27. none 28. Student B; Sample: Student A graphed all numbers less than 9, and “at least 9” means that the number is equal to or greater than 9. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 51–3 Saxon Algebra 1 Lesson 52 Warm Up 52 1. slope 2. 2 3. 6 4. n = 18 5. x = 5 Lesson Practice 52 a. y 4 -4 x O 4 -4 b. 4 y 2 -4 -2 O x 2 4 -2 -4 c. y - 9 = 6(x - 7) 29 7 _ x d. y = _ 5 5 e. -9 points © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 52–1 Saxon Algebra 1 Lesson Practice 52 52 13. -4 - x ≤ 0 1. {-5, -2, 1, 4} 1 14. -1_ 4 2. {2, 3, 4, 5} 15. 150 bags 3. x > 3 16. mean: 7; median: 7; mode: 8 4. x ≥ 5.15 5. 6.25 × 10 17. a. y = 10x + 10 -9 b. $60 6. 4 y 18. a. y = 2x + 40 2 x O 2 4 b. $60 6 -2 4 19. y ≥ _ 5 7. 80 miles 8. 42 inches 5t3 t5 _ + 9. a. _ 6 3 y my b. y ≠ 0, m ≠ 0 10. $6950.00 11. a. It is 0 at x = 0 and at x = 5. 20. Student A; Sample: Student B graphed b as greater than 2.5, but should have graphed 2.5 as greater than b. Rewriting the inequality with the variable on the left, such as b < 2.5, would have been less confusing. b. It is 0 at x = 5. 21. b ≠ 0 c. It is undefined at x = 0 and at x = 5. 22. 185 meters 12. 13 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 52–2 Saxon Algebra 1 Lesson 23. If a polygon does not have four sides, then it is not a quadrilateral.; True 52 30. a. 24. Student B; Sample: Student A forgot to rewrite each term with positive exponents before trying to combine like terms. As a result, the expressions did not appear to be like terms. b. 240 miles 4 25. _ x 12a + 4 meters 26. _ 3a - 1 27. A 28. m = 0; Sample: It is a horizontal line, which has zero slope. 29. a. y = 8x + 24 b. c. 6 days © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 52–3 Saxon Algebra 1 Lesson 53 Warm Up 53 1. term 2. 1 2 3. _ 3 4. 25b Lesson Practice 53 a. 9 b. 3 c. 6 d. -2w4 + 3w2; -2 e. 3a2b2 + 5ab2 + 8ab -1; 3 f. -5a2b + 2ab - 7; -5 g. 3x2 + x + 12 h. n2 + 6n i. -6y3 + 3y2 + 5 j. 8c - 8 k. 5t - 2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 53–1 Saxon Algebra 1 Lesson Practice 53 13. 13,407.125 days; 2508 days 1. 22 14. A 2. 10 3. 6 53 8 10 12 4. x > 2.5 5. > 6. 9ab3c(2a - 5b3) 7. h = -8(2t2 - 10t - 1) 18. k ≠ -2; cannot be simplified any further 2(k + 3) than _ k+2 20 + 3t 9. _ 5(2 + t) Inflation Rate 16. 19% decrease 17. m = -0.5; b = 2 8. 648a7b3 10. a. 15. Sample: Locate the number on the number line. If the number is in the region indicated by the shading, then it is part of the solution. 2.70% 2.60% 2.50% 2.40% 2.30% 2.20% 2.10% 2.00% 19. 60 meters 1 2 3 4 5 6 Month (2007) b. 0.122 c. 2.812% 20. Student A; Sample: Student B cancelled parts of a term. Only factors can be cancelled. 2 1 x+_ 21. D (-2, -1); y = _ 3 3 11. Sample: greater than or equal to, at least, no less than A(-2, 3) y B(4, 3) 2 -4 1 _ O -2 D(-2, -1) 12. -b 2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 4 LSN 53–2 x 2 C(4, -1) Saxon Algebra 1 Lesson 53 29. yes; Sample: x0 = 1 and 4 × 1 = 4. 22. a. y = -50x + 800 b. y = -50x + 600 30. 3x2 + 7x; Sample: 3x2 + 7x - 6 -3x2 - 7x _ c. 300 acres and 100 acres -6 23. y = -2x + 9 24. B 25. -33x3 + 670x2 - 1695x + 31948 26. 7 1 (x - 4) or 27. a. y - 5 = -_ 2 1 y - 4 = -_ (x - 6) 2 1 b. y = -_ x+7 2 c. 11 d. x = 6, y = _ 2 28. y - 1 = -(x - 3) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 53–3 Saxon Algebra 1 Lesson Warm Up 54 54 e. Sample: The plot with the outlier represents the data better. There are no values between 3.8 and 8.1. A whisker makes it look like data are distributed throughout that range. Identifying an outlier shows that most of the data are less than 3. 1. outlier 2. $40.00 3. a. 184.93 b. 66.96 4. 6.2 7 1 _ or 1 5. _ 6 6 Lesson Practice 54 a. no outliers b. 476 and 557 State Test Scores 350 400 450 500 550 600 650 c. Number of Yards Run 0 10 20 30 40 50 60 70 80 90 d. 3.8 and 8.1 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 54–1 Saxon Algebra 1 Lesson Practice 54 54 11. B 1. x = 40 12. no outliers Planet Distance from the Sun (in millions of miles) 2. x = -30 3. x = 0 4. x - 5 5. 0 d4 3b4d 5 _ _ - 3 4 f °F -4 32 50 77 °C -20 b. 40 800 1200 1600 2000 2400 2800 13. 10% increase 6. 4 7. a. 400 0 10 25 °C 14. Sample: the mean value of 90; The median value (91) is not a part of the data set and there is more than one mode (86, 92, 94). 20 -10 10 °F 15. y = 115x + 467 16. x ≤ -6 5 c. _ 9 8. LE: 1; Q1: 2; median: 2.5; Q3: 3; UE: 5; IQR: 1 9. LE: 12; Q1: 18; median: 25; Q3: 27; UE: 30; IQR: 9 1 mm/mi 17. m = _ 2500 ( ) 18. a. false; Sample: A vehicle can be a standard truck. b. true 10. Sample: 62, 64, 70, 70, 71, 84, 85, 86, 86, 90, 95 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 54–2 Saxon Algebra 1 Lesson 19. Sample: The square root of a negative real number is undefined, whereas the square root of 1 is 1. 20. Sample: In the denominator, the 2g and the 6 cannot be separated and canceled. The GCF of the numerator and the denominator is 2. 54 27. 9x + 16 28. 16x + 10 29. a. J = 375g3 + 410g2 + 50g + 200 b. 675g3 + 810g2 + 250g + 225 30. 25x3 - 4x + 14 21. C 22. y = 500 - 25x; y 400 200 O x 2 4 6 8 23. -5 24. Sample: a horizontal line passing through (-1, 1) 3 27 x+_ 25. y = -_ 5 5 26. Student B; Student A didn’t combine like terms. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 54–3 Saxon Algebra 1 Lesson Warm Up 55 55 d. (4, 3) y = -3x + 15 y 4 (4, 3) 2 1. solution 2. n = 24 -4 -2 x 4 O -2 3. yes; Sample: Substituting the values for the variables makes the equation true. -4 y = 2x - 5 e. (8.4, -3.6) 2 x+2 4. y = -_ 3 Lesson Practice 55 a. Yes, (1, 3) is a solution to both equations. f. 3 weeks; $35 b. No, (3, 4) is not a solution of either equation. c. (2, -1) 4 y 2 x -4 O -2 -2 y=x-3 4 (2, -1) y = 2x - 5 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 55–1 Saxon Algebra 1 Lesson Practice 55 12. a. Sample: 620x = 272.8 1. d = 16 b. 44% 2. p = 2.9 3. b = c. Sample: Round 272.8 up to 300. Round 620 down to 600. 300 ÷ 600 = 0.5 = 50%. Therefore, 44% is a reasonable answer compared to the estimate of 50%. 1 _ 2 4. r = -2 5. 1 _ 2k 4 4 10t 6. _ 3 r 3 s 7. _ 9 4 2 13. 40m + 250 ≥ 500, where m is the number of miles walked p q r 8. a. Sample: Which beverage do you prefer to drink with your lunch? 14. a. 10,648 cubic inches b. 22 inches b. Sample: What is your favorite class? c. Sample: When would be the best time for the class to exercise? 5 5 ps z 7r -_ + 5rsz 9. _ 4 2 2 r 55 15. 2% greater 16. the mode value of 5; Sample: This represents half of the values that fall below the median (7). 17. a. y = 20x + 500 b. 660 p z 2 8 10. 16a b 18. C 1 11. _ 12 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 55–2 Saxon Algebra 1 Lesson 19. 2 y x -2 -1 O 2 4 29. a. Talk-A-Lot: y = 0.25x + 1.25 Save-N-Talk: y = 0.50x b. (5, 2.5); 20. s ≥ 13,468 13,465 55 13,470 f5 _ 21. f ≠ 0; 4 22. Student A; Sample: Student B found the sum of all the exponents of each monomial. c. Sample: Both phone companies will charge the same amount of $2.50 when 5 minutes are used. 23. 156 feet; 100 feet 3 24. 2n + 3n - 5 30. a. Fat Grams in Meat 25. LE: 2.32; Q 1: 2.75; median: 2.89; Q 3: 2.94; UE: 3.02; IQR: 0.19 0 26. 50% 2 3 4 5 6 7 8 9 10 b. The upper whisker is missing because the values of the whisker are contained in the upper quartile. 27. (8, 0) 28. C © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 1 LSN 55–3 Saxon Algebra 1 Lesson 56 Warm Up 56 1. 3 3 x+4 2. y = -_ 2 3 x 3. y = _ 5 4. {0, 3, 6} Lesson Practice 56 a. no b. yes, -3 c. no 1 d. yes, _ 3 e. yes f. no g. y = 8x i. Volume (cu. cm) h. 24 35 30 25 20 15 10 5 0 ; 2 4 6 Height (cm) 21.75 cubic centimeters © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 56–1 Saxon Algebra 1 Lesson 56 1 1 _ x 16. y = _ 4 2 Practice 56 1. x = 5 17. z ≤ 4.6 2. x = 3.5 18. 8 feet 6 1 _ w 3. p = -_ 5 5 19. Sample: 3, 7, 8, 9, 12, 12, 12 4. 315 = 3 · 3 · 5 · 7 20. 210 feet 5. 55% 1 (x - 2) 21. y - 8 = _ 2 6. 98 8. yes 22. Sample: the degree of the highest-degree term in the polynomial 9. yes 23. C 7. 90 10. -800x12y 24. 4 Average High Temperature in Phoenix, AZ 60 11. 13,860 customers 25. 2 12. a. π100x b. 400x π c. _ 80 90 100 110 ; Marathon Completion Times (min) 200 2 70 240 280 320 360 400 360 is an outlier. 13. Sample: The origin (0, 0) will always make the equation y = kx true. 26. Student A; Sample: Student B used the median instead of Q3 in the outlier formula. 14. D 27. 3 4 15. 5.84 euros © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 56–2 Saxon Algebra 1 Lesson 56 28. Student A; Sample: The solution of Student B is incorrect because it only satisfied one equation. 29. x + y + 81 = 180 2x + 2(5.5y) = 360; x = 81, y = 18 30. a. t = 2m + 3 t=m+5 b. Thomas is 7 years old and Miguel is 2 years old. c. Sample: If 5 years were taken away from Thomas’s age, the result would be 2 years, which is Miguel’s age. If 3 years were taken away from Thomas’s age, the result would be would be 4 years, which is equivalent to twice Miguel’s age. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 56–3 Saxon Algebra 1 Lesson 57 Warm Up 57 1. prime 2. 2 · 3 · 3 3. 2 · 5 · 11 4. 3(x + 9) 5. 2x(2x2 + 7) Lesson Practice 58 a. 336 b. 408 c. 30c5d7 d. 20n4k4p3 e. (3x + 5)(2x - 7) f. 21c(5c - 1) g. 72f 3(f 3 - 3)(1 - 3f ) h. 360 backpacks © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 57–1 Saxon Algebra 1 Lesson Practice 57 57 11. a. 2.16°F per hour 1. s = r - 4t b. -3°F per hour p + 7n c. 1.7°F per hour 2. m = _ 3 12. a. 3. a = 10.75 X 26 X 28 30 X X X X X X X X X X X 32 34 36 38 X X X X X X 40 42 X X X X 44 46 X 48 50 4. y = 30 b. It is a curve. 5. 60% decrease c. Sample: Most of the students could hop on one leg for 31 to 46 seconds. 6. 700% increase 7. Sample: The GCF uses the factors that appear in both numbers. The LCM uses all factors the greatest number of times they appear in either number. 8. 168 9. 12 10. 13. 50% 14. -9z3 - 8z2 + 10z 15. a. Sample: The domain is whole numbers and the range is rational numbers greater than or equal to 5.95. b. y = 0.04x + 5.95 y 1 ;k≠3 16. _ 7 6 (6, 5) 4 17. 2 ≤ n 2 -2 O x 2 4 -2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 18. m = 2w + 40; in 11 weeks LSN 57–2 Saxon Algebra 1 Lesson 19. Q3 + 1.5(IQR) = 165.5 + 1.5(36.5) = 220.25 and 221 > 220.25; Therefore, 221 is an outlier. 20. C 27. a. y = 62.4x, where x represents feet below surface and y represents pressure in pounds per square feet b. 21. a. y = 2x + 16 y = 3x + 14 b. 2 22. (0, 4) 24. 22.86 centimeters 25. Student B; Sample: Student A substituted 24 months instead of 24 years. 500 400 300 200 100 0 ; 2 4 6 8 about 560 pounds per square foot c. 20 23. no 57 c. 5 feet 28. Sample: The LCM is the least common denominator of the fractions. 29. C 30. 12x4y6 minutes 26. 58π feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 57–3 Saxon Algebra 1 Lesson 58 Warm Up 58 1. trinomial 2. 6x3y3 + 10x2y3 - 12x2y2 3. -3x4y3 + 12x2y2 + 21x2y3 4. 3x2 - 3x + 7 5. 6x3 - 13x2 - 15x + 25 Lesson Practice 58 a. 3x 3 + 9x 2 - 21x b. -4x3 - 8x2 + 12x c. x2 + 7x + 12 d. x2 - 7x + 10 e. x 2 + 10x + 24 f. x2 - 9x + 8 g. 2 x 3 - 4x2 - 10x - 4 h. 5x3 - 17x2 - 4x + 4 i. x3 + 10x2 + 22x - 12 in2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 58–1 Saxon Algebra 1 Lesson Practice 58 1. 2. -6 0 -4 2 -2 4 58 14. The angles in a parallelogram add up to 360 degrees, but it is not a rectangle. 0 6 15. a. 120 3. no solution b. 16 4. m = 9 16. no 5. D 17. 17 kilometers 3 2 6. 3x + 21x + 34x + 20 in2 18. Student A; Sample: Student B reversed the original x- and y-values in the equation. 7. x2 + x - 6 8. 4x2 - 9 9. No; Sample: He multiplied the exponents instead of adding. 10. 5x2 + 15x - 35 11. 2100 12. every 8 feet or 96 inches 13. Student B; Sample: Student A only used factors that both expressions had in common—the GCF. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 19. LE: 3, Q1: 14, median: 23, Q3: 38, UE: 62, IQR: 24 20. 75% 9 , x ≠ 0, 9 21. _ 4x 2x - 3 , x ≠ 4. 22. _ 7 23. It is undefined at v2 _ = 1 or when the c2 velocity equals the speed of light. LSN 58–2 Saxon Algebra 1 Lesson 1 1 _ 24. a. 5_ + n ≤ 10 2 2 1 and b. The sum of 5_ 2 half a number is no greater than 10. 25. St. Paul 26. Sample: x 0 2 3 4 y -5 -1 1 3 2 -4 -2 y O x 4 -2 58 30. 10 or fewer guests could come; Sample: A number line shows all the real number solutions for an inequality, and because the number of guests must be a natural number, the graph shows too many possible solutions. -4 The pairs of values that satisfy the equation are recorded in the table of values and form coordinates that are points on the line in the graph. 27. A = 1.417t2 + 3.575t + 253.091 1 x + 10; 11 28. y = - _ 8 29. 2; m ≠ 2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 58–3 Saxon Algebra 1 Lesson 59 Warm Up 59 1. solution 2. yes 35 3. _ 2 4. 12 Lesson Practice 59 a. (-2, -11) b. (-2, 3) c. (8, -10) d. (1, 5) e. Books cost $7, and pencils cost $0.10. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 59–1 Saxon Algebra 1 Lesson 14. 3x3 + x2 + 2x - 6 square feet Practice 59 1 1. k = _ 6 2. k = 15. 4x3 + 8x2 - 36x 2 -_ 3 16. y = 2x - 1 3. -8 17. 7 7 4. Sample: _ 4 18. 5. true 6. (4, 7) 0.5 0.6 0.7 20. C 21. 48c6 22. 60x3y3c 10. (39, 25) 11. Student A; Sample: Student B multiplied the exponents instead of adding them. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 0.4 19. Sample: $76.50 9. A b. 125x3 + 75x2 + 15x + 1 inches cubed 0.3 There are no outliers. 8. Sample: The point satisfies every equation in the system. 13. a. 25x2 + 10x + 1 Percentage of Games Won 0.2 7. (3, -3) 12. 4x2 + 40x + 64 square feet 59 23. LCM = 2 · 2 · 3 · 3 · 5 · 5 · d · d · d · d = 900d4 x-8 24. _ 8x + 3 25. m = -1 26. A bird is an animal that has wings, but it is not an insect. 27. a. 28π = 7πr 2 b. 2 inches LSN 59–2 Saxon Algebra 1 Lesson 59 28. slope: 2.34; y-intercept: 0; y = 2.34x 29. If a number is a rational number, then it is an integer; The number 0.5 is a rational number, but it is not an integer. 30. Sample: An excluded value is the value of the variable that makes the denominator equal 0. It is excluded because division by 0 is undefined. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 59–3 Saxon Algebra 1 Lesson 60 Warm Up 60 1. C 2. 6x2 - x - 15 3. 15x2 + 53x + 42 4. 9x3 - 9x2 + 23x - 14 Lesson Practice 60 a. x2 + 18x + 81 b. 9x2 + 30x + 25 c. x2 - 2x + 1 d. 64x2 - 96x + 36 e. x2 - 64 f. 9x2 - 4 g. 784 h. 3596 i. x2 - 36 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 60–1 Saxon Algebra 1 Lesson Practice 60 60 14. Student A; Sample: Student B did not distribute the 6 over the 19. 1. k2 + 2k + 2 2. 6m2 - 3m - 1 4. 6x3 + 16x2 + 13x + 10 15. $3 for each natural-light bulb, $4 for each ceiling bulb 5. 9t2 - 6t + 1 16. girl: 19; boy: 29 6. 9t2 + 6t + 1 17. The width is 2 centimeters and the length is 10 centimeters. 3. x2 - x - 20 7. (3x + 6)(3x + 6) = (3x + 6)2 = 9x2 + 36x + 36 square inches 18. Average Monthly Rainfall in Cloudcroft, NM (in inches) 8. (5, 1) 0 9. C 11. Sample: You can use the FOIL method to check your work. 12. false; (9x + 8)(9x + 8) = 81x2 + 144x + 64 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 2 3 4 5 6 7 6.04 and 6.10 are outliers. 10. (9,14) 13. The width is 9 feet. The length is 30 feet. 1 19. Sample: 6f 4 = 2 · 3 · f 4 and 4f 2 = 2 · 2 · f 2, so the LCM = 22 · 3 · f 4 = 12f 4. 20. A 21. yes 22. A = 8x 2 + 110x + 375 sq. ft LSN 60–2 Saxon Algebra 1 ; Lesson 60 23. The slope is undefined. 24. x2 + 11x + 18 25. Sample: The difference of a number and 2.5 is greater than 4.7. 26. 2t < 79, where t is the number of José’s cards, so José could have 39 cards. 27. a. 12%, 9% b. 20% 28. Sample: The graph should only include non-negative numbers, because negative speed means moving backward and this cannot happen when driving legally on a road. 29. 2 yards 30. m = 1; b = -4; Sample: Using the slope-intercept equation of a line, the slope is the coefficient of x and the y-intercept is the number added to or subtracted from x. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 60–3 Saxon Algebra 1 Lesson 61 Warm Up 61 1. square root 2. 6 3. 9 1 4. _ 2 5. 7 and 8 Lesson Practice 61 3 a. 5 √ 7 b. 3 √ 3 c. 11 √ d. 1000 10 e. 3bc2 √ f. 5xy3 √xy 5m g. 4 √ © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 61–1 Saxon Algebra 1 Lesson Practice 61 3 1. 2 √ 61 15. 40 cars; 65 SUVs 16. a. 5 b. 2 2. 10 √ 8 4 3. not real -8 -4 O y (2, 8) (1, 3) x 4 8 -4 4. 7 5. First, Outer, Inner, Last c. y - 3 = 5(x - 1) or y - 8 = 5(x - 2) 6. 288 feet d. y = 5x - 2 1 e. x = -_ , y = -12 7. Student A; Sample: Student B squared -8 instead of 8. 5 17. 3.75 pounds 8. C 18. C 9. (-3, -1) 10. (9, 5) 11. about 27.5 ft 19. Sample: I can write the radicand using prime factorization: √ 2 · 32 · a2 . Then, 12. a. 6482 because squares and square roots are inverses, 3 and a can be removed from under the radical sign which leaves 3a √ 2. b. Sample: The outlier raises the mean attendance value to 7171. 13. 16b2 - 24b + 9 14. 4x2 - 20x + 25 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. x2 - 16 square inches 20. _ 2 21. 3x2 - 5x - 4 LSN 61–2 Saxon Algebra 1 Lesson 61 22. 3003 23. 96 24. a. 9 b. x2 c. 9 - x2 25. (8x - 16)2 = 64x2 256x + 256 square inches 26. a. A _ √ π cm 20 cm = 2 √5 b. √ 27. Sample: The quotient of an unknown and 7 plus 3 is greater than or equal to 5. 28. Sample: The product of an unknown and 3 minus 4 is less than -2. 29. 30 cm/s 30. Shoe Sizes 5 6 7 8 9 10 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 61–3 Saxon Algebra 1 Lesson Warm Up 62 e. 62 Low Temperatures in New Orleans First 15 Days of April 2007 10 Frequency 1. A 2. 5; 5; 5; 6 3. 15; 14.5; no mode; 8 8 6 4 2 40 50 60 70 80 Temperature (°F) Lesson Practice 62 a. Low Temperatures (°F) April 2007 for New Orleans, LA Stem 4 5 6 7 Leaves 2, 3 0, 1, 2, 2, 4, 6 0, 0, 1, 3, 5, 9 0 Key: 5 6 = 56°F b. Low Temperatures in New Orleans First 15 Days of April 2007 Frequency 10 8 6 4 2 40 50 60 70 80 Temperature (°F) c. median: 60; mode: 59, 63, 64, 68; range = 26° −− − 2 ; 0. 13 ; 13. 3% d. _ 15 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 62–1 Saxon Algebra 1 Lesson 62 13. b2 - 16b + 64 Practice 62 1. 40 years 3 1 x+_ 14. x2 + _ 4 8 2. 34 years 15. $57 million decrease; 62% 3. 39 years 16. 59.66 inches 4. 10% 17. (0, 6) 22 5. 2 √ y 5 6. 12 √ (0, 6) 4 7. 6 √5 2 8. Sample: Graph the point (0, 2) for the y-intercept. Then graph the point that is one unit down and 3 units to the right of that, or (3, 1), and draw a line between the two points. -4 -2 x O 4 18. Sample: the upper and lower quartiles of the data 19. 9. Student A; Sample: Student B used the wrong pattern to find the product. Money Raised in Homerooms Stem 10 11 12 13 14 15 Leaves 6, 8 5, 9 4, 5 4, 9 0, 7 Key: 10 5 means $105 10. Sample: 3x - 2y = 0 11. C 12. -4x2 - 16x + 4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 62–2 Saxon Algebra 1 Lesson 62 20. $1100 y 1200 (50, 1100) 800 400 O x 20 40 60 21. 3 22. 4 23. y = -9x 24. a. 1100 + 1600r + 500r2 b. $1148.45 25. $87.72 26. $116.00 27. after 8rs(r - s) days 28. D 29. (9x - 20)2 = 81x2 360x + 400 square inches 30. Sample: (0, 0), (0, 5), (5, 0), and (5, 5) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 62–3 Saxon Algebra 1 Lesson 63 Warm Up 63 1. linear 2. (12x - 15) 3. 28y + 48 6 7 4. k y 5. -3xy + 2xy 2 Lesson Practice 63 a. (-1, -1); See student work. b. (3, -2) c. (7, 4) d. (-4, 2) e. 180 adult tickets © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 63–1 Saxon Algebra 1 Lesson Practice 63 16. C 17. Sample: Substitute the values of the variables back into the original equations to ensure that they make both of the original equations true. 1. 16 2. 6 √3 3. 7 √6 2 e _ 4. 8 8 2 5. 63 g r t 1 _ 5 7 3 2 b f n s st -_ 6 2 18. a. Deer Antler Points at 4.5 Years b fn 6. 1350 0 1 2 3 4 5 6 7 8 9 10 7. yes b. no; Sample: There is a wide range on this graph. 4 4 8 8. 30s t v 7 5 9. 28ds v 19. 200 m 10. A 11. in 12 years 2 20. A = 3x + 45x + 150 square feet 12. (2, 0) 21. $946.74 13. (3, 1) 22. $26,105.80 14. (-1, 3) 23. $32.29 y (-1, 3) -2 O x 2 4 -2 -4 ⎡(a + b) 2 = a 2 + 2ab + b 2⎤ 24. ⎢ 2 2 2 ⎣(a - b) = a - 2ab + b ⎦ 25. 4x2 + 24x + 36 square feet 26. A 15. 10x - 12 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 63–2 Saxon Algebra 1 Lesson 63 27. Student A; Sample: Student B found the stem with the most data points, 17 or 170. 28. Sample: The second equation is the first equation multiplied by 3 -_ , so the equations 2 would be the same line on a graph. There are an infinite number of solutions. 29. The absolute value of that coefficient would be greater than 1. 30. 45% © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 63–3 Saxon Algebra 1 Lesson Warm Up 64 64 c. x = 7 4 d. y = _ x 1. inverse operation y 2. 7 2 3. -3 -2 O x 2 -2 4. Sample: y = 3x 5. Sample: y = -0.5x e. 5.6 hours Lesson Practice 64 a. This is not an inverse variation; Sample: The equation solved for y is x . This equation y=_ 4 does not match the inverse variation equation y = _kx . b. This is an inverse variation; Sample: The equation solved for y 3 is y = _ x . This equation matches the inverse variation equation y = _kx . © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 64–1 Saxon Algebra 1 Lesson Practice 64 1. 24m5n4 1 2 6 2. _ w x 2 3. no 4. yes 5. The value of y would be close to 50. 6. 1 and 20 7. $40; $0.05 8. b2 + 4b + 4 64 13. Sample: The mean value for waste generated is 192.125 million tons, and the mean value of materials recovered is 45.25. On average, the United States generates about 150 million tons of waste a year after recycling. 4 14. _ a centimeters 15. $32,000 16. $23,000 2 9. x - 6x - 16 a 10. a. √ 121 cm2 b. √ c. 11 cm 17. $47,000 18. about 9% 19. no outliers Weights d. cm 100 11. 1.5 hours; 11 miles 12. C 120 140 160 180 200 20. contrapositive; The original statement and the contrapositive are false. 6 21. 2 √ © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 64–2 Saxon Algebra 1 Lesson 5 3 1 √ _ _ 22. _ and 15 ; 5 3 3 Sample: The two ways depend upon whether the fraction under the radical is simplified. √ 23. Student B; Sample: Student A subtracted to eliminate the variable x, but then added the other terms in the equation. 24. Rectangle A is 12 square units. Rectangle B is 27 square units. 25. 8 y x -8 -4 4 8 64 c. 2(6) - (-2) = 14 12 + 2 = 14 14 = 14 (6) + 4(-2) = -2 6 - 8 = -2 -2 = -2 28. 90 mm3 29. Sample: The number of points varies directly with the number of touchdowns. 30. Sample: When k is positive, the graph is in Quadrants I and III; when k is negative, the graph is in Quadrants II and IV. -8 26. (-2, -6) 27. a. y 8 4 -8 -4 x O -4 (6, -2) 8 -8 b. (6, -2) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 64–3 Saxon Algebra 1 Lesson 65 Warm Up 65 1. point-slope 2. -2, -5 3. 3, 4 2 x-5 4. y = _ 3 Lesson Practice 65 a. no; The lines are perpendicular. 5 4 _ x + 3 b. y = _ 7 7 c. no; The lines are parallel. 1 7 x + 1_ d. y = -_ 4 4 e. Sample: The slope of −− 1 AB is -_ , the slope of 2 −− 1 BC is 2, and - _ (2) = 2 −− −− -1. AB ⊥ BC. Therefore, ABC is a right triangle. ( ) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 65–1 Saxon Algebra 1 Lesson Practice 65 11. Student A; Sample: Student B wrote a direct variation equation. 10 1. 6 √ 2. 6 √7 12. no; Sample: He needs 84 centimeters of wood for the twelve 7-centimeter pieces, and he only has 80 centimeters of wood leftover. 3. 8 √6 4. x4 + 10x2 + 25 5. x2 - 11x + 18 6. -7 -5 -3 -1 13. (1, -1); 7. Sample: Treat the (x - 5) like a single variable. Then, take each factor the greatest number of times it appears. LCM = 2 · 3 · (x - 5)7 = 6(x - 5)7 14. (-3, 8) 8. B 15. (2, -6) 9. 16. 6 weeks 2007 NCAA Division II Final Results Men’s 50M Freestyle Stem 203 204 206 208 209 210 212 213 214 215 65 Leaves 2, 6, 9 3 2, 7, 8, 8 1 7 7 4, 5 1 5 6 Key: 201 7 = 20.17 seconds y 2 -4 -2 O -2 x 2 4 (1, -1) 17. a. Sample: The range of the data is 221.25. To make it easier, I would create 5 intervals that are each 50 points apart. 10. y = 4x + 22; $50 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 65–2 Saxon Algebra 1 Lesson b. 2007 NCAA Division II Championship Women’s 3-Meter Diving Results 8 6 4 2 250 300 350 400 450 500 Points c. Sample: A histogram is better. The data is so dispersed across a wide range that a stem-and-leaf plot would not be very useful. 18. y = -2x + 6 19. (x - 11)(x - 11) = x2 - 22x + 121 dollars 65 23. yes; Sample: Choose two points along each line and find the midpoint between the corresponding points on each line. Use this point and the slope of lines a and b to create the line of reflection. 24. There are an infinite number of parallel lines for any given slope. 25. The slope of the parallel line is -2. 26. a. 20. (7x - 24)2 = 49x2 - 336x + 576 square feet 4 (-4, 0) -4 -2 y (4, 2) 2 O x 2 4 -2 -4 21. WXYZ is a parallelogram. The −−− −− slopes of WX and YZ are both undefined, so −−− −− WX_ || YZ. The slopes _ of WZ and XY are the −−− −− 3 same, _ , so WZ || XY. 5 1 b. y = _ x+1 4 c. no; Sample: The first 1 line has a slope of _ 4 and the second line 1 has a slope of -_ . 4 They are not parallel. 22. yes © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 65–3 Saxon Algebra 1 Lesson 65 27. Student B; Sample: Student A tried to add the equations without aligning like terms first. 28. 13.5 meters 29. 36 cm2 30. 10 minutes © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 65–4 Saxon Algebra 1 Lesson 66 Warm Up 66 1. inequality 2. 8 3. 17 4. 5. -2 0 2 -4 -2 0 2 Lesson Practice 66 1 ; a. x > 3_ 2 0 1 2 3 4 5 6 1 b. z ≥ 2 _ ; 2 -1 0 1 2 3 4 c. y ≤ 2.1; 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 d. She intends to crochet at least 1.9 feet more; x + 2.5 ≥ 4.4; x ≥ 1.9 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 66–1 Saxon Algebra 1 Lesson Practice 66 11. a. M = 1164.16t + 75,622.43 2p 1. _ 4 s b. M = 145,472.03 -x 2. _ 4 12. A 5w 12y 3. _ 4 13. Sample: y = 3 - x is a line of symmetry for the figure. y = 3 - x has a slope of -1 and is −− perpendicular to AB and −− EF, which each have a slope of 1. 3x + 1 4. z ≥ -7 5. x ≤ 13 6. 66 1 2 3 7. The inequality x > 5 does not include 5. The inequality x ≥ 5 does include 5. When graphing x > 5 starts with an open circle and x ≥ 5 starts with a closed circle. 14. a. 336 students b. 3 students 15. (58, 6) 10 m/s 16. 2 √ 17. A 8. f(x) = x + 3 9. 0 4 8 12 16 20 24 Sample: The graph would only include non negative numbers because there cannot be a negative time. 10. 3 millimeters © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 66–2 Saxon Algebra 1 Lesson 18. Sample: First I would multiply the first equation by 3, and then I would multiply the second equation by 2. Then I would subtract the second equation from the first, eliminating the variable x. After solving for y, I would substitute the y-value into one of the original equations to solve for x. 19. EFHG is a trapezoid because it has one pair −− of parallel sides. EF || −−− GH because they have the equal slopes of 0. −− −− EG and FH are not parallel because they have different slopes. 20. Student B; Sample: Student A did not write down the product rule correctly. 21. y = 6x 80 22. y = _ x © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 66 23. 4x2 - 12x + 9 24. t2 - 144 25. y6 - 8y3 + 16 26. Distributive Property: (2y + 4)(3y + 5) (2y)(3y + 5) = 6y2 + 10y (4)(3y + 5) = 12y + 20 6y2 + 22y + 20 FOIL method: (2y + 4)(3y + 5) 6y2 + 10y + 12y + 20 6y2 + 22y + 20 1,000,000,000 ; 27. y = _ x 4.2 years 1 −− _ 28. m−− PQ = -2, mPR = 2 , 1 = -1; and (-2) _ 2 −− −− PQ ⊥ PR. Therefore, PQR is a right triangle. ( ) 29. false; Sample: The lines are perpendicular because their slopes are negative reciprocals: 1 _ , -3. 3 30. x - 25 ≥ 5; x ≥ 30 miles LSN 66–3 Saxon Algebra 1 Lesson 67 Warm Up 67 1. system 2. 4, -7 3. 3, -9 4. -5 5. 4 Lesson Practice 67 a. no solution b. infinitely many solutions—any ordered pair (x, y) that satifies the equation y = -x + 10. c. consistent and dependent d. (-1_23 , -_13 ); consistent and independent e. 4 service calls; Both plans cost $88 at 4 service calls. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 67–1 Saxon Algebra 1 Lesson Practice 67 2 1. 4b -12b + 9 6 3 2. b - 10b + 25 3. 5x 13. Student B; Sample: You need to subtract 2 from each side to eliminate 2 from the left side. 14. 2 67 Ages of Players on Eastern Conference Team for NBA 2007 All-Star Game 5 4 3 3 4. 12x √y 2 1 4x 5. _ 2 20 y 24 28 32 36 Age (years) 6. y = 3x + 9; 27 pages 15. a. 4x2 + 8x + 4 in2 b. 8x 3 + 24x 2 + 24x + 8 in3 7. z ≥ 13 8. z < 3 9. 324 cards and 356 cards 10. 308 minutes 11. a. Deposits Received 0 10 20 30 40 50 60 70 80 90 100 b. LE: 25, Q1: 60, median: 75, Q3: 80, UE: 100 12. inverse; The original statement is true, but the inverse is false. 16. Sample: 5(20) - 2(15) = 100 - 30 = 70, and 3(20) + 4(15) = 60 + 60 = 120. 17. y = 1 and x = 3 are both lines of symmetry; y = 1 is −−− perpendicular to DG −− and EF, and x = 3 _ is perpendicular to DE −− and GF. 18. $400,000 19. inconsistent 20. parallel © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 67–2 Saxon Algebra 1 Lesson 67 21. (-1, 5) 22. (2, -3) 23. D 24. no; Sample: The value of x can never equal 0 because that would mean the product of x and y would equal 0. 1 25. _ 18 26. x < 8 27. a. x - 25,000 < 55 + 48 + 72 b. x < 25,175 c. x > 25,000 28. Student B; Sample: Student A did not classify the graph correctly. Parallel lines have no common solutions. 29. neither; Sample: These equations form a set of consistent and dependent equations. 30. (_54 , 3) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 67–3 Saxon Algebra 1 Lesson 68 Warm Up 68 1. independent events 1 2. _ 2 1 3. _ 3 5 4. _ 6 5 5. _ 12 Lesson Practice 68 1 a. _ 9 3 27 _ = b. _ 4 36 15 c. _ 32 d. about 122 people © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 68–1 Saxon Algebra 1 Lesson 68 16. A = 2x2 + 17x + 30 square feet Practice 68 1. 9 17. boy: 5 years old; girl: 13 years old 2. 8 3. 7 8. x > 0.1 18. false; Sample: (x + 2) 2 (x + 2) = (x) 2 + 2 = x2 + 4 Check work by using the FOIL method: (x + 2)(x + 2) = x 2 + 2x + 2x + 4 = x 2 + 4x + 4 ≠ x2 + 4 9. x ≤ 9.9 19. 14 chairs; 6 tables 1 1 _ 4. _ 4 3 √ 5. 2 _ 5x 2 6. yes 7. no 2 10. _ 9 20. Student B; Sample: Student A did not correctly substitute the values of x and y from the known pair. 11. 0 50 + 30 2 _ ; 12. _ 75 + 50 + 75 5 13. y = .10x + 50; $60 21. a. y (-2, 5) 4 1 A - 8; -7°F 14. B = - _ 4 15. a. 4 y -2 -2 2 -4 -2 O O (0,-4) x 2 (0,1) 2 x 4 6 (5,-2) 4 (-2, -4) 2 b. Line 1: y = _ x - 4; 5 Line 2: y = -2x + 1 -4 b. (-2, -4) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 68–2 Saxon Algebra 1 Lesson c. no; Sample: The slopes of line 1 and line 2 are not negative reciprocals. 68 d. no; Sample: There is no whole-number solution common to both equations. 22. x - 2 < 14.99; x < 16.99 26. consistent and independent 23. Student A; Sample: The solution of the equation is x ≤ -3. 27. about 22 24. (12, 12) 29. 55% 25. a. 3 30. The probability is higher if A and B are mutually exclusive. 28. D b. consistent and independent c. Systems of equations that are consistent and independent have a common solution. However, because that solution is a decimal number, and there can only be a whole number of stations, there is not a point where the plans cost the same amount. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 68–3 Saxon Algebra 1 Lesson 69 Warm Up 69 1. like terms 2. 11s - 3t 3. 9m - 8wv 2 4. 6 √ 2 5. 5 √ Lesson Practice 69 a. 17 √5 ab b. -12 √ 7 + 3 √ 2 c. 5 √ 4 √ 2x d. _ 5 3 - 8c √ 2 e. 4c √ 10a f. 8 √ 3 + 2 √ 15 meters g. 6 √ 3 feet h. 16a √ © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 69–1 Saxon Algebra 1 Lesson Practice 69 b. 69 y Miles 300 1. 2 √2 200 100 7 2. -9 √ 0 3. 7 √3 x 2 4 6 8 Inches on Map 10 4. 1 c. approximately 103 miles 5. 2 12. 13 bananas, 22 apples 6. 2 13. a. x2 1 7. _ 18 b. (x + 10)(x + 10) 8. 1 c. x2 + 20x + 100 d. x2 + 20x + 100 - x2 = 20x + 100 square feet 2 9. -7.3t + 12.7t + 7.4 meters 10. 18 is an outlier. Hours a Candle Burns 2 4 6 8 10 12 14 16 18 11. a. y = 15.8x, where x represents inches on a map and y represents miles. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 14. The square root usually indicates the positive, or principal square root. If a negative number is under the radical sign and is squared, the simplified answer will be the opposite of that value. For example: √ -4 · √ -4 = √ -4 · -4 = √ 16 = 4 LSN 69–2 Saxon Algebra 1 Lesson 12 25. a. _ 59 15. (0, 1) 16. $60 14 b. _ 59 17. perpendicular 26 c. _ 59 18. x ≥ 90 19. -7 -5 69 -3 5 26. _ 8 -1 0 1 Sample: Together they include all real numbers but have no solutions in common. 20. B 21. Any ordered pair (x, y) that satisfies the 1 x - 2. equation y = _ 4 27. true; Sample: If n is an even number greater than or equal to 2, the radical will be eliminated. If n is an odd number greater than 2, an x will remain under the radical. 28. Student B; Sample: The radicals have different radicands and the radicands cannot be further simplified. Therefore, the radicals cannot combine. 22. Student A; Sample: Student B did not interpret the solution correctly. 23. Sample: The equations are dependent, so the truck is on schedule. 29. Sample: 34 30. 110 in. 24. Student A; Sample: Student B multiplied the individual probabilities instead of adding them. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 69–3 Saxon Algebra 1 Lesson 70 Warm Up 70 1. solution 2. x = -7 3. x = 13 4. -4 -2 0 5. 2 4 6 2 Lesson Practice 70 a. n < 6; -2 0 2 4 6 ; See student work. b. x > -32; -32 -30 -28 See student work. 1 ; c. w ≤ 9_ 2 6 7 8 9 10 See student work. 1 ≤ a; d. - _ 8 1 0 _ 1 _ 2 _ 3 _ 4 _ 5 _ 6 _ 7 1 _ 8 8 8 8 8 8 8 8 See student work. e. $18,750 or more © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 70–1 Saxon Algebra 1 Lesson Practice 70 70 12. (1, -3) 7 1. _ 12 13. a. 90 3 2. _ 4 b. 2 1 4. y < 2_ 2 14. (8x + 18)2 = 64x2 + 288x + 324 square feet 1 5. y < -1 _ 4 +5 15. √5 3y 6. 26 √ 16. a. 3. 0 Customers Served Per Day Stem 8 9 10 11 12 13 14 3x 7. 3 √ 81 8. y = _ x Leaves 0, 0, 2, 3, 5, 6, 6, 6 0, 1, 5 1, 5, 9 4 7, 7, 7 5, 6, 7 0, 1, 1, 6, 8, 8, 8, 8, 9 9. yes; a ≤ 2.5 b. Sample: The data is not distributed evenly; it is clustered at the upper and lower extremes. This means the diner is usually extremely busy or relatively slow. 10. a. 22 b. c. Sample: about 50 points; Excluding the outlier, both the mean and median of the scores are 50 points. 11. 17. (4, 4) 18. about 32 meters Ages at a Family Party 0 10 20 30 40 50 60 70 80 90 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 70–2 Saxon Algebra 1 Lesson 3 3 _ _ 19. mAB = 2 , = 2 , mCD 28. Multiply both sides by 5 and reverse the -_ 2 inequality sign. . mAD CD and AB 2 2 , m = -_ , = -_ 3 BC 3 , and BC AD ⊥ BC ⊥ AD ⊥ CD AB . Therefore, ABCD ⊥ AB is a rectangle. 20. A 70 29. 4s ≤ 100; s ≤ 25; The solutions are between 0 and 25 and are rational numbers to the hundredths place. 1 b ≤ 20; at most 30. _ 3 60 burgers 21. Sample: The system is consistent and dependent because both equations are the graph of the same line. 22. Student B; Sample: Student A treated the events as being mutually exclusive. 100 25 =_ 23. _ 172 43 24. 24 meters 25. The absolute value of that coefficient would be between 0 and 1. 26. 352 ft 27. A © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 70–3 Saxon Algebra 1 1 x-2 3. y = _ 2 Year l. 1.5 million Lesson Practice 71 80 2 0 3 x-4 4. y = _ 8 a. 4 2000 2. -2 6 1980 1. slope-intercept 71 8 1960 k. 1940 Warm Up 71 Population (in millions) Lesson m. y = -.111x + 223.782 n. 0.5 million y 60 40 20 O x 2 4 6 b. Sample: y = 14x c. y = 1.486x + 10.048 d. negative correlation e. positive correlation f. negative correlation g. no correlation h. Graph 2 i. Graph 1 j. Graph 3 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 71–1 Saxon Algebra 1 Practice 71 1. 12. a. y 30 20 71 120 100 80 60 1990 1994 1998 2002 2006 Year 10 O Voters (in millions) Lesson x 2 4 6 b. no; Sample: The data appear to show no correlation. 2. yes 3. yes 5 4. 18 √ 3 5. √ 13. Sample: As one set of data values increases, the other set of data values decreases. 7. Any ordered pair (x, y) that satisfies the 1 x+2 equation y = _ 6 14. Student A; Sample: The square root of 4 is 2. Student B did not correctly calculate the square root of 4. 22 8. y = _ x 3 miles 15. 4 √ 84 9. y = _ x 16. B 6. no solution 10. Student B; Sample: Student A divided the left side by 0.2 instead of -0.2. 11. B © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 17. probability = 1; Sample: A probability of 1 means that the outcome is certain to happen. Since heads and tails are the only outcomes and are mutually exclusive, the coin is certain to land on either heads or tails. LSN 71–2 Saxon Algebra 1 Lesson 18. x + 15 + 15 + 5 ≥ 40; x≥5 71 25. negative correlation 5 21. no; b < _ 11 26. no; Sample: A histogram does not show exact values, but rather how the values are distributed within intervals. It would not be possible to determine exact values and find the mode given only a histogram. 22. 3s ≤ 36; 12 in. or less 27. 4πs 23. a. 0.02s ≥ 250,000 28. a. y = 921x + 200,770 y = 2419x + 183,106 19. perpendicular 20. 38 y 34 30 26 0 x 40 50 60 70 80 b. s ≥ 12,500,000 b. 2016 c. at least $12,500,000 24. Sample: If one variable had the same coefficient in each equation, I would eliminate that variable. If one of the coefficients of a variable in one equation is a multiple of a coefficient of the same variable in the other equation, I would multiply to eliminate that variable. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 29. y = 7x 2 30. a. 10x + 12x + 2 inches squared LSN 71–3 3 2 b. 60x + 112x + 60x + 8 inches cubed Saxon Algebra 1 Lesson 72 Warm Up 72 1. binomial 2. 10x2 - 14x - 12 3. 25x2 - 60x + 36 4. x3 + x2 + 3x + 3 Lesson Practice 72 a. (x + 1)(x + 2) b. (x - 2)(x - 8) c. (x - 2)(x + 6) d. (x - 9)(x + 4) e. (x + 4y)(x + 5y) f. (x - 4y)(x + 3y) g. (x + 2)(x + 10) h. (x - 4)(x + 11) i. x 2 + x - 6 = (x + 3)(x - 2); 4 2 + 4 - 6 = 14; (4 + 3)(4 - 2) = (7)(2) = 14 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 72–1 Saxon Algebra 1 Lesson Practice 72 72 1 3. _ 3 14. a. 1. x > 1; -2 0 2 4 6 4. (x + 3)(x + 8) 5. (k + 5)(k - 8) Circumference (in.) 2. 1 13. Student B; Sample: A trend line on a scatter plot does not have to contain any data points. It is used to indicate a trend in the data. 30 20 10 0 2 4 6 8 10 Diameter (in.) 6. (m + 4)(m + 5) b. Sample: y = 3.1x + 0.2 7. (x + 3)(x + 11) c. Sample: The equation is close to the formula since the slope of the line is approximately π and the y-intercept is very close to zero. 8. Student A; Sample: Student B incorrectly factored -6 and then subtracted the values rather than adding them to obtain b. 9. 17 × 20 15. a. Sample: 65 10. 9 b. Sample: 13 11. the term -1x 12. y 30 20 10 O x 10 20 30 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 72–2 Saxon Algebra 1 Lesson 16. yes; Sample: Since the products of two negative numbers is a positive number, the square root of a perfect square can be negative. An example is -7 · -7 = 49. 17. yes; Sample: The equations for the flight path and runway form a set of consistent and dependent equations. The airplane is on the same path as the runway. 18. Each system of paired equations will be consistent and independent. 20. 72 Length Width Area 1 100 100 2 50 100 4 25 100 5 20 100 10 10 100 20 5 100 25 4 100 50 2 100 100 1 100 21. 14 quarters 22. (5x - 9)(3x + 8) 23. A 24. 19 min 25. 22, 14; 308 26. y = x 27. 175 meters 19. parallel 1 28. a < -_ 2 29. p < 3 30. 0.20x ≤ 35,000; $175,000 or less © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 72–3 Saxon Algebra 1 Lesson Warm Up 73 73 h. 8 ≤ x < 12 or x ≥ 8 AND x < 12 1. inequality 2. x < -7 3. x ≥ -2 4. x ≤ -5 5. x ≥ -12 Lesson Practice 73 a. x > 5 AND x < 10 or 5 < x < 10; 4 6 8 10 12 b. 16 ≤ t ≤ 20; 16 18 20 22 c. 40 ≤ 20 + 0.05x ≤ 50; 400 ≤ x ≤ 600 d. x < 1 OR x > 6; 0 2 4 6 8 10 e. x ≤ 0 OR x ≥ 5; -2 0 2 4 6 8 f. x < -3 OR x > -1 g. x ≤ 1 OR x > 2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 73–1 Saxon Algebra 1 Lesson 3 xy 13. 2x √ Practice 73 14. (x + 9) and (x + 3) 1. consistent and independent 15. (x - 1)(x + 4) 2. inconsistent 16. B 3. x ≤ 7 17. Sample: y = 0.375x + 5.5 5. -11 ≤ x ≤ -8 6. x < -7 OR x ≥ 7 -6 -4 -2 0 2 4 6 8. x ≤ 1 OR x ≥ 6 9. A 10. x < 0 OR x > 120 11. Sample: Use AND when you are looking for the intersection of two inequalities or where two graphs overlap. Use OR when you are looking for the union of two inequalities or all numbers where two graphs are shaded. 12. (x - 4)(x - 8) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 18. Student B; Sample: If the data are rearranged so that one set of data values are in ascending order, the corresponding data values in the other set also increase. A scatter plot of the data shows a positive correlation even though the data values are not in increasing order. 19. 20 Atomic Weight 4. z ≥ -3.5 7. 73 16 12 8 4 0 2 4 6 8 Atomic Number 10 20. B LSN 73–2 Saxon Algebra 1 Lesson 73 27. (x - 3)(x + 3); x2 - 9 square units 21. Sample: In both cases, divide by -2 to solve. For the inequality, the direction of the inequality needs to be switched because you are dividing by a negative number. 3 2 28. x + 4x + 6x + 4 29. 30(4r - d) 9 30. 266b n books 13 22. _ 20 13 23. _ 20 24. a. 4 y 2 x -4 -2 2 -2 -4 b. line 1: y = x + 6; line 2: y = -x c. yes; Sample: The slopes of line 1 and line 2 have a product of -1. 25. 60 cm 26. There are 0.4 cubic centimeters of gold and 0.3 cubic centimeters of nickel. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 73–3 Saxon Algebra 1 Lesson 74 Warm Up 74 1. absolute value 2 2. - _ 5 3. 2 1 4. _ 2 9 5. _ 5 Lesson Practice 74 a. {11, -11} b. {3, -9} c. {6, -6} d. {7, -1} e. {5} f. Ø g. ⎪x - 30⎥ = 0.4; 29.6 lb, 30.4 lb © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 74–1 Saxon Algebra 1 Lesson Practice 74 74 11. a. Sample: ⎢D - 10 5 =_ π or π ⎢D - 10 =5 1. (x - 2)(x + 14) 2. (x + 5)(x + 10) b. 11.6 cm, 8.4 cm 3. (x + 2)(x + 9) 12. 4. (x - 3)(x + 6) 13. x < 2 OR x > 5 5. {13, -13} 14. Student B; Sample: Student A incorrectly isolated the absolutevalue term as z; the term should be z + 3. 6. {-4, -10} 7. y = _3 x - 2 2 8. ⎪h - 12⎥ = 2; 14 in., 10 in. b. 5 units ⎪x 3⎥ = 5 0 2 4 6 8 10 -12 -6 0 6 12 18 18. a. (x + 4)(x + 5) and (x + 1)(x + 20) x = 8 units -2 4 17. (x - 8) (x + 5) -3 -4 2 16. a. x > 15 OR x ≤ -12 10. {-2, 8} -6 0 15. 5 < x < 17 9. Sample: When the equation is evaluated at -3, the term on the right side of the equation has a value of -9. Such a solution would indicate that the absolute value of ⎢-3 - 6 is negative, which is not possible. x = -2 units -2 6 b. the second set; Sample: The dimensions of the rectangles described by this trinomial are much longer than they are wide. 5 units ⎪x 3⎥ = 5 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 74–2 Saxon Algebra 1 Lesson 19. A c. Sample: The book will not fit because one side of the container’s dimension is less than the book’s dimensions. 20. yes; c ≥ -9 21. 48 in. 3 22. _ 4 23. a. $2.55 b. $7.55 c. consistent and independent 74 29. (4, 1) 30. 6x3 + 54x2 + 54x + 48 24. _xy will always be greater a _x will than _ because y b always have a larger numerator and smaller a denominator than _ . b 25. y ≈ 7.9 26. true; Sample: The lines are parallel because they have the same 1 and different slope of _ 4 y-intercepts. 27. 60 people cm 28. a. 20 √2 cm < 30 cm; b. 20 √2 cm > 25 cm 20 √2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 74–3 Saxon Algebra 1 Lesson 75 Warm Up 75 1. trinomial 2. (x + 5)(x - 2) 3. (x + 6)(x - 7) 4. 12x2 + 7x - 10 5. 4x2 + 20x + 25 Lesson Practice 75 a. (9x + 2)(x + 4) b. (5x - 4)(2x - 3) c. (3x - 1)(x + 2) d. (2x + 1)(3x - 4) e. (3x + 4y)(2x + y) f. (2x - 1)(7x - 3) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 75–1 Saxon Algebra 1 Lesson 75 10. a line Practice 75 1. (3x + 2)(2x + 3) 11. {5, -5} 2. (3x + 1)(x - 5) 12. a. Sample: ⎢x - 36 = 4(1.5) 3. (2x - 3)(x - 6) b. {42 in., 30 in.} 4. (2x - 3)(x + 5) 13. a. ⎢x + 2 = 11 de 5. (22c - 9) √ b. x + 2 = 11, x + 2 = -11 + 3 √ 11 6. 5 √7 7. Sample: Because the coefficient of the squared term is not 1, b is found by adding the product of factors of c and factors of a. 8. Sample: (7x - 10)(x - 1) = 7x2 - 17x + 10, (7x - 1)(x - 10) = 7x2 - 71x + 10, (7x - 5)(x - 2) = 7x2 - 19x + 10, and (7x - 2)(x - 5) = 7x2 - 37x + 10. These are all the possibilities and none are correct. c. {9, -13} 14. ⎢x - L = 0.0012L 15. 5 ≤ x ≤ 8 16. Student A; Sample: If you substitute 0 into the equation, it is a solution. Therefore, the points between the endpoints should be shaded since 0 is a solution. 17. 65 ≤ x ≤ 88; x ≥ 65 AND x ≤ 88 18. D 9. C © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 75–2 Saxon Algebra 1 Lesson 19. Since 2 < 3, 2 is a solution of the compound inequality because the inequality uses OR and the solution needs to be true only for one inequality. 28. a. 5 3 2 1 0 0.1 0.2 0.3 0.4 Rainfall (in.) b. No; Sample: the histogram only reports the days for which rainfall was measured. The frequency of days without rain would need to be represented as well for the plot to be accurate and fully useful. 21. 96 servings or fewer 22. less than 48 seconds 23. d = 4t; direct; rate 5 24. _ 9 26. consistent and independent Measurable Rainfall 4 20. Sample: y = -0.9x + 17.4 25. 11 weeks 75 29. 16y2 - 16 30. (2, -3) 27. a. 7a + 5b ≤ 45 b. no c. 4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 75–3 Saxon Algebra 1 Lesson 76 Warm Up 76 1. radical expression 5 2. 100 √ 3 3. 6 √ 2 4. -8 √ 5. 40 √3 Lesson Practice 76 15 a. √ 21 b. 6 √ c. 54 d. 3x √6 7 e. 4 √ 5 - √ 15 f. 2 √ 6 g. 32 - 8 √ 7 h. 23 - 8 √ 13 square i. 1037 + 64 √ feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 76–1 Saxon Algebra 1 Lesson Practice 76 76 16. B 5 ≥p 1. - _ 12 17. $482 2. {1, -9} 4. (x - 3)(x + 13) 18. Student A; Sample: Student B’s trinomial would have a middle term of 6x, not -6x. 5. (5z + 7)(z - 1) 19. (4x - 5)2; (4x - 5) 3. (3x - 1)(4x - 7) 6. (3x - 2)(x + 9) 20. a. 297 b. (2x + 9)(x - 3) 3 7. 864 √ 7s 8. -21 √ 9. 80 10. 6 √6 x x _ 11. _ 2 √ 15 12. 391 13. 21. Student B; Sample: Student A incorrectly isolated the absolute-value term by subtracting the coefficient 3 instead of dividing. (8 - √4) 2; 36 square 22. ⎢w - 27 = 3; 30 in., 24 in. feet 23. B 14. Sample: Use the Distributive Property to multiply the radicals: √ 6 - √ 16 . Then - 4. simplify: √6 24. all real numbers; Every real number is more than three OR less than five. 625 · √ 16 15. Sample: √ © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 76–2 Saxon Algebra 1 25. a. Apparent Air Temp. (°F) Lesson 110 76 y 100 90 80 0 x 10 30 50 70 90 Humidity Level (Percent) b. positive correlation 26. y 30 20 10 x 2 4 6 27. land animals 28. a. 2 b. y = $32 + $6x c. inconsistent 29. less than 3 inches 30. 8 years old © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 76–3 Saxon Algebra 1 Lesson Warm Up 77 e. y ≥ 2; 1. equation -6 1 2. x > 2_ 3 -1 0 1 77 2 3 -4 -2 0 2 4 6 f. t ≥ 6; Her time will be at most 150 seconds in 6 weeks. 4 3. x < 2.2 0 1 2 3 4. x ≤ -6 -8 -6 -4 -2 0 0 2 2 5. x ≤ -2 -6 -4 -2 Lesson Practice 77 a. x ≤ -1; -6 -4 -2 0 2 -6 -4 -2 0 2 2 4 6 8 10 b. k > -6; -10 -8 c. f < 8; -2 0 d. p > 6; 0 1 2 3 4 5 6 7 8 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 77–1 Saxon Algebra 1 Lesson Practice 77 77 15. 2 square meters 1. 48 lb 16. 2(3x - 2)(2x + 1) 2. 47 lb 17. Student A; Sample: Student B didn’t 150 . correctly simplify √ 3. 2(3x + 1)(x - 2) 4. r < 30 5. x > 8; 2 meters per 18. a. 70 √ second 0 2 4 6 8 10 b. 140 meters per second 6. x ≥ -9 1 7. x ≥ _ 3 15 - 6 √ 5 + 5 √ 15 - 10 √ 3 19. __ 2 square inches 8. x > 65 20. Student A; Sample: Student B’s trinomial would have a middle term of -16x, not 16x. 9. 1 < r < 4 3 10. 8x √ 11. 20g3 12. Sample: The only difference is having to remember to reverse the inequality sign when you multiply or divide both sides by a negative number. 21. D 13. B 23. 30 × 80 22. Sample: To solve the equation, the absolute value of ⎢x + 11⎢ would be -2. However, an absolute value cannot be less than zero. 14. b ≤ 3; The bottles can cost at most $3 each. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 77–2 Saxon Algebra 1 Lesson 77 24. positive correlation 25. 3.97 ≤ x ≤ 4.03 275g7h9 26. 3gh √ = 3gh √ 275 · g7 · h9 = 3gh √ 25 · 11 √ g7 √ h9 11 · g3 √ g · h4 √ h = 15g4h5 √ 11gh = 3gh · 5 √ 81 27. a. _ 176 81 b. _ 176 c. Sample: The answers are the same because the events describe the same set of possible outcomes, but in two different ways. 28. consistent and independent 29. 6 bricks wide by 6 bricks long 30. Student B; Sample: Student A removed the perfect-square factor rather than the square root of that factor. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 77–3 Saxon Algebra 1 Lesson 78 Warm Up 78 1. rational 2. true 3. false 4. when x = 0 Lesson Practice 78 a. m ≠ 0 b. m ≠ -2 c. m ≠ 2 d. x = -1; y = 0 e. x = -7; y = 6 f. x = -4; y = 0 g. x = 6; y = -5 h. x = 0; y = 5 i. 60 clubs © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 78–1 Saxon Algebra 1 Lesson Practice 78 11. 1. (1, -7) 2. (-3, -2) 3. (x + 3y)(x + 7y) 78 1 y=_ x +5 1 5=_ x +5 -5 -5 __ __ 1 0=_ x There is no value 1 x such that _ x = 0. 4. (x - 15)(x + 2) 5. m ≠ 0 12. x = -1.9; y = 0.3 6. m ≠ -3 13. C 7. x = 3 14. 11 ≥ c; You can spend at most $11 on each CD. 8. m > -3; -6 -4 -2 0 2 4 9. 40 10. x = 0; y = 6 16 16. g > 7 y 8 -16 -8 O 8 15. Student A; Sample: Student B did not reverse the inequality sign when dividing by -5. x 16 17. h ≥ 7; You will hike at least 7 hours. 18. Student B: Sample: Student A multiplied a radical and a whole number. 2 square 19. 103 + 71 √ inches © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 78–2 Saxon Algebra 1 Lesson 78 20. Sample: (2x - 3y) (5x + 2y) = 10x2 + 4xy - 15xy - 6y2 = 10x2 - 11xy - 6y2 21. C 22. 100 square inches 23. {12, -12} 24. x ≤ 12 OR x ≥ 65 25. no correlation 26. n ≤ -15; See student work. 5 + 24x √ 6 27. 20x √ 111 28. _ 216 29. C 30. Average Milk Production 10 8 6 4 2 35 40 45 50 55 60 65 Gallons © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 78–3 Saxon Algebra 1 Lesson 79 Warm Up 79 1. polynomial 2. (x + 5)(x - 2) 3. ( p - 9)( p - 4) 4. (2x + 3)(x - 7) 5. (5x + 2)(x - 3) Lesson Practice 79 a. p3( p + 12)( p + 1) b. 6n2(n + 1)(n - 2) c. -1(r + 5)(r - 6) d. -5d(d + 4)(d + 1) e. xy( y + 9)( y - 6) f. 5bx(x + 3)(x - 4) g. 6h(f - 5)(f + 8) h. 90x(x + 3)(x + 2) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 79–1 Saxon Algebra 1 Lesson Practice 79 79 6. k2(k + 4)(k + 2) 14. 3(x + 4)(x + 11) = 3(x2 + 15x + 44) = 3x2 + 45x + 132 and 3(x + 11)(x + 4) = 3(x2 + 15x + 44) = 3x2 + 45x + 132; Sample: By the Commutative Property of Multiplication, the order of the factors does not matter. 7. (5x - 2)(x + 1) 15. D 8. 2x(x + 3)(x + 5) 16. -16(x - 1)2 9. ab(x + 3)(x - 8) 10. 3m(5x - 2)(x + 1) 17. Student A; Sample: Student B wrote the horizontal asymptote. 11. m ≠ -3 18. a. y = 1 1. y = 4.5 2. (2, 0) 3. (1, -1) 4. b < -2 OR b > 2 5. (x - 9)(x + 5) 12. d ≤ 1; -6 -4 -2 b. x = 0 0 2 c. 51 instruments 4 13. yes; Sample: The answer will be the same, but factoring may be more difficult due to larger numbers. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 19. a. y = 15 b. x = 0 c. 69 dinners y _ 5 _ = ; 5 =y 20. _ x-8 1 x-8 LSN 79–2 Saxon Algebra 1 Lesson 1 21. g ≤ 4_ ; He can buy up 3 1 gallons. to 4_ 28. a. $5100 b. 4.80r > 5100 3 c. r > 1062.5 22. Student B; Sample: Student A reversed the inequality sign when dividing by a positive number. d. at least 1063 DVDs per month 29. 46 ft 23. Sample: Use the FOIL method, simplify radicals, and then combine like terms. 30. a. 185 + x ≤ 750; x ≤ 565 24. D 25. 1296 square inches 26. ⎪x - 65⎥ = 8; 73°, 57° 27. Sample: The trend line for a positive correlation rises from left to right. The trend line for a negative correlation falls from left to right. There is no trend line when there is no correlation. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 79 LSN 79–3 b. no; Sample: The total weight of the weights is 720 pounds. This would mean that Alicia could weigh no more than 30 pounds, which is not reasonable. Saxon Algebra 1 Lesson 0 P(6) = _ = 0, 50 Warm Up 80 6 3 =_ , P(7) = _ 50 25 1. measure of central tendency 17 , P(8) = _ 50 1 or 50% 2. _ 2 8 4 _ = , P(9) = _ 50 25 3 or 30% 3. _ 10 11 P(10) = _ 50 1 2 or 16 _ % 4. _ 6 3 b. 1 or 25% 5. _ 4 Lesson Practice 80 a. 80 Tails Heads Tails TT TH Heads TH HH 1 2 _ , P(TH) = c. P(HH) = _ 4 4 1 1 , P(TT) = _ =_ 4 2 d. 0 = 0, P(2) = _ 50 Clam Chowder 0 = 0, P(1) = _ 50 Potato 1 P(0) = _ , 50 8 7 6 5 4 3 2 1 0 Tomato 0 1 2 3 4 5 6 7 8 9 10 Number of Pins on the First Try Types of Soup 4 2 =_ , P(3) = _ 50 25 3 1 _ e. P(tomato) = _ = , 12 4 6 1 _ = , P(vegetable) = _ 12 2 2 1 _ P(potato) = _ = , 12 6 1 P(clam chowder) = _ 12 1 , P(4) = _ 50 2 1 _ = , P(5) = _ 50 25 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. Soup Cans Vegetable 20 18 16 14 12 10 8 6 4 2 0 Number of Cans Frequency Bowling LSN 80–1 Saxon Algebra 1 Lesson Practice 80 1. Sample: y = -5x - 1 2. x = 108 3. x = 98 80 13. Sample: Use a table when organizing the data for further calculations. Use a graph to display the data. 14. D 4. y = 0 15. 5. y = -5 6. {5, -5} 7. x < -3 OR x ≥ 5 Physical Success CS PS Failure CF PF ( )3 3 16. P(red, red, red) = _ 10 27 =_ 1000 8. c10(c + 8)(c + 3) 9. 7x2(3x - 2)(2x + 5) 17. -16(x - 3)(x + 1) 10. -3(m + 2)(m + 8) 11. (x - 1)(x + 2)(x + 5) 12. Red Blue Yellow Green 1 R1 B1 Y1 G1 2 R2 B2 Y2 G2 3 R3 B3 Y3 G3 4 R4 B4 Y4 G4 5 R5 B5 Y5 G5 6 R6 B6 Y6 G6 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. Chemical 18. Student B; Sample: Student A did not factor out the GCF, 2. 19. 3m(m - 3) inches 20. a. 3x(x - 2)(x + 3) b. (3x) × (x - 2) × (x + 3) 21. Student B; Student A didn’t change the sign when subtracting 3 from both sides after setting the denominator equal to 0. LSN 80–2 Saxon Algebra 1 Lesson 28. a. y = 1.556x + 10.6 22. x = 0; y = 12 40 b. Sample: Look at the value of the slope of the line (the coefficient of the x-term). If the slope is positive, then the correlation is positive. If the slope is negative, then the correlation is negative. In this example, there is a positive correlation. y 20 -40 -20 O 20 x 40 -40 23. Sample: In the first inequality, you would solve by dividing both sides by positive 6. In the second, you would solve by dividing both sides by -6. It is what you are dividing by, not what is being divided, that determines whether the sign is reversed. 24. D 29. 0.065x ≥ 20,000; any house with a sale price of $307,692 or greater 30. a. consistent and dependent 6 25. 6 + 2 √ b. Neither train travels farther; they both travel the same distance because the equations are identical in slopeintercept form. 26. (3x + 1)(3x - 13) 27. Sample: The sum of 5 + 9z2 does not contain a factor of z, which is necessary for the coefficient b, 18z. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 80 LSN 80–3 Saxon Algebra 1 Lesson 81 Warm Up 81 1. identity 2. x ≤ 7 5 3. k < -_ 6 4. p < -14 5. x ≥ 3 Lesson Practice 81 a. x > 2; 3 b. a ≤ 1 _ ; 5 0 2 0 c. x ≤ 0; 4 1 -4 -2 0 2 2 d. never true e. always true f. September © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 81–1 Saxon Algebra 1 3. (5x - 2y)(6x + y) 90 70 0 2000 2. -1(q - 7)(q + 6) 110 1990 1. (w - 4)(w - 9) 81 130 1980 14. 1970 Practice 81 Employment (in millions) Lesson Year 4. (x - 5)(x + 11) 15. Since 2 < 3, 2 is a solution of the compound inequality because the inequality uses OR and the solution needs to be true only for one inequality. 5. {17, -11} 6. {3.5, -11.5} 7. n ≤ 8 8. d ≥ 5 9. v > -1; 10. y < 5.5; -4 -2 0 2 16. 3 4 5 square inches 6 1 1 11. Sample: y = - _ x - 1_ 2 2 12. y = -x + 11 1 13. a. _ 2 1 b. _ 10 c. mutually exclusive 3 d. _ (8 + √8 ) 2; 72 + 32 √2 17. x > 14 18. Sample: The vertical asymptote of the graph will be moved horizontally to a value of b on the x-axis. 5 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 81–2 Saxon Algebra 1 Lesson 2 1 _ 19. P(2) = _ = , 36 18 4 1 _ = , P(3) = _ 36 9 6 1 =_ , P(4) = _ 36 26. a. Sum of Two Spins 6 6 1 =_ , P(5) = _ 36 6 6 1 =_ , P(6) = _ 36 6 6 1 _ = , P(7) = _ 6 36 4 1 _ = , P(8) = _ 36 9 1 2 =_ P(9) = _ 18 36 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 10 3 4 5 6 7 8 9 10 11 4 5 6 7 8 9 10 11 12 5 6 7 8 9 10 11 12 13 6 7 8 9 10 11 12 13 14 28. over 100 miles per day 22. Student A; Sample: Student B did not include the GCF in the final factoring. 7 23. _ 12 1 ( )5 = _ 1024 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 2 27. C 21. -5(t - 2)(t - 3) 25. Student A; Sample: Student B included the sum of 6 but the question asked for less than 6. 1 7 b. _ 16 20. B 1 24. P(five 3s) = _ 4 81 29. Sample: Distribute -3 through the parentheses on the right side. Then add 3x to both sides. Then subtract 5 from both sides. Finally, divide both sides by 5. The solution is x > 8. 30. junior and senior years LSN 81–3 Saxon Algebra 1 Lesson 82 Warm Up 82 1. compound inequality 2. x > -6 3. y ≥ 8 4. x < -5 OR x ≥ 5.5 5. A © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 82–1 Saxon Algebra 1 Lesson 82 Lesson Practice 82 1 or x > 3; a. x < -_ 2 -2 -1 0 1 2 3 4 b. 8 ≤ x < 14 8 c. 10 12 14 6 ≤ 2(x + 12) < 12 6 ≤ 2x + 24 < 12 -24 -24 -24 __ __ __ -18 ≤ 2x -18 2x _ ≤_ 2 2 -9 ≤ x < -12 -12 < _ 2 < -6 Distributive Property Subtraction Property of Inequality Simplify. Division Property of Inequality Simplify. d. -16 > 2(x - 2) OR 27 < 3(x + 2) -16 > 2x - 4 OR 27 < 3x + 6 Distributive Property +4 +4 +(-6) +(-6) __ __ ___ ___ Addition Property of Inequality -12 > 2x OR 21 < 3x Simplify. 3x -12 2x 21 _ _ >_ OR <_ Division Property of 2 2 -6 > x 3 OR 3 7<x Inequality Simplify. e. between 5 and 13 lb © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 82–2 Saxon Algebra 1 Lesson 82 1 15. 33 _ ; You can talk at 3 most 33 minutes. Practice 82 1. (x + y)(2x + 7y) 1 16. y = _ x 2. (2m + n)(-2m + 5n) 5. m ≠ 5 17. Sample: -8u5y + 56u4y - 80u3y = -8u 3y(u 2- 7u + 10) = -8u 3y(u - 5)(u - 2) 6. y ≠ -3 18. A 3 3. 147 - 24 √ 2 4. 4x - 3 7. z ≤ 6; 8. x > 3; 0 0 2 2 4 4 4 1 _ = , 19. P(A) = _ 7 28 6 7 1 =_ , P(B) = _ 4 28 6 9 , P(C) = _ 28 9. inconsistent 5 3 _ , P(F) = P(D) = _ 28 28 10. consistent and dependent 11. 12 feet; Sample: One possible way to express the answer as a radical . number is 6 √4 12. 24 cm 20. 0; Sample: “tt” does not occur in this chart. 21. Student B; Sample: Student A found the probability of rolling a 1 _ 1 · 1 =_ 2 or 3 to be _ 6 10 12 14 16 18 22. a. 75 + 3p < 100 + 2p b. p < 25 14. 19.8 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 36 2 1 _ when it is actually _ = . 6 3 13. a. x < 12 OR x > 15 b. 6 LSN 82–3 Saxon Algebra 1 Lesson 82 c. Sample: The solution set is all natural numbers less than 25 since Veejay can only invite whole numbers of people, and at 25, the costs are equal. 23. 3 days 24. x < 9 25. Student A; Sample: Student A is correct because -2 + x > x + 3 is an inequality that will never be true, while Student B wrote an inequality that is sometimes true. 26. Sample: -17 > -2x - 7 OR 27 > 3(x + 6) -17 > -2x - 7 OR 27 > 3x + 18 Distributive Property +7 +7 __ -18 -18 Addition Property of __ __ __ Inequality -10 > -2x -10 -2x _ <_ OR 9 > 3x 9 3x OR _ >_ 5<x x>5 OR 3 > x OR x < 3 -2 -2 3 3 Simplify. Division Property of Inequality Simplify. Write with the variable on the left. 27. C 28. 3 ≤ c ≤ 83 29. x ≥ 90 OR x < 70 30. Felipe must score between 87 and 100 on his final test. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 82–4 Saxon Algebra 1 Lesson 83 Warm Up 83 1. perfect-square trinomial 2. 3x(x3 - 4) 3. 8y2(6 + 2y - 7y3) 4. 4b2 - 12b + 9 5. 9x2 - 49 Lesson Practice 83 a. yes; (x + 7)2 b. yes; 6(n2 - 1)2 c. no d. 6 miles e. yes; (5x + 2)(5x - 2) f. yes; (3b + 10a)(3b - 10a) g. no h. yes; (x5 + 9)(x5 - 9) i. 342 - s2 = (34 - s)(34 + s) ft2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 83–1 Saxon Algebra 1 Lesson Practice 83 83 15. a. 0.03d ≥ 60 6 1. 7 + √ b. d ≥ 2000 3-6 2. x2 + x √ c. at least $2000 d. 3. b ≤ 1 1000 2000 3000 4. h ≤ -5 16. 7.8 ≤ x ≤ 8.2; x ≥ 7.8 AND x ≤ 8.2 5. 3x3(x - 9)(x + 8) 17. a. ⎢x + 3 = 24 6. -12x(x2 + 4) b. x + 3 = 24; x + 3 = -24 7. perfect-square trinomial; (x + 5)2 8. perfect-square trinomial; (x + 6)2 9. m −− = -1, m −− = 1, TU UV and (1)(-1) = -1; −− −− TU ⊥ UV; Therefore, TUV is a right triangle. 10. 49x2 - 4y2 or 4y2 - 49x2 c. {21, -27} 18. Sample: If c is positive, then both are the same sign as b: either both positive or both negative. If c is negative, then they have opposite signs. 19. a. y = 1 b. x = 0 11. x > 4 c. 201 toys 12. inconsistent 13. consistent and dependent 2 14. _ 9 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 20. 4m2(m + 10) 21. P(heads, heads) = 1 1 1 2 1 _ · _ = _ =_ (2) (2) (2) LSN 83–2 4 Saxon Algebra 1 Lesson 83 22. A 23. Sample: The expression is a difference of two squares. Factor as (45 + 15)(45 - 15), which equals 60 · 30 = 1800. 24. no; Sample: The inequality is only true if x is 0 or greater. 25. more than $5 an hour 26. Student B; Sample: Student A forgot to change the direction of the inequality symbol when using the Multiplication Property of Inequality. 27. a. 32 < F ≤ 40 b. 20 < F ≤ 60 28. 28 < 2(x + 3) < 42 28 < 2x + 6 < 42 22 < 2x < 36 11 < x < 18 Distributive Property of Inequality Addition Property of Inequality Multiplication Property of Inequality 29. D 30. s2 - 64; (s + 8)(s - 8) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 83–3 Saxon Algebra 1 Lesson 84 Warm Up 84 1. function 2. 48 3. 24 4. -200 5. B Lesson Practice 84 a. yes b. yes c. no y d. 12 8 4 x O -2 -1 1 2 -4 e. upward f. downward g. 12 feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 84–1 Saxon Algebra 1 Lesson Practice 84 84 14. a. 48 1. perfect square trinomial; (q + 9) 2 b. 12(2x - 3)(3x - 2) 14 · √ 21 = √ 14 · 21 15. √ = √ 2 · 7 · 3 · 7 = 7 √ 6 2. difference of two squares; (6x - 12) (6x + 12) 16. x = -10.3 3. 3 √3 17. -5(t - 1)(t - 7) 2 4. 12 √ 18. 6. 4 < x OR 2 > x Freshman 5 Sophomore 0 Junior -20 -15 -10 -5 Senior 5. p > -17; Student Committee 15 12 9 6 3 0 Class 19. 2 7. y = 15x + x - 4 3 8. _ 5 Salad Request 24 20 16 12 8 4 0 1 9. _ 2 2 10. _ 5 Carrot 6 Caesar 4 Cucumber 2 Pasta 0 Salad 1 11. _ 5 20. k = 3; a = 3bc 12. a. y = 40x + 180 21. b. positive correlation 13. ⎢W - 162 = 3; 165 lb, 159 lb © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. -6 -4 -2 0 22. B 23. 100 ≤ c ≤ 300 LSN 84–2 Saxon Algebra 1 Lesson 84 24. Student B; Sample: The trinomial is not of the form a2 + 2ab + b2 or a2 - 2ab + b2. 25. a. 30π (r - 1)2 b. 1 cm c. 30 cm 26. x + 3 27. D 28. Sample: f(x) = -x + 3; f(x) = x2 + x - 3 29. Sample: The shape of the parabolas is the same, but the graph of y = x2 opens upward and the graph of y = -x2 opens downward. 2 3 πr ; yes 30. A = _ 4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 84–3 Saxon Algebra 1 Lesson 85 Warm Up 85 1. perfect square 2. 25 3. 14 6 4. 6 √ 5. 19.7 Lesson Practice 85 a. 20 b. 10.8 c. 7 10 d. 3 √ e. no f. yes g. no h. 33.0 ft © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 85–1 Saxon Algebra 1 Lesson Practice 85 85 15. Sample: x _ + 6 ≤ 10 -5 x _ ≤4 1. 8 √5 4 pq x 5 _ 2. _ c + 3 -5 q w x ≥ -20 3. -3t(t + 8)(t + 1) 5 16. 2 √ 2 4. 4x (x - 2)(x + 2) 17. x = -4.5 5. (x - 7)(x - 2) 18. k = 8 6. difference of two squares; 3(g + 2) (g - 2) 19. 2034 7. perfect-square trinomial; (3x - 4)2 21. a. 5 ≤ c ≤ 60 20. 29 feet b. 41 ≤ f ≤ 140 8. not quadratic c. f < 41 OR f > 140 2 9. y = 2x - 10x + 12 10. y = 0.3 4 11. x = 2 _ 7 12. x ≤ 4; -2 0 2 4 6 8 13. Sample: 1 1 _ x + 8 y = -3_ 2 2 14. 18 ft 10 22. 9 < x < 15; Sample: This is an AND inequality since the solution falls within a specific range. 23. Student B; Sample: The polynomial is a difference of two squares. 24. 18 inches © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 85–2 Saxon Algebra 1 Lesson 85 25. y = 6x2 40 y 30 20 10 0 x 2 4 6 26. Sample: The triangle is not a right triangle. 27. x2 + (2x)2 = 45; 3 cm and 6 cm 28. B 29. a. (3x + 5)(2x - 7) b. 87 30. 2 (6 + √ 36 ) ; 144 square meters © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 85–3 Saxon Algebra 1 Lesson 86 Warm Up 86 1. y-coordinate 2. -9.3 3. 9 4. 4.5 ft 5. B Lesson Practice 86 10 ≈ 3 city blocks a. √ 65 b. √ c. no d. (1, 5) 442 ≈ 42 yd e. 2 √ © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 86–1 Saxon Algebra 1 Lesson 8 ≥ C; The 13. 48 _ 9 temperature in Texas has never been above 8 48 _ degrees Celsius. 9 Practice 86 1. y < 4; -2 0 2 4 6 8 10 14. Sample: The value of c determines vertical translation. 2. 1 < x OR -1 > x; -2 0 2 86 4 3. -2(g + 9)(g - 5) 15. 4. (4b + 5)(5b - 1) Lettuce TL HL CL Tomato TT HT CT Cucumber TC HC CC Onion TO HO CO Peppers TP HP CP 5. -1(13w - 25)(w - 1) 2 6. y = -20x + 14x Turkey Ham Chicken 7. not possible 16. 11 games or more 8. 5 17. 4 < s < 6 units 9. 0.04x ≥ 100; at least $2500 18. C 2 11. a. x ≤ 13 AND x ≥ 5 b. 5 ≤ x ≤ 13 c. 4 6 8 10 12 14 12. 30 + 10 √ 15 square feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 2 19. (y - 25) - (x + 8x + 16) 10. positive correlation 20. Student A; Sample: Student B did not use the Distributive Property correctly. LSN 86–2 Saxon Algebra 1 Lesson 21. downward; Sample: If the price of the product is too low, people may buy a lot, but the company will not make much compared to its expenses. If the price of the product is too high, people will not buy it. 22. 4 2 23. a. 3 √ 2 b. 5 √ 2 c. c = a √ 24. Student B; Sample: Student A used p as the hypotenuse; 7 is the length of the hypotenuse. 86 27. Sample: Dawn’s values for x2 - x1 and y2 - y1 will be the opposite of Dan’s values, but when the differences are squared, they will be the same positive numbers. 28. yes; Sample: Using the distance formula, the lengths of the sides of the triangle are 5, 5, ; 5 2 + 5 2 = 25 and 5 √2 2 ) . + 25 = 50 = (5 √2 Because the lengths of the sides of the triangle satisfy the equation a 2 + b 2 = c 2, the triangle is a right triangle. 29. B 5 ≈ 4.5 city blocks 25. 2 √ 30. 216 feet 26. a. 80 ft b. 83 ft © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 86–3 Saxon Algebra 1 Lesson 87 Warm Up 87 1. greatest common factor 2. 15k 3(6k + 1) 3. (x - 3)(x - 5) 4. (4n - 7)(n + 3) 5. (9x + 8y)(9x - 8y) Lesson Practice 87 a. (y + 2z)(3y + 4) 2 b. (y + 1)(3 - 4y) 2 c. 11x [(3y - 1)(3x + 1)] d. (ab - 5)(3a - 4) e. (x + 7)(x - 11) f. (2a + 3)(3a - 5) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 87–1 Saxon Algebra 1 0 Year 3 3. g > _ 4 13. a. ⎢x - 50 = 0.5 1 4. k > 1_ 3 1 5. P(4, 4, heads) = _ 6 1 1 _ =_ ( ) 2 4.00 2006 9(2a 2b - 1) 5.00 2002 2 2. 16a (4b - a) + 6.00 1998 1. (x - 6y)(x + 9y) 87 7.00 1994 12. 1990 Practice 87 Ticket Price (dollars) Lesson 2 b. 50.5 lb, 49.5 lb · 14. m ≤ 2; She can hike at most 2 hours. 72 6. P(less than 4, less than 1 2 _ 1 4, heads) = _ · 12 = _ 2 8 ( ) 7. difference of two squares; (10 + c3) (10 - c3) 8. perfect-square trinomial; (2x + 5) 2 9. 5 10. 4 √2 11. hours of practice and your golf score 15. a. y = 100 b. x = 0 c. 250 books 16. Sample: There are no common factors that can be factored out of any grouped terms. 17. Sample: Marco painted either fewer than 40 big walls or more than 60 small walls. 18. 3000x – 1000 meters 19. C © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 87–2 Saxon Algebra 1 Lesson 20. Sample: Rewrite the equation in the standard form of a quadratic function. Use the function to make a table of values. Plot the points from the table in a coordinate plane. Draw a smooth curve through the points. 26. a. 30 yd b. 27 yd c. the receiver at (50, 20) 1 bh 27. a. _ 2 b. bh = 2A = 2(x2 + 2x) = 2x2 + 4x c. 2x(x + 2) 2x(x + 2) d. _ = 2x; The 6 21. √ 22. yes; Using the Pythagorean Theorem, 2 5 ) = (15)2. (10)2 + (5 √ 23. no 24. Student A; Sample: In calculating x2 - x1, Student B subtracted 1, instead of -1, from 4. 25. a. (3, 5) and (5, 7) 2, b. MN = 2 √ PR = 4 √2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 87 (x + 2) length of the height is 2x. 28. yes; Sample: Any number of monomials expressed as a sum or difference is a polynomial. 29. (n - 4)(n + 20) 30. (y2 + 5) + 2(y + 1) dollars LSN 87–3 Saxon Algebra 1 Lesson 88 Warm Up 88 1. rational 2. x 8 2 3. _ 5 3b 2 3y 4. _ 7 5. (x - 2)(x - 12) Lesson Practice 88 4 a. b. 4q z _ 3 4 20x _ 7 63y c. 3(x + 3) d. e. f. m(4 + 3mn) _ 6(3 + n) 4j _ 9 x+ 4 _ x+5 2 g. y x(x + 5)(x + 4) h. __ 10(2x + 1) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 88–1 Saxon Algebra 1 Lesson Practice 88 16. a. y = 5 1. x > -8 b. x = 0 2. x ≤ -1 OR x > 2; c. 19 uniforms -2 0 2 d. no; Sample: The horizontal asymptote is y = 5. The value, 5, for y is undefined. The uniform company would not give away the five free uniforms unless other uniforms were purchased. 4 3. not quadratic 4. y = 3x2 + 2x 10 5. 2 √ 6. 2 √2 7. (-1, -4) 8. (2, -1) 88 1 (x + 2)(x + 5) 17. a. _ 2 2y 9. _2 b. 20 square feet x 2 18y 10. _ 2 x + xy 7x 11. _ 4 12. (x - 5)(x + 12) 2 13. 8a (2b - 1)(4a + 1) 14. (x - 3) × (x + 7) 18. Sample: They are easier to read than a long list of outcomes. 2s + 9 feet 19. _ 2 ; √ 3 ; √ 4 ; √ 5. 20. a. √2 11 b. √ 21. C 15. -2 < x < 2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 88–2 Saxon Algebra 1 Lesson 22. Student B; Sample: The midpoint formula involves adding the x-coordinates of the two points, not subtracting them. 88 30. a. (9x - 2)(9x - 2) b. Sample: It is the product of an expression times itself. 23. 106.5 24. width = 5 ft, length = 10 ft; (x + 5)(x) = 50, x2 + 5x - 50 = 0, and (x + 10)(x - 5) = 0. 25. 3(24x4 + 10x2y + y2); Sample: It is simpler to express the area as binomials before multiplying (12x2 + 3y)(6x2 + y). 26. D 27. Sample: Add exponents when multiplying and subtract exponents when dividing. 28. B 29. $10c + $20 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 88–3 Saxon Algebra 1 Lesson Warm Up 89 89 i. x = 3 j. 18,223 ft; 19 seconds 1. parabola 2. downward 3. upward 4. 26 5. C Lesson Practice 89 a. (-1, -4), maximum: -4; D: all real numbers, R: all real numbers less than or equal to -4 b. (5, -3), minimum: -3; D: all real numbers, R: all real numbers greater than or equal to -3 c. 6 d. -9 and -3 e. no zeros f. x = 4.5 g. x = -2.5 h. x = -2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 89–1 Saxon Algebra 1 Lesson Practice 89 1. {-17, 13} 2. {-11, -1} 3. x > 9 OR x ≤ 7; 6 8 10 12 4. perfect-square trinomial; 4(5y - 2)2 5. difference of two squares; (9x + 1) (9x - 1) 6. (3c - 7)2 7. 2 √2 1 8. _ ab 9. 6y 10. x = -2 1 11. x = _ 2 89 12. Sample: Use the formula for the axis of symmetry and sketch the axis on a graph. Substitute the x-value into the equation to find the y-value, and then plot the vertex. Use a table of ordered pairs to find values on the left (or right) side of the vertex, and then use symmetry to find the points that are mirror images of those points. 13. 45 ≤ x ≤ 65; x ≥ 45 AND x ≤ 65 14. x > 1 AND x ≤ 5; 1<x≤5 1 h(b1 + b2) 15. A = _ 2 1 (2)[( √ 49 + 4) + A=_ 2 36 + 8)] ( √ A = (7 + 4) + (6 + 8) A = 11 + 14 A = 25 square meters 16. -16(x - 5)(x - 3) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 89–2 Saxon Algebra 1 Lesson 1 17. a. P(brown) = _ ; P(red) 2 1 1 ; P(yellow) = _ =_ 4 4 b. brown red yellow brown 23. D 24. The function is reflected about the x-axis and is vertically stretched by a factor of 4. 25. a. 8hr π b. _ 18. 334 minutes 6 3 19. x < 0; 2(0) + 8 > 2 + 5(0) + 6, 8≯8 2(-1) + 8 > 2 + 5(-1) + 6, 6>3 2(-3) + 8 > 2 + 5(-3) +6 2 > -7 20. 6 ft 21. 8 89 2 2 (3x + 6x y + x + 2xy) 26. __ y 27. Student B; Sample: Student A forgot to put the 1 in the numerator when switching to multiplication. 28. A 29. 88 meters in 4 seconds y 6 4 2 x O 1 2 Sample: The volume of the cylinder increases faster than that of the rectangular prism. 30. Sample: If the value of a is positive, the graph opens upward and has a minimum. If the value of a is negative, the graph opens downward and has a maximum. 22. 15 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 89–3 Saxon Algebra 1 Lesson 90 Warm Up 90 1. factor 31 2. _ 36 3. -x4y + 7y2 4. 18r 3 - 48r 2 5. x2 - 10x + 21 Lesson Practice 90 5n a. _ 8 b. 6 3 d c. _ d-9 3 d. _ 2p x-1 e. _ x+2 -t - 10 f. _ 4 t -2 15 g. __ (1.5 - c)(1.5 + c) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 90–1 Saxon Algebra 1 Lesson Practice 90 14. x ≥ 75; Sample: He needs to make a score of 75 or better on his third test to have an 80 average. 6. perfect-square 3 trinomial; (x + 8) 2 -4 O y -2 16. a. 2f > 20 - 3f; f > 4 b. Sample: The solution set is all whole numbers greater than 4, so after 4 days there will always be more adult formula than puppy formula. 4 -2 -4 -6 -8 2 y +x 8. _ 2 3x 9. {-3} 1 10. x = 1_ 3 7x - 2 11. _ y Pawns Pieces x 2 Knights 5. perfect-square 2 trinomial; (3x + 7y) 2 Bishops 4. (t + 7)(4t - 7) Chess Pieces 20 16 12 8 4 0 Rooks 15. Queens 3. (2x + 3)(3x + 4) Kings 2. 8 Number of Pieces 58 1. √ 7. 90 17. Sample: that each inequality must be satisfied in the range of answers 3y 12. _ 2x 13. ⎪x - 210⎥ = 33; 243 mm, 177 mm © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 90–2 Saxon Algebra 1 Lesson 18. a. Sample: The vertical segment joining (2, 2) and (2, -3) is perpendicular to the horizontal segment joining (2, 2) and (5, 2). b. 5 and 3 25. a. Sample: It has a minimum because the value of a is positive, which means it opens upward and the vertex is the lowest point. b. Sample: The minimum population occurred 41 years after 1900, or during 1941. The population was about 2.86 million people. 34 c. √ 19. yes 20. a. s 2 b. (x + 3)(x + 3) = (x + 3) 2 c. (x + 3) 2 = s 90 c. about 4.66 million people 2 d. (x + 3) = s 1 1 ;A=_ bh 21. k = _ 2 2 22. C 23. x – 5 hours 24. Student B; Sample: Student A did not take the opposite of b. 26. Sample: Find the axis of symmetry to find the x-coordinate of the vertex: 35 = 17.5. x = -_ 2(-1) Substitute 17.5 into the equation for x to find the area, y: y = -x 2 + 35x = -(17.5) 2 + 35 · 17.5 = 306.25. 27. C © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 90–3 Saxon Algebra 1 Lesson 90 x + 10 28. _ x + 30 29. Sample: Multiplying by these expressions makes each of the denominators equal to the LCD of n4p5. 30. Sample: Factor the denominator of the first term: (x + 3)(x + 3). Multiply the second x+3 expression by _ . x+3 The numerator of the second expression becomes x 2 + 3x. The sum of the numerators is x 2 + 3x + 2, which factors into (x + 2) (x + 1). No common factors cancel, so the (x + 2)(x + 1) answer is __ (x + 3)(x + 3) (x + 2)(x + 1) . = __ 2 (x + 3) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 90–4 Saxon Algebra 1 Lesson 91 g. ∅ Warm Up 91 1. absolute-value equation h. 2. 7 i. m - 15 ≤ 0.2 3. 6 j. 14.8 ≤ m ≤ 15.2 4. x = 11, -3 5. x = -5, -9 Lesson Practice 91 a. -12 < x < 12 -12 -8 -4 0 4 8 12 b. x < -19 OR x > 19 -24 -16 -8 0 8 16 24 c. -7.6 ≤ x ≤ 7.6 -12 -8 -4 0 4 8 12 d. x < -5 OR x > 5 -6 -4 -2 0 2 4 6 e. -2 ≤ x ≤ 22 -4 0 4 8 12 16 20 24 f. x < -30 OR x > 6 -30 -20 -10 0 10 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 91–1 Saxon Algebra 1 Lesson Practice 91 91 13. Student A; Sample: Student B multiplied the denominator of one of the expressions by -1, but forgot to multiply the numerator of that expression by -1 also. 1. x = 1 6(s + 3) 2. _ 2 rs b2 - 16b - 6 3. __ (2b + 1)(b - 4) x-2 14. a. _ x + 18 4. -y(4y2 - 5)(y - 2) b. about 60% 5. 3(a + 3)(a - 3) 6. (2x - 1)(2x + 4) 2(x - 1) 15. _ 5(x + 9) 7. (9x + 16)(x - 2) 16. 16 8. -96 < x < 96; 17. Sample: Factoring makes it easier to simplify complicated expressions. -96 -48 0 48 96 9. Sample: x can be any value that is 54 or more units from 0. 18. a. 2(2 + y) 10. Sample: No matter what I substitute for x, its absolute value is going to be greater than -5 because absolute value is always positive. 11. B 12. 8.24 ≤ t ≤ 8.84 8.24 8.44 8.64 8.84 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. b. 2 + y 19. Student B; Sample: Student A used the wrong values for a and b. The equation in standard form is 2 y = 2x + 8x, so a = 2 and b = 8. 20. 29.25 feet in 1.5 seconds LSN 91–2 Saxon Algebra 1 Lesson 91 21. 0.364 mile 22. 12.6 feet 23. 5.3 24. above; 342 - 72 > 332 25. 16 y 12 8 4 x -4 -2 2 4 26. (am + bn)2 27. x ≥ 3 and 5x ≤ 40; 3≤x≤8 28. a. y = 20 b. x = 0 c. 120 29. width = (4x + 1), length = (x + 2) or width = (x + 2) and length = (4x + 1) 10 30. 12 √ © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 91–3 Saxon Algebra 1 Lesson 92 Warm Up 92 1. reciprocal 2. 4(x - 4) 3. 18x2 4. (x + 7)(x - 11) 5. 2(3x + 1)(3x + 1) Lesson Practice 92 x2 a. _ 12(x - 3) 1 b. _ 2d c. 12x 1 + 5m d. _ 2-x 3 miles per minute e. _ 3 x © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 92–1 Saxon Algebra 1 Lesson 92 x2 + x 9. _ miles per minute 30 Practice 92 2 5x (x - 6) 1. _ (x + 4) 10. D 2. x + 6 11. -65 < x < 65; -65 -32.5 3. r < -2 2 4. y < _ 3 x 5. _ 30 5 6. 48 √ 7. Sample: when the denominator equals zero 0 32.5 65 12. Student B; Sample: Student A did not realize that an absolute value can never be less than -4 because absolute value is always positive. 13. 7 < s < 39; 2 8x y ______ 7 15a2b 8. Sample: _ 2xy 5ab4 5ab4 _ 2xy 2 15a b 2 4 15 · 2 · x · y · a2 · b 3 4b x =_ 3a and 4 8x y · 5ab _ 15a2b · 2xy 2 31 39 b. 65 ≤ x ≤ 95 8·5·x ·y·a·b = __ 2 23 14. a. ⎪x - 80⎥ ≤ 15 _____ 8x y · =_ 2 15 4 40x yab =_ 2 30a bxy 15. Student A; Sample: Student B did not fully distribute the negative sign through the numerator of the second expression. c + 42 16. __ (6 - c)(6 + c) 17. B 4b3x _ = 3a © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 92–2 Saxon Algebra 1 Lesson 4 21. _ f+8 18. Sample: One way is to use the zeros of the function. The axis of symmetry goes through the zero when there is 1 zero because the zero is contained in the vertex. It goes through the average of the 2 zeros when there are 2 zeros. The second way is to use the b formula x = -_ . This 2a is the only way to find the axis of symmetry when the function has no zeros. 22. yes 23. about 83 miles 24. Student B; Sample: Student A did not distribute the negative sign correctly. 1 25. _ 3 26. a. 2(x - 3)(x - 1) b. Sample: The length is (x - 1) and the width is (x - 3). 27. -15 ≤ t < -5 19. Answers will vary. Accept any function that can be written in the standard form of a quadratic function and any function that cannot. Students should explain that they must be able to write the function in standard quadratic form for it to be quadratic. 20. 10.5 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 92 28. a. length: 2x + 2, width: 2x - 2 b. 4x2 - 4 c. x4 - 4x2 + 4 = (x2 - 2)2 29. h = -16t2 + 14,400; 16(30 + t)(30 - t) 30. In the equation, r is jointly proportional to s and t, and inversely proportional to p. LSN 92–3 Saxon Algebra 1 Lesson 93 Warm Up 93 1. polynomial 2. 9x - 1 3. 3x 4. (2x + 3)(x - 1) 5. (5x + 3)(5x - 3) Lesson Practice 93 a. x2 + x - 12 b. x - 5 c. -3x - 1 d. x2 + 10x 5 e. 6x2 + 9x + 19 + _ x-2 336 f. 5x2 + 20x + 86 + _ x-4 g. (x-6) feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 93–1 Saxon Algebra 1 Lesson Practice 93 93 11. (x - 9) feet 12. A 1. 13 2 ; 2. y ≥ _ 5 -1 0 1 3. 2(x + 4)(x + 2) 4. (3x - 5)(x2 - 3) 2 5. (2x + 21x - 1) 13. Student A; Sample: Student B did not write solution in simplest form. 21x2 miles per minute 14. a. _ 4 21x3 b. _ miles per minute 4 6. x = 1 7x2 7. _ 2 3(m + n) 15. _ inches 2 2 1 8. _ 2 16. x < -84 OR x > 84 9. Sample: Multiply the divisor by the quotient. The product should equal the dividend. 10. Method 1: (x - 2)(x + 2) x2 - 4 _ _ = x+2 (x + 2) = (x - 2) Method 2: x-2 x + 2 x2 + 0x - 4 ____ -x2 - 2x -2x - 4 +2x +4 ____ 0 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. m +n -84 -42 0 42 84 17. ⎢x - 52,041,916 ≤ 104,000; 51,937,916 ≤ x ≤ 52,145,916 18. Student A; Sample: Student B did not realize that all absolute values are greater than -15. 19. D LSN 93–2 Saxon Algebra 1 Lesson 26. a. (1, 240), (2, 192), (3, 112) 20. Sample: Multiply either of the expressions -1 by _ because b. -1 y 240 -1(3 - r) = -3 + r = r - 3, or -1(r - 3) = -r + 3 = 3 - r. 21. 93 180 120 60 3 _ 5 x O 1 22. Student A; Sample: Student B did not multiply by the reciprocal of the rational expression. 2 3 4 c. about 4 seconds 27. about 2 sec 4 y 3 23. 2b(9 + 2b) dollars 2 24. x = -2; y = 0 O 1 y 8 4 x O 4 8 -4 -8 25. s + 3 centimeters © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. x 1 2 3 4 28. Sample: Substitute 5 for a, 7 for b, and 10 for c in the equation a2 + b2 = c2 and simplify the equation. If the equation is true, then the triangle is a right triangle. If the equation is false, then the triangle is not a right triangle. LSN 93–3 Saxon Algebra 1 Lesson 93 7 1 _ 29. _ = 14 2 30. k = 3 y 1 3 6 9 2 x 1 2 4 6 8 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. z 3 2 2 2 12 LSN 93–4 Saxon Algebra 1 Lesson 94 Warm Up 94 1. absolute value 2. 4 3. 11 4. x = 3 5. x = 3 Lesson Practice 94 a. {56, -56}; -56 -28 0 28 56 3.5 7 b. {7, -7}; -7 -3.5 0 c. Ø d. {3, -3} e. {5, -5} f. {4, -6} g. {12, -8} h. 18 items, 22 items © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 94–1 Saxon Algebra 1 Lesson Practice 94 94 6. Sample: The droplet is at ground level when y = 0. This first occurs at 0 seconds, before the water has shot out from the sprinkler. The maximum value b = occurs at x = - _ 2a 80 _ - -32 = 2.5. Because of symmetry, the droplet is at ground level 2.5 seconds before and after its maximum point, so it hits the ground 5 seconds after it shoots up. 1. m + 4 w + 11 2. _ w+5 3. Sample: An absolute value cannot be negative, so any absolute-value equation that sets an absolute value equal to a negative number has no solution. 4. D 2 30(x + 4x + 4y + xy) dollars 5. __ y 7. 2(a + 3)(a + 4b) 8. zx8(x - 7)(x + 3) 9. (b - 4)(b + 2) 10. Student B; Sample: Student A did not put the dividend in descending order or insert a placeholder. 1-x 11. _ 5 x x+4 12. _ 9x 13. $5, $15 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 94–2 Saxon Algebra 1 Lesson 14. 4x3 - 8x2 + 6x - 12 25 +_ x+2 22. Sample: ⎪0 - 14⎥ = ⎪-14⎥ = 14 and 14 < 30 15. (5x - 1)(x + 1) 23. C 16. {-66, 66}; -66 -33 0 33 94 24. (y2 - y1)2 66 17. Sample: Subtract 1 from both sides to get ⎪x⎥ _ = 4. Then multiply -3 both sides by -3 to get ⎪x⎥ = -12. Because absolute values cannot be negative, there are no solutions. 92 18. a. x2 - 8x - 1 - _ x+6 ( 8 3 15.5 _ _ 25. a. _ + = r 2.5r 2.5r b. 3.1 hours 26. x = 2; y = -4; y x -2 4 -2 -6 ) 27. a. 12 + 0.06m > 15 + 0.04m feet b. (x - 6) feet b. m > 150; 150 minutes 19. 4y centimeters 20. Student B; Sample: Student A did not multiply by the reciprocal. c. 28. 40 50 100 150 200 ; y 30 x3 - 5x2 miles per minute 21. _ 6x 20 10 x O 1 2 3 4 about 5 feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 94–3 Saxon Algebra 1 Lesson 94 29. a. 25 √ 3 ft b. 136.6 ft 30. The volume of a sphere is directly proportional to the cube of its radius. The constant of 4 π. variation is equal to _ 3 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 94–4 Saxon Algebra 1 Lesson 95 Warm Up 95 1. factor 4 2 2. 24x y 3. 36(x - 3) 4. (x + 7)(x - 3) 5. (5x - 1)(2x + 3) Lesson Practice 95 a. LCD = 5(x - 9)(x + 9) b. LCD = (x + 4)(x - 2) 2 13x + 4x - 5 c. __ 4(x - 5)(x + 5) 3 2 x + 4x - 9x + 12 d. __ 3(x - 4)(x + 4) 7 e. _ 5(x + 1) 1 f. _ x(x - 6) 40x + 96 g. __ miles 7(x - 8)(x + 8) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 95–1 Saxon Algebra 1 Lesson Practice 95 1. 3x(x + 2)(x - 5) 2 2 2. 4xy(2x y + x - 3y ) 3. 4x3(x - 2)(x - 4) 4. mn(n - 6)(n - 4) 5 5. _ 51m 12. Sample: Factor each denominator. The LCD must contain each factor of each denominator and use each factor the greatest number of times it occurs in either denominator. 7x2 + 9x - 10 miles 13. __ 2(x + 10)(x - 10) 6. (x - 8) 25x2 + 176x 14. a. __ 2(x - 7)(x + 7)(x + 8) 7. no zeros meters 25x + 176 minutes b. __ 4(x - 7)(x + 7) 8. LCD = (x + 4)(x + 2) x2 + 6x + 40 9. __ (x - 8)(x + 8)(x + 1) 10. {-4, 4}; -4 95 0 4 11. Student A; Sample: Student B didn’t distribute the negative all the way through the second numerator. 15. Student B; Sample: Student A did not isolate the absolute value and assumed that because the equation was equal to a negative number, the absolute value would be equal to a negative number. 16. 8 inches, 9 inches 17. a. ⎢5 + 5x - 35 = 2 b. $5.60, $6.40 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 95–2 Saxon Algebra 1 Lesson 18. Student B; Sample: Student A canceled terms that were not common factors. 2 95 2 27. Sample: 8a b + 4a + 12ab + 16ab2; 4a(2ab + a2 + 3b + 4b2) 19. (x - 9x) feet 28. 1 second; 265 feet 3 4 _ 1 _ · = 2 · 20. Sample: _ 2 9 3 4 · 3 2 12 2 _=_=_ and =_ 2·9 3 18 3 15(2x - 5) hours 29. _ x(x - 5) 3 1 30. _ 10 21. A 22. x < -17 or x > 17; -20 -10 0 10 20 23. 15.5 ≤ x ≤ 15.7 24. a. 65 degrees up or 55 degrees down b. heat: t ≤ 110 minutes; cool: t ≥ 120 minutes c. To heat up the stew is faster. 25. 55.9 meters 26. a. PQ = 89 pixels, QR = 77 pixels, PR = 94 pixels −−− −− −− b. QR, PQ, PR © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 95–3 Saxon Algebra 1 Lesson Warm Up 96 96 d. -5 1. axis of symmetry e. 2, 5 2. -6 f. no real zeros 3. -20 g. 1.5 seconds 4. x = 1 3 5. x = _ 2 Lesson Practice 96 a. y 6 4 2 -4 b. -2 24 x O 4 y 16 8 x O 4 8 -8 c. y 8 4 x -4 4 -4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 96–1 Saxon Algebra 1 Lesson Practice 96 11. Sample: -b 24 _ x=_ = = 3. Then, 2a 8 1. 0 and 4 2. substitute 3 into the equation to get 4(3)2 - 24(3) + 9 = -27. 50y3 + x3 _ 32x2y4 3. Ø; no graph 4. n = 22 12. A 5. x = 23 13. 7 feet 6. LCD = (x + 6)(x + 2) 14. A 7. function -4 yards 15. _ 3(x + 2) -4 8. _ 4 x3 + 2x2 - 12x + 15 16. __ yards 3(x - 2)(x + 2) 15x 9. -4 96 O y x 2 17. 90 ≤ x ≤ 310; -2 90 -4 -8 10. Sample: The second point will have the same y-value and will be the same horizontal distance from the axis of symmetry, but on the other side. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 145 200 255 310 18. Sample: It helps line up like terms for the dividend and quotient. 19. B 20. 45 miles per hour; 55 miles per hour 21. Student A; Sample: Student B graphed all values between -9 and -1 in addition to the solution set. LSN 96–2 Saxon Algebra 1 Lesson 96 0.3125x2 22. __ (x - 8)(x - 10) 5ac ; d = 18 29. k = 5; d = _ b x(3x + 2) 23. _ ; Sample: 9(y + 2) 30. no; If (x + 10)(x - 2) is multiplied, the result is x2 + 8x - 20. Changing the signs to (x - 10) (x + 2) would produce the correct factorization. Substitute real numbers for the variables x and y before and after dividing. 24. a. 2x(3x2 + 7x + 2) b. 2x(3x + 1)(x + 2) 25. 100 feet 26. a. 4 cm b. 6b + 5 c. 29 cm; 841 cm 2 27. sometimes true; It is true for all negative values of x. 6 1 _ = , 28. P(red) = _ 24 4 2 1 P(green) = _ =_ , 24 12 8 1 _ = , P(yellow) = _ 24 3 5 , P(blue) = _ 24 2 1 _ = , P(orange) = _ 24 12 1 P(purple) = _ 24 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 96–3 Saxon Algebra 1 Lesson Warm Up 97 97 f. 1. slope-intercept form 1 ; y-intercept 2. slope is - _ 3 is -5 g. 3. slope is -1; y-intercept is 3 4. -2 0 2 5. -2 0 2 4 h. y ≤ 4 i. y > x - 5 Lesson Practice 97 j. 15x + 5y ≤ 25; a. yes y b. no 4.00 2.00 c. yes O d. 4 x 0.5 1 1.5 y 2 x O -4 2 4 4 8 -4 e. 8 y 4 -8 -4 O x -4 -8 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 97–1 Saxon Algebra 1 Lesson Practice 97 17 5y 1. _ 2 x 2. 0.5q √r 3. (4g2 + 9)(2g - 3) 4. 59 3 2 5. 8x - 28x + 16x - 56. 1 6. _ x+4 -x2 - 2x - 2 miles 7. __ (x + 1)(x + 1) 8. (x - 7) 9. 3 ≤ x < 4; 1 2 3 4 5 6 10. x < -48 or x > 48; -40 -20 0 20 40 97 14. Sample: All the points that are on a solid boundary line and all the points that fall in the shaded half-plane satisfy the inequality. 15. Sample: Choose a test point and evaluate the inequality for that point. If the point satisfies the inequality, shade the half-plane that contains that point. If it does not satisfy the inequality, shade the remaining half-plane. 16. B 11. never true 17. 5x + 3y ≥ 9000 12. Yes, it satisfies the inequality. 18. Student B; Sample: Student A did not substitute the x-value into the original equation to find the y-value. 13. 10 y x -8 -4 -10 -20 -30 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 19. 4 inches LSN 97–2 Saxon Algebra 1 Lesson 20. a. 0 97 24. C 27. Sample: When the vertex is on the x-axis, there is 1 zero. When the vertex is not on the x-axis, the related function could have either no zeros or 2 zeros. There are no zeros when the vertex is above the x-axis and opening upward, or below the x-axis and opening downward. There are 2 zeros when the vertex is above the x-axis and opening downward or below the x-axis and opening upward. 18x2 + 3x + 1 miles 25. _ 50 x2 _ 28. 2 b. Sample: The ball starts on the ground. c. -155 feet d. Sample: After 5 seconds, the ball has already landed. It cannot have a negative height. -1 miles 21. _ 2 2x 22. A 23. Sample: ⎢3 (-11) - 2 = ⎢-33 - 2 = 33 - 2 = 31 per minute 19 21 ≤ x ≤ 95_ 26. 95 _ 32 32 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 12y 125 29. _ days x(x + 30) LSN 97–3 Saxon Algebra 1 Lesson 97 30. a. A = πx2; A = 9πx2 b. 8 y 6 4 2 x O 1 2 3 4 c. Sample: The graph of the area of the larger circle is much narrower. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 97–4 Saxon Algebra 1 Lesson 98 Warm Up 98 1. zero of a function 2. (x + 11)(x - 8) 3. (3x - 5)(2x + 1) 4. (2x + 7)(2x + 7) 5. 3(2x + 3)(2x - 3) Lesson Practice 98 a. 3, -7 b. 3, -6 3 , -5 c. - _ 2 d. 3 ⎧ e. ⎨0, ⎩ 3⎫ _ ⎬ 5⎭ ⎧ 4 _ 4⎫ , f. ⎨- _ ⎬ ⎩ 5 5⎭ g. The width is 10 feet, and the length is 36 feet. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 98–1 Saxon Algebra 1 Lesson Practice 98 1. 1 _ < x < 5; 2 -2 0 2 4 2. -6.1 ≤ x ≤ 6.1; -6.1 0 12. Sample: The Zero Product Property 13. A 14. The mother is 36 years old and the girl is 9 years old. y 6 x -4 11. Sample: If two numbers multiplied together equal 0, then at least one of the numbers has to be 0. 6.1 3. difference of two squares; (3x + 11)(3x - 11) 4. 98 2 4 15. a. 20x + 10y ≤ 70 -2 b. y 4 3 5. S = 35x + 28x - 24 -8 4 2 _ x + 6. Sample: y = _ 3 3 -4 O x 8 -4 -8 7. {18, -18}; -18 -9 0 9 c. Sample: 3 pairs of jeans and 1 pair of shorts 18 6 8. _ 5 9. 225y4z2 16. 10. no; It does not satisfy the inequality. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 98–2 Saxon Algebra 1 Lesson 17. -4, 9 18. Student A; Sample: Student B wrote an inequality with a solid horizontal line. 19. x5 miles per minute 20. 8x - 12 meters 21. x(x + 5)(x + 1) dollars 27. a. __ 100 b. $1402.50 28. a. x(x - 9) = 36; Sample: The formula needs to be set in the form ax2 + bx + c = 0 in order to solve for x. 230 (x2 + 5x + 45 + _ x - 5) b. 12 feet long and 3 feet wide. inches 22. Sample: No, the LCD is found in addition and subtraction problems so that parts of equal size can be added or subtracted. 4x2 + 36x + 48 miles 23. a. __ 3(x + 9)(x + 3) x2 + 9x + 12 b. _ hours 3x(x + 9) 24. 36 feet 25. Student B; Sample: Student A found the y-intercept. 26. a. 23 cm; 17 cm b. 28.6 cm © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 98 29. Sample: Distribute the negative sign so that you are subtracting x and adding 6 to x2 - x - 30. Then combine like terms to get x2 - 2x - 24. Finally, try to factor out x + 5 from the numerator. Since you can’t, your answer in simplest form x2 - 2x - 24 is _ . x+5 30. No. A sign error has occurred; The correct expression would be 32x2 - 20x - 42. LSN 98–3 Saxon Algebra 1 Lesson 99 Warm Up 99 1. rational expression 2. 21x2y3 3. 9x(x - 2) 4. (x + 3)(2x - 1) 5. 35(2x - y) Lesson Practice 99 a. x = -6 b. x = 2, -6 c. x = 2 14 d. x = - _ 5 e. x = -12 1 hours f. 1 _ 5 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 99–1 Saxon Algebra 1 Lesson 99 1. x = 4 12. 6x4 + 12x3 + 24x2 + 66x 144 + 132 + _ x-2 2. {13, -22} 125 13. _ 27 Practice 99 3. 1.8 hours, 2.2 hours 4. Sample: y = (2)2 + (2) - 12 = -6 4x2 - 13x - 15 __ 5. 24 6. (4x + 5)(x - 1) 7. y = 180 - 2x; 164 pounds 8. Sample: It is an answer that solves the transformed equation, but not the original one. 9. LCD = 2(x - 6)(x + 6)(x + 7) 10. (50, 2.05); The population reached its maximum of about 2,050,000 people in 1950. 11. a. (7, 3) b. (6, 6) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 14. Sample: If it would cause one of the denominators to equal 0, the solution is extraneous. 15. C 24 hours 16. _ 7 17. Student A; Sample: Student B has the incorrect signs on both solutions. 18. The base is 4 centimeters and the height is 12 centimeters. 19. a. 2x - 2 and x - 2 b. 10 feet c. 20 feet 20. Sample: There is no solution when the absolute value is less than 0 because it would be a negative number. LSN 99–2 Saxon Algebra 1 Lesson 28. 21. (x - 8) feet y 4 22. C 2 158 3x - 12x + 40 - _ x+4 ( 2 x O 23. 3x + 2y ≥ 200 24. 99 -4 2 4 -2 ) 29. s + 8 inches kpq 25. Student A; Sample: Student B wrote an inequality with a dashed vertical boundary line. 26. 4 30. j = _ mn y 2 x O -4 -2 2 4 -2 -4 9 36 27. a. _ =_ x 0.25x b. Sample: The expression for the 12 street time, _ x , would be multiplied .5 .25 instead of _ , by _ .5 .25 making the simplified 12 24 _ = expression _ x . .5x © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 99–3 Saxon Algebra 1 Lesson 100 Warm Up 100 1. parabola 2. 11 3. -1 4. upward 5. downward Lesson Practice 100 a. x = 7 and x = -7 b. no solution c. x = 5 d. x = 8 e. no solution f. x = -0.8 and 1.2 g. t = 1.10 seconds © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 100–1 Saxon Algebra 1 Lesson Practice 100 8. no solution 11 1. 0, _ 2 9. x = 21 2. x = -3 3. Sample: The path creates a parabola that opens downward. The maximum point on the parabola shows the maximum height. The positive zero shows the time that the ball hits the ground (when height is zero). 4. Sample: The graph does not cross the x-axis when there is no solution. The graph has its vertex on the x-axis when there is one solution. The graph crosses the x-axis two times when there are two solutions. 10. P(black, black, 6) 1 2 _ 1 · 1 =_ = _ (2) 7. B © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 6 24 11. 4 units 12. a. t + 0.5 b. 1 hour 30 minutes c. 2 hours 13. (a + 12) 2 14. 7y √y 15. 80 objects,100 objects 16. 320 points, 360 points 17. {-9, 9} 2 -2x + 54x + 3 miles 18. __ 7(x - 3)(x + 6) 19. 5. k = 2 6. h = 7.77 feet and t = 0.92 seconds 100 28 -4 -2 O y x 2 4 20. Sample: Shade the halfplane to the left of the vertical line. LSN 100–2 Saxon Algebra 1 Lesson 21. D 100 29. no; Sample: If there are no common factors, the expression is in the simplest x2 - 4 __ = form; 22. The boy is 2 years old and the father is 25 years old. 23. Student B; Sample: Student A did not put the equation in standard form before factoring. 2x 2 + 12x + 18 (x - 2)(x + 2) __ 2(x + 3)(x + 3) 30. $250,000 24. downward 25. yes 2 26. a. 3x(x + 4x + 3) b. 3x(x + 1)(x + 3) c. 3x, x + 1, x + 3 60(13x - 80) 27. _ x(x - 10) 28. a. x - 120 ≤ 5 b. 115 ≤ x ≤ 125 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 100–3 Saxon Algebra 1 Lesson Warm Up 101 101 g. ⎢w - 21 ≤ 1; 20 ≤ w ≤ 22; 22 ounces 1. inequality 2. -4 3. 26 4. x > 8 5. x ≤ -5 Lesson Practice 101 a. -5 < x < 5; -5 0 5 b. x ≤ -28 OR x ≥ 28; -30 -20 -10 0 10 20 30 c. -2.5 < x < 2.5; -2 0 2 d. 2 ≤ x ≤ 16; 0 4 8 12 16 e. -24 < x < 4; -20 -10 0 f. x < -1 OR > 3; -4 -2 0 2 4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 101–1 Saxon Algebra 1 Lesson Practice 101 8. a. h = 9.1 feet b. t = 0.82 seconds 1. x ≤ -1 or x ≥ 1; -4 -2 0 2 c. t = 0.06 seconds 4 3 10. t = 7.09 seconds 11. x = -3 12. {-3, 3} 3. Sample: (1) Subtract 11 from each side. (2) Multiply each side by 2. (3) Rewrite as a compound inequality. 2 6pt pw w _ _ + 4. _ 2 3 2 wm 2 9. 18w (1 - 8w ) 2. Student A; Student B did not isolate the absolute-value expression before removing the absolutevalue bars. 4ptm 101 13. -(r + 2) miles 3x - 4 14. __ (x - 3)(x - 2) 15. 42 feet 16. 27 years 17. Yes, it satisfies the inequality. t 5. AND 18. Sample: 3 3 _ 4·_ 3 5 · +7 4 4 6. ⎢t - 475 ≤ 9; 466 ≤ t ≤ 484; 484°F 7. Student A; Sample: A parabola can cross the x-axis once, twice, or not at all. )( ( ) 43 =0 _ =0 4 ( ) 19. D 20. x = -6, 11 21. upward 2 hours 22. _ 3 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 101–2 Saxon Algebra 1 Lesson 101 23. Student A; Sample: Student B did not check to see that -2 is an extraneous solution. 24. no 25. no 3 ; Sample: 26. c. _ 2 5xy simplifying before multiplying, because I can cancel out like terms before needing to multiply anything 27. 974.5 ≤ x ≤ 974.7; 974.5 974.6 974.7 6 28. a. _ miles per hour 7x 6x miles per hour b. _ 7 5 29. _ 2 3x + 7x + 8 30. f(x) = x 2; Its graph is a parabola opening upward with its vertex at the origin, (0, 0). © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 101–3 Saxon Algebra 1 Lesson 102 Warm Up 102 1. square root 2. 9 3. -5 6 4. 2 √ 3 5. _ 7 Lesson Practice 102 a. x = ±9 b. no real solution c. x = ±7 d. x = ±5 e. x = ±8.485 f. x = ±3.464 g. 10 seconds © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 102–1 Saxon Algebra 1 Lesson 3 Practice 102 102 2 10. -7x + 48x + 14x - 49 2 4 1. 144p q 11. y 20 2. 392 3. Student B; Sample: Both have worked the problem correctly, but Student A did not realize that a negative measurement is impossible in this situation. -4 b. x = 120 ft x O 2 4 -10 12. 14 feet 13. a. -189.3 < t < -186 -190 -188 -186 b. -186°C; -189.3°C 2 4. a. x = 12,600 + 1800 -2 14. a. (x + 5) 2 b. (x + 5)(x - 5) c. 480 ft 15. 5. 6% 8 y 4 x O 6. true -8 -4 4 8 -4 7. 26.077 km -8 8. -21 < x < 21; -20 -10 0 10 16. 2x + 10y ≤ 40 20 9. a. -5 ≤ x ≤ 3 b. 1 ≤ y ≤ 7 c. (-5, 7), (3, 7), (3, 1), (-5, 1) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 17. {0, -12} LSN 102–2 Saxon Algebra 1 Lesson 1 18. Sample: _ = 1-1 3 3 1 _ ;_ =_ , which is 2(1) - 2 0 102 b. 16 feet long and 9 feet wide. 0 undefined. This shows that 1 is an extraneous solution. 19. B 5m - 4 20. __ 3(m + 2)(m - 2) 21. Student A; Sample: Student B wrote an equation that forms a parabola that crosses the x-axis twice, so it has two solutions. 22. h = 10.25 feet and t = 0.93 seconds 23. no solution 24. (3, -3) 2 25. (-3y + 5)(y + 3z) 26. a. x(x + 7) = 144; Sample: the formula needs to be set in the form 2 ax + bx + c = 0 in order to solve for x. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 27. no 2 20x - 23x + 81 28. __ 6 miles per minute 29. a. (x - 8) feet 2 b. x + 6x - 16 feet 30. Sample: When the operations are on the inside, write two equations to represent the absolute-value equation and solve them. When the operations are on the outside, isolate the absolute value first, then write two equations to represent the absolutevalue equation and solve them. LSN 102–3 Saxon Algebra 1 Lesson 103 Warm Up 103 1. radicand 6 2. 5 √ 3. 18 √2 3x 4. 4x √ 5 5. 6 √ Lesson Practice 103 √ 15 a. _ 3 √ 11x b. _ x 2 x √ 2x c. _ 3 15 + 3 √ 6 3 √ 6 15 _ _ d. _ or + 19 19 19 √ √ 7+ 1 7 1 _ e. _ or +_ 2 2 2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 103–1 Saxon Algebra 1 Lesson Practice 103 13. 1. 5 √7 103 y x O 4 -4 2. x = -7, 8 -4 3. Student A; Sample: Student B did not use a conjugate to rationalize the denominator. 1000 √ 21 ft/s 4. _ 21 14. Student B; Sample: Student A did not reverse the inequality symbol when dividing each side by -12. 5. 160 15. 126 6. no; Sample: The radical in the denominator needs to be rationalized. 16. 5 1 _ ≤ ; ⎪d - 2 _ ⎥ 16 16 3 3 1 _ _ 2_ ≤ d ≤ 2 ; 2 4 8 8 inches 239 7. √ 17. 20 8. a. 15 units y 10 b. 225 square units -4 -2 O x 2 4 c. 5 9. ≈4.243 seconds 10. (4, 3) 18. It is on the ground at 0 and 4 seconds. 11. false; The correct -1 . answer is ±5 √ 19. 70, 100 20. Sample: zeros or roots 12. -3 ≤ x ≤ 3 -4 -2 0 2 4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 21. D LSN 103–2 Saxon Algebra 1 Lesson 22. (2xy - 7yz)(x + 2) 28. Write each term in the numerator separately over the common denominator, and then simplify, if possible, to 4y 2y 5 5 or _ - _ . get _ - _ 9ab 23. _ 10 24. yes 300 ; 25. a. west: _ 230 + w east: 103 6 220 _ ; Sample: 230 - w The numerators represent distance and the denominators represent rate. Add the wind speed to the rate when the plane is going with the wind and subtract it from the rate when the plane is going against the wind. 119,600 - 80w b. __ (230 + w)(230 - w) 6 3 6 29. It cannot be factored. The only whole-number factors of 1 are ±1, and neither will produce a middle term of x. 30. narrower c. Sample: the total time the plane flew in both directions 26. (x - 9) feet 27. a. ⎢2(8 + 10x) - 66⎢ = 10 b. 2 hours, 3 hours © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 103–3 Saxon Algebra 1 Lesson 104 Warm Up 104 1. perfect-square trinomial 64 2. _ 9 3. 11 4. x = -3 5. x = 9 Lesson Practice 104 a. x2 + 24x + 144 b. x = 2 or x = -4 c. x = -1 or x = 15 7 or d. x = -4 + √ x = -4 - √ 7 ; -6.646 or -1.354 e. Ø f. h = 2 cm, b = 10 cm © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 104–1 Saxon Algebra 1 Lesson 104 Practice 104 1. 2500 2. 169 3. D 4. 2 6x - 12x = 18 2 x - 2x = 3 x 2 - 2x + 1 = 3 + 1 (x - 1) 2 = 4 (x - 1) 2 = ± √ 4 √ Add 18 to both sides. Divide both sides by 6. Complete the square. Write in factored form. Take the square roots. x - 1 = ±2 x = -1 or x = 3 Solve both equations. To check substitute each value into the original equation. 6(-1) 2 - 12(-1) - 18 = 0 AND 6(3) 2 - 12(3) - 18 = 0 6 + 12 - 18 = 0 54 - 36 - 18 = 0 0=0 0=0 5. width: 3 in.; length: 8 in.; height: 3 in. 6. √ 33 _ 11 10. 3 in. × 3 in. 11. r ≈ 2.449 m 3 7. _ 14 A _ 8. a. r = √ π b. r = √ 47 9. _ 6 7A _ √ 22 √ 231 c. _ 11 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 12. Student A; Sample: Student B didn’t correctly factor the GCF of -3 in the second denominator. LSN 104–2 Saxon Algebra 1 Lesson 104 26. a. ⎪x - 3000⎥ ≤ 200 13. x = 0 ⎫ ⎧3 , -8 14. ⎨ _ ⎬ ⎩4 ⎭ 15. x = ±10 b. 2800 ≤ x ≤ 3200 27. 1 second 16. _ 2 (-1, _72 ) 28. 200 minutes, 400 minutes 60 hours 17. _ 11 18. x = 9 19. 25 feet 20. a. -10 ≤ x ≤ -4 b. Sample: x = -5: -8⎪-5 + 7⎥ = -8⎪2⎥ = -8 · 2 = -16 -16 ≥ -24; x = -7: -8⎪-7 + 7⎥ = -8⎪0⎥ = -8 · 0 = 0 0 ≥ -24 29. Sample: The common denominator should be xb. Also, you have to have like denominators to be able to add the numerators without writing equivalent fractions. 30. Sample: It only has one zero when its vertex is on the x-axis. 21. B 22. -6 and 2 2 3 35xy + 15y 23. _ 2x 24. 36y2 - 9 2 25. 4(x + 4)(x + 2)(x - 2) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 104–3 Saxon Algebra 1 Lesson 105 Warm Up 105 1. sequence 2. -32 3. 81 4. 2.4 1 5. _ 27 Lesson Practice 105 a. 8 1 b. -_ 3 c. 7 d. 405, -1215, 3645, -10,935 5 1 1 _ _ , 5 , 2 e. 21, 10 _ 2 4 8 f. -3072 1 g. - _ 8192 h. -544 i. 13.1072 16 j. _ 135 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 105–1 Saxon Algebra 1 Lesson Practice 105 105 9. a. (x + 4)(2x + 4) = 880 1 1. - _ 4 b. x2 + 6x = 432 2. B c. 18 ft 3. $7414.80 d. 232 ft2 4. no; Sample: The formula to find the third term of a geometric series is A(n) = ar 2. If the first term is not 0, then the only way any term of the series could equal 0 would be if r = 0. Since the second term is not 0, this cannot be true. So the sequence cannot be geometric. 13. Student B; Sample: When rationalizing the denominator, Student A did not multiply by a factor of 1. 1 , 5. a1 = _ 2 15 meters 14. _ 2 1 an = an-1 + _ ; 2 1 1 _ , 1, 1_ ,2 2 6. or 12. base = 24 units; height = 10 units { _17 , -_32 } 12 16. _ hours 7 5(-11) n-1 17. 841 7. 81 8. no; Sample: The correct value is 196; 14 is the constant value in the factored form. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. √ 14 11. _ 2 15. 2 5(11) n-1 1 10. _ ,x≠0-2 2x 18. h = 6.56 feet and t = 0.83 seconds 19. t = 5.26 seconds LSN 105–2 Saxon Algebra 1 Lesson 20. x < -3.5 or x > 3.5; -4 -2 0 2 29. a. 0 feet b. Sample: the height the ball was thrown from 4 21. false; The correct answer is ±4. 22. Student A; Sample: Student B made a transformation error when attempting to isolate the variable and arrived at the wrong answer. 105 c. Sample: 48 feet below the top of the cliff 30. Sample: < and > are graphed with dashed lines and ≤ and ≥ are graphed with solid lines. 23. (0, 0); maximum: 0 24. 1 25. x = 1 4 miles per minute 26. a. _ 3 x 4 b. _ miles per minute 2 x 32x2 - x + 2 27. __ miles 4(x - 2)(x - 9) 28. (-2, 7) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 105–3 Saxon Algebra 1 Lesson Warm Up 106 1. B 106 l. no solution m. 6 yd2 2. 5 3. x + 2 4. x = -2, x = -3 5. x = -2, x = 7 Lesson Practice 106 a. x = 36 b. x = 45 c. x = 141 d. x = 16 e. x = 169 f. x = 49 g. x = 16 h. x = 2025 i. x = 5 j. x = 1 k. x = 6 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 106–1 Saxon Algebra 1 Lesson Practice 106 106 11. x = 104 days 1. x = ±8 12. (5, -3) 2. (x - 5)(x - 4) 13. 243 3. Sample: The sum of three times a number and 4 is less than 10. 14. x = 0.5 or x = -9.5 4. D 5. no solution; When 3 , the radicand x = -_ 2 3 -_ -1 is negative: √ = 2 5 -_ . √ 2 6. x = 16,384; √x _ = 32; √x = 128, 4 multipled both sides by 4; x = 1282, squared both sides; x = 16,384. 15. Student A; Sample: Student B did not divide all terms by 2 in the initial step. 16. 1100 units 17. x = 8; 60 45 15 9 _ +_ =_ +_ 4(8) 5(8) = 8 24 _ 8 8 =3 18. x = 81; √ 81 = 9 19. h = 5.27 feet and t = 0.85 seconds 1 7. -_ 2 20. x = 4 and x = -4 8. 160 21. 1 ; 2 ounces 2 ≤ w ≤ 2_ 6 9. a. 0.75 meter b. 0.75 n c. 0.18 meter 1 1 ≤_ ; ⎪w - 2_ 12 ⎥ 12 22. B 10. 327,680 square feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 106–2 Saxon Algebra 1 Lesson is 23. Sample: Since √145 close to √ 144 , Anton should find the square root of 144 for the numerator (12) and multiply the square root of nine(3) by 2 in the denominator (6). The estimated quotient would be 2. 24. 106 29. Sample: The roots are the opposite of the constant term in each factor. 30. b = -8 2(r + 1) _ r-4 25. 4 ≤ x ≤ 28; 0 10 20 30 26. (9x - 1) feet 27. 10 feet 28. a. 5x + 4y ≥ 2500 b. y 400 O -400 x 400 800 -400 -800 c. yes © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 106–3 Saxon Algebra 1 Lesson Warm Up 107 107 c. (1, 2) y 1. parent function 4 2 2. 16 2 4 -2 3. 16 4. -13, 17 d. Since ⎢a > 1, the graph is stretched vertically. 5. no solution e. Since a < 0, the graph is reflected across the x-axis. Since ⎢a > 1, the graph is stretched vertically. Lesson Practice 107 a. (0, 2) 8 y 4 f. Since a < 0, the graph is reflected across the x-axis. Since ⎢a < 1, the graph is compressed vertically. x O -8 x O -2 -4 4 8 -4 -8 b. (-2, 0) 8 g. f(t) = 2⎢t + 25 y 4 x -8 -4 4 8 -4 -8 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 107–1 Saxon Algebra 1 Lesson x + 5 ) 2 + ( √ x)2 12. a. ( √ Practice 107 = l2 1. down 2. x = 98; 107 b. 2x + 5 = l 2 95 c. x = _ 2(98) √ = √ 196 = 14 2 13. (0, 0), (1, 1) 3. 14x + 5y = 29 14. 0.2, 0.04, 0.008 4. C 5. Sample: The sum of 3 times an unknown 2 is greater than or and _ 5 3 . equal to 1_ 5 6. (50, 30) 9. x = 25 cm 10. Student A; Sample: Student B squared incorrectly and should have subtracted seven from both sides, first. 16. Student A; Student B incorrectly multiplied by 4 rather than using 4 as an exponent. 17. x = -0.6 and 0.7 7. Sample: The absolutevalue function has a minimum value and that is the y-value at the vertex. 8. (-4, 2) 15. about 0.2% 18. x ≤ -2 OR x ≥ 10 -4 19. {∅}; 0 4 -4 -2 8 12 0 2 4 20. ⎢c - 21 ≤ 0.25; 20.75 ≤ c ≤ 21.25; 20.75 inches 21. a. π(r + 3)2 = 200.96 b. r = 5 m c. 16 m 11. (x - 10) feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 107–2 Saxon Algebra 1 Lesson 22. 6 107 y 4 2 x O -4 -2 2 4 -2 23. C 24. c < -625 7(x + 2) 25. _ 24x 2 √ 15 26. _ 3 27. a. ⎢50x - 950 = 100 b. 17 items, 21 items 28. 4x + 6y ≥ 600; y 200 x O 100 29. a. 5 + 2x, 4 + 2x b. 1 inch 30. Sample: cross multiply © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 107–3 Saxon Algebra 1 Lesson Warm Up 108 e. 1. exponent x -2 108 y 2 _ 2. 16 -1 9 2 _ 3 1 3. _ 216 0 2 2 4. _ 25 1 6 5 5. _ 2 2 18 y 6 Lesson Practice 108 4 1 , f(0) = 1, a. f(-4) = _ 16 2 x -8 f(5) = 32 1 , f(1) = -9, b. f(-3) = -_ 9 f. f(3) = -81 c. No, the y-values do not have a common ratio. d. Yes, as x increases by 1, the ratio of the y-values = 3. -4 4 x -2 y -1 -1 0 -2 -4 1 2 -8 -16 8 O y -8 -4 x 4 8 -4 -8 -12 -16 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 108–1 Saxon Algebra 1 Lesson g. x i. Sample: Alike: Both graphs are below the x-axis and symmetic about the y-axis. Different: When b is 3, the y-values decrease as the x-values 1 increase. When b is _ , 3 the y-values increase as the x-values increase. y -2 32 -1 8 0 2 1 _ 1 2 1 _ 8 2 16 108 y 12 j. 8,897,900; 2013 x O -4 -2 2 4 h. Sample: Alike: Both are symmetric about the x-axis. For any x-value, the absolute values of the y-values are the same. Different: When a is positive, all the range values are positive. When a is negative, all the range values are negative. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 108–2 Saxon Algebra 1 Lesson Practice 108 6. Sample: When the ordered pairs are arranged so that the x-values are 2, 3, 4, and 5, then the y-values are -1, -4, -16, and -64; -64 ÷ -16 = 4, -16 ÷ -4 = 4 and -4 ÷ -1 = 4. Because the x-values increase by the constant amount of 1, the common ratio is the value of b. 2 , 2, 50 1. _ 25 2. 4 -4 -2 O y x 2 108 4 -2 -4 3. Sample: Because 1 raised to any power is 1, and 4 would be multiplied by 1 for every value of x, the resulting constant linear function is f(x) = 4 _ _ _ 4. B NV ; ST 7. RS _ and _and _ VQ ; RT and NQ ; ∠R and ∠N; ∠S and ∠V; ∠T and ∠Q 5. 6,002,563 8. f(x) = -⎢x - 2 9. no; Sample: There is no axis of symmetry. 10. -4 11. Sample: The output is the same for x and -x. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 108–3 Saxon Algebra 1 Lesson 12. Student B; Sample: Student A squared the number 3 within the radicand instead of squaring the expression √ x + 3. 100 - 2 13. x = 100; √ = 10 - 2 = 8 14. f(x) = -2⎢x - 2⎢ + 3 25. no; Sample: The absolute values of the terms have a common 4 , but the ratio of _ 5 signs of the terms do not follow a geometric pattern. 26. 3(2x + 5) 29x2 - 8x + 7 miles 27. a. __ 4(x + 7)(x - 7) 15. y = 79.75 29x2 - 8x + 7 _ hours b. 4(x - 7) 16. x = 81 17. -8 < x < 8; -8 -4 0 4 108 8 18. no solution 28. The width is 8 inches, and the length is 11 inches. 19. {-10, -8} 29. a. 9.6 hours 9.6 9.6 +_ =1 b. _ 20. 13 ft × 13 ft c. 24 hours 21a 21. _ b 49 = 12.25 22. _ 4 16 K 30. Sample: It represents the time it takes for the ball to reach that height. 23. C √ 1370 meters 24. _ 12 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 108–4 Saxon Algebra 1 Lesson Warm Up 109 d. 4 y 2 1. inequality x O -4 2. 109 2 4 2 4 2 4 -2 y 4 x O 2 -4 4 e. -2 4 y 2 -4 x O -4 3. solid -2 4. above f. 4 Lesson Practice 109 y 2 x O -4 a. y -2 2 x -4 -2 2 4 g. -4 b. 4 y 2 4 12 8 4 0 -2 y 16 x O -4 20 Pounds of Pineapple -2 x 2 4 6 8 10 Pounds of Strawberries -4 c. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 109–1 Saxon Algebra 1 Lesson 1 6. 27, 3, _ 3 Practice 109 1. A 7. $625 2. x ≥ 9 x ≤ 9.25 y≥5 y ≤ 5.25 2y 8. -15xy √ 3. 4 4 2y √ x 9. _ 2 x 10. Student B; Sample: The x-values do not increase by a constant amount. y 2 x O -4 -2 2 4 1 13. _ 3 4. Sample: Graph y = -3x + 4 with a solid line and shade below the line. On the same plane, graph y = 2x - 1 with a dashed line and shade below it. The solution set is represented by the region where the shadings overlap. 4 y 2 x -4 2 -2 11. $30.06 1 inch, 16 inches 12. 1 inch, _ 4 -4 5. 109 4 -4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 14. No; Sample: It does not make a V. 15. 4 y 2 x O -4 -2 2 4 -2 -4 16. The graph would shift to the left. 17. 48x2 = 6,912; x2 = 144; x = 12. The 12 in square tiles will work best. 18. 2 seconds LSN 109–2 Saxon Algebra 1 Lesson 19. 3.2805, 2.95245, 2.657205 109 22. (x + 12) feet 29. Sample: In both cases, subtract 1 from each side and divide each by 2. When solving 2⎢x + 1 < 7, do these operations before removing the absolutevalue bars, but when solving ⎢2x + 1 < 7, do these operations after writing as a compound inequality. 23. {-9, 5} 30. (3x - 5) 20. C 21. Sample: The equation is easier to solve if the radical is by itself, because squaring the equation then eliminates the radical. 24. no solution 25. {8, 40} 26. a. 36 feet b. 5 feet c. 47 feet per second 4 hours 27. _ 3 28. a. t = 0.97 seconds b. t = 2.14 seconds c. h = 22.02 feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 109–3 Saxon Algebra 1 Lesson 110 Warm Up 110 1. quadratic 2. 16 81 3. _ 4 4. 2, -12 Lesson Practice 110 a. -6 and 3 b. -4 and 18 c. 5 and 16 -1 ± √ 2 ≈ 0.1381 d. _ 3 or -0.8047 e. no real solution f. 3.8648 seconds © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 110–1 Saxon Algebra 1 Lesson Practice 110 11. 4 1. -5, 7 y x O -4 4 -2 2. 5 110 -2 -4 2 3. a. 16h - 40h + 25 = 0 b. Sample: It equals zero. 12. 5x + 15y ≥ 300 ; 10x + 30y ≤ 480 ; 25 y Detail Washes c. when b2 = 4ac 4. 12,000 > 1.2 × 103 5. -6 20 15 10 5 x 0 6. a hyperbola with the x- and y-axes as asymptotes 20 40 60 80 Basic Washes Sample: With these conditions, the goal will never be met because the system has no solutions. 7. 6 8. quadratic formula is -15 ± √ 465 necessary; _ 6 13. ; y 32 Width 9. about 1.6 seconds 10. Student A; Sample: The ordered pair (4, 2) is a solution to one of the inequalities, but not to both of them. 24 16 8 0 x 8 16 24 Length 32 Sample: length 14 units and width 9 units 1 , -3, -108 14. - _ 12 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 110–2 Saxon Algebra 1 Lesson 15. Student B; Sample: Student A should not multiply 2 and 3 because 3 is the base of an exponent. 110 27. a. 14x + 4y ≤ 32 b. 4 y 2 x O -4 2 -2 4 -2 16. Graph A -4 c. Sample: 2 books and 1 magazine √ 6 17. _ 6y 3 2 x + 3x - 4x + 10 18. __ 2(x - 3)(x + 3) 3 √ 6 19. _ 4 20. B 28. h = 14.14 feet and t = 1.03 seconds 29. a. -248.6 < t < -246.1; 21. no real solutions 22. $1567.50, $1638.04, $1711.75, $1788.78 -250 -248 -246 b. -246.1°C; -248.6°C 30. ≈7.249 m 245 + 11 23. x = 245; √ = √ 256 = 16 24. Yes; Sample: Multiplication does not change the absolute value like addition and subtraction do. 25. 6, 18 26. (x + 6)(x + 7) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 110–3 Saxon Algebra 1 Lesson 111 Warm Up 111 1. Theoretical 1 2. _ 2 3. 0 4. independent 5. dependent Lesson Practice 111 a. 8 b. 2592 c. 120 d. 120 e 5040 f. 720 1 g. _ 30,240 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 111–1 Saxon Algebra 1 Lesson Practice 111 7. 111 English Math Outcomes A A B C A-A-A A-A-B A-A-C B A B C A-B-A A-B-B A-B-C C A B C A-C-A A-C-B A-C-C A A B C B-A-A B-A-B B-A-C B A B C B-B-A B-B-B B-B-C 3. 90 C A B C B-C-A B-C-B B-C-C -d 4. _ 3 A A B C C-A-A C-A-B C-A-C B A B C C-B-A C-B-B C-B-C C A B C C-C-A C-C-B C-C-C 1. First Toss Second Toss H H T H T T Third Toss Outcomes H HHH T HHT H HTH T HTT H THH T THT H TTH T TTT History A B 2. A x 5. 4 C 6. -13, 1 8. Sample: Multiply 5 times 4 to get 20 possible outfits. 9. 2, -18 10. 1, 51 11. Sample: The student should have made both lines dashed because the points on the boundary lines are not solutions. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 111–2 Saxon Algebra 1 Lesson 12. 4 21. C y 2 22. Sample: To show that the exponent of x only applies to the value of 3, and not to the product of 5 and 3. x O -4 -2 2 4 13. r = 12 23. irrational, real numbers 14. Student B; Sample: Student A did not substitute the correct values for a, b, and c and did not rearrange the equation correctly. 24. 35 = (-5)(-7) 25. ⎢t - 350 ≤ 9; 341 ≤ t ≤ 359; 341°F 26. a. x + 3, x + 2 15. No. Sample: The formula involves the initial velocity and height. 16. 111 5.91 ≤ l ≤ 6.69 3.54 ≤ w ≤ 4.33 b. 8 inches by 10 inches 27. a. x2 = 21,000 + 1500 b. x = 150 ft c. 301 bulbs 17. 157,700 units 1 _ 1 _ 1 , , 18. _ 27 9 3 19. x = 2916 20. 4 y x -4 2 -2 4 -2 -4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 111–3 Saxon Algebra 1 Lesson 111 28. Sample: First, multiply by a factor of 1 using the conjugate of √ 5 - 7, which is √ 5 + 7. Then use the Distributive Property to multiply across the numerators, and the FOIL method to multiply across the denominators. Finally, combine like terms and simplify. 3 2 2x + x + 49 29. __ (x - 7)(x + 7)(x + 1) 30. g(x) represents exponential growth and f(x) represents exponential decay. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 111–4 Saxon Algebra 1 Lesson Warm Up 112 112 d. (-1, 1.5) and (-2, 3) 1. system e. (1, -3) and (-0.5, -1.5) 2. 2x2 + x - 8 = 0 f. (5, -7) and (-5, 23) 3. y = -4x - 4 g. (-2, -5) and (-3, -7) 4. 0 h. 6 feet 5. A Lesson Practice 112 a. y (-4, 16) (4, 16) 12 8 4 x -4 -2 2 4 y b. 12 (3, 9) 8 4 x -4 -2 2 c. 4 y 12 8 (-3, 9) (1, 1) -4 -2 x 4 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 112–1 Saxon Algebra 1 Lesson Practice 112 1. 7. 216 8. Student B; Sample: 0! = 1, not 0. y (-2, 8) 8 9. a. 9 4 x -4 112 (3, 3) -2 2 4 b. 2; equilateral obtuse triangle and equilateral right triangle 2. C 7 3. _ 2 5 c f 4. -4 < x < 8 10. a. 840 relay teams 4 b. _ 5. (1, 3) 11. 3, -20 6. one; Sample: Because the two linear equations can only intersect at one point, that point must also be the point where they both intersect the parabola. So, the maximum number of points of intersection for all three equations is one. 12. C 7 13. Sample: She’s using measurements, therefore negative values of x are irrelevant. 14. 40 feet by 60 feet 15. -20, 100, -500 16. 4096 √ 5184 72 =_ 17. x = 5184; _ 6 6 =12 18. 11,412,000 people 1 , -2, -32 19. - _ 8 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 112–2 Saxon Algebra 1 Lesson 20. D 21. Sample: The first inequality should have < and the second inequality should have >. 22. 12, -6 23. 8 4 x -8 -4 4 8 -8 t t t 24. a. _ +_ +_ =1 4 3 6 4 hours b. _ 3 c. 80 minutes 112 28. Sample: Divide each term of the quadratic equation by the coefficient of the quadratic term. The coefficient of the quadratic term must be 1 in order to complete the square. 29. The graph of the function is reflected about the x-axis (opens downward) and is shifted up two units. 30. exponential growth; f(x) = 1000 · 2x; 6; $64,000 25. ≈ 94.667 ft 26. a > -3 85 27. a. t = _ 10,800 √ 17 √ 3 b. t = _ 36 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 112–3 Saxon Algebra 1 Lesson 113 Warm Up 113 1. radicand 2. -29 3. 53 4. -68 5. -54 Lesson Practice 113 a. 144; 2 real solutions, 2 x-intercepts b. 0; 1 real solution, 1 x-intercept c. -47; no real solutions, no x-intercepts d. The discriminant is 3728, so there are 2 real solutions. The ball will reach a height of 45 feet because its maximum height is 58.25 feet. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 113–1 Saxon Algebra 1 Lesson Practice 113 113 9. Student A; Sample: Student B added the linear equation to the quadratic equation rather than substituting it for y. 1. -23 2. 26x2 + 6x + 76 3. {0, 6} 4. 40,320 10. 9 feet 5. A 11. (-3, 5) and (4, 7) 6. Sample: 12. Student A; Sample: Student B did not use the correct formula for permutations. 13. 45 1 14. _ 504 7. Sample: all positive values for b2 - 4ac 8. 14 y 36 + 2 = 6 + 2 15. x = 36; √ =8 16. x = 6 12 17. 10 8 y 8 (2, 6) 6 -4 -2 -8 -4 O 4 -4 2 -8 O x 4 8 x 2 4 -2 18. a. 11 feet by 13 feet b. 48 feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 113–2 Saxon Algebra 1 Lesson 113 19. a. t = 0.44 seconds 27. a. t2 + 6t = 7 b. t = 2.26 seconds b. t = -7 or 1 c. h = 53.1 feet c. 1 minute; Time cannot be negative. 1941 feet 20. 2 √ 21. 4 28. yes; Sample: If the 1 , the common ratio is _ y 2 -2 O x 2 fifth term is -81 4 -2 3 1 4 _ 3 ( ) = -1. If the common ratio 1 , the fifth term is is -_ -4 3 1 -81 - _ 3 ( ) 22. Sample: The first equation has a variable for the initial height while the second equation assumes that the initial height is 0. 4 = -1 29. wider 30. They are mirror images of each other reflected about the y-axis. 23. y > x - 6 24. Use the equation 200 = -16t2 + 84t. Since 0 = -16t2 + 84t - 200 and the discriminant is -5744, the projectile will not reach 200 feet. 25. 2 26. B © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 113–3 Saxon Algebra 1 Lesson Warm Up 114 b. x ≥ 0 c. x ≥ 2 1. like radicals, unlike radicals d. a shift of 2 units down 2 2. 2 √ e. a shift of 2 units to the right 3. 18 √5 6 4. 7 + √ f. a reflection over the x-axis, then a shift of 3 units to the left 3 5. 147 - 24 √ g. a reflection over the y-axis, then a shift of 4 units down Lesson Practice 114 a. y ; x 114 -1 0 0 3 3 6 8 9 h. Sample: about 1.27 seconds 15 12 y 12 y = 3 √x + 1 8 4 x O 2 4 6 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 114–1 Saxon Algebra 1 Lesson Practice 114 1. {} 2. 0, 7 3 3. 0, _ 4 4. x = 1 5. C 6. ≈ 63 meters per second 7. x > 19.5; Sample: 2 (f(x)) < (√ 4x _ -1 3 2 ), 114 11. yes; Sample: The equation 50 = (x + 12)(x + 8) represents the area of the rectangle. Then 50 = x2 + 20x + 96 and 0 = x2 + 20x + 46. The discriminant of this equation is 202 - 4(1)(46) = 400 - 184 = 216. Since the discriminant is positive, there is a value for x that makes the equation true. 12. a. 0 = -270 + 3x - x2 4x 4x _ 1, 25 < 5 <_ 3 3 4x _ - 1, 26 < , 2 b. a = -1, b = 3, c = -270 3 78 < 4x, 19.5 < x c. -1071 8. Sample: Translate the parent function, f(x) = √x, 2 units to the right and then translate the resulting graph 3 units up. d. no; There is no base possible because the discriminant of the equation is negative. 13. y (-2, 7) 6 9. 57 2 10. Student B; Sample: The values of a, b, and c are found when the equation is set equal to 0. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 114–2 (0, 3) x O -4 -2 4 Saxon Algebra 1 Lesson 114 14. Student B; Sample: Student A did not add 4 to both sides when setting the equation equal to zero. 23. Sample: When you are trying to find the number of ways to pick items and the order of the items matters. 15. 6 feet 24. a. 720 inches 1 1 _ ; 719 b. |d - 720| ≤ _ 2 2 1 _ ≤ d ≤ 720 16. 1 unit: 2 cm 17. 4 2 y 7 inches c. 717_ 16 2 x O -4 4 25. 7 26. base: 60 yards, height: 30 yards -4 18. 60° or 70° 27. a. 32,000(1.04) n 19. no 20. b. 6 ; Motorcycles 16 c. $51,233.03 12 2 28. 4x - x - 3 = 0 8 4 0 2 4 Cars 6 Sample: 2 cars and 6 motorcycles or 3 cars and 4 motorcycles 21. 4, 15 29. Because the coefficient of x2, (i.e., 4) is greater than 1, the graph has been vertically stretched (which means the graph is narrower than the parent quadratic function). 22. B © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 114–3 Saxon Algebra 1 Lesson 114 30. Both are exponential functions with the same shape, but g(x) has been vertically stretched by a factor of four. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 114–4 Saxon Algebra 1 Lesson Warm Up 115 c. ; y 4 1. standard -8 2. 2; x2 + 2x + 8 4 115 -4 O x 4 8 -4 -8 3 3. 4; x + 2x - 6x x ≈ 1.70998 4. 5 d. 5. B ; Lesson Practice 115 a. 8 x ≈ -0.47, x ≈ 0.54, x ≈ 3.94 y 4 O -8 x -4 b. 4 32 e. 8 ; ;x=0 y V ≈ 16,648 cubic units 16 x -4 -2 2 4 -16 -32 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 115–1 Saxon Algebra 1 Lesson Practice 115 115 1. x = 0 10. Student B; Sample: Student A incorrectly subtracted the 5 from 6. 2. x = 13 11. a. 3. 8 0.8 4 -4 -2 O 0.4 x 2 4 x 4 -4 -8 8 12 b. Sample: ≈ 1.6 seconds 4. C 12. d = 28; two real solutions 5. x = 3 ; 6. y 1.2 ;x=0 y 1.6 13. Student B; Sample: The value of c is -4, not 4. 33.51 cubic inches 7. Sample: The ends of the graph go in opposite directions, it is a smooth curve, and the graph crosses the x-axis at least once and at most three times. 14. A = (6 + x)(10 - x); 50 = 60 + 4x - x2 and the discriminant is 56; Yes, the garden can have an area of 50 square meters. 8. Sample: y = 10x 3 9. y ≈ -1.5 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 115–2 Saxon Algebra 1 Lesson 20. 72 area codes 15. no; Sample: The equation 200 = (15 - x)(12 + x) represents the area of the rectangle; 200 = 180 + 3x - x2 and 0 = -x2 + 3x - 20. The discriminant of this equation is 3 2 - 4(-1)(-20) = 9 - 80 = -71. Since the discriminant is negative, there is no value for x that makes the equation true. 21. C 22. none; Sample: The second parallel line could intersect the parabola, at least once. However, since it never intersects the other linear equation, there can be no solution to the system. 23. 5x + 2y ≤ 20; y 16. yes 17. 8 4 -16 y -8 O x 8 -8 2 -2 115 -16 x O 4 24. x = -0.3 and 7.3 -4 25. C 18. h = 8 units, b = 12 units 19. 32 ;x=0 y 16 -4 -2 O 26. 6 sets of calls x + 1 units 27. a. 4 √ x 2 b. x = 3 4 -32 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 28. Sample: The negative sign indicates that the “V” will open downward. LSN 115–3 Saxon Algebra 1 Lesson 115 29. The graph would be compressed. 30. linear, quadratic, exponential © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 115–4 Saxon Algebra 1 Lesson Warm Up 116 116 h. 6 , 0.24 2. _ 25 3. 0.025, 2.5% 4. 62.5 Total Principal Rate Years Amount in Account $2500 12% 1 $2800 $2500 12% 2 $3136 $2500 12% 5 $4405.85 $2500 12% 10 $7764.62 i. 5. 3.2% Lesson Practice 116 a. $2240 b. $43,000 Total Amount in Account 1. proportion 8000 6000 4000 2000 0 2 4 6 Years 8 10 The account earning compound interest increases more rapidly. c. 5 years d. 4% j. The 30-year-old man’s investment will be worth more by $1367.98. e. $38,920.77 f. $39,604.64 g. Years Prt = I 1 2 5 10 $300 $600 $1500 $3000 Total Amount in Account $2800 $3100 $4000 $5500 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 116–1 Saxon Algebra 1 Lesson Practice 116 9. 8 ; 8 cubic units y 4 1. $135 x O -8 2. Sample: Simple interest is just paid on the principal. Compound interest is paid on the principal and interest earned. 10. a. 3. $200 4. 2025 5. B -4 4 16 2 4 -8 ;x=0 y -16 16 x O -2 x O -4 -4 y 8 6. $20,182.50 32 8 x y -2 -3 -1 4 0 5 1 6 2 13 b. 7. 116 2 c. 32 cubic feet 4 -16 11. 5 -32 8. Student A; Sample: The word “cubed” means to the third power, not to the second power. 12. ≈ 22.6 feet per second 13. Student B; Sample: Student A just removed the radical sign and then set the entire right side greater than or equal to zero. 14. 25 feet © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 116–2 Saxon Algebra 1 Lesson 15. y 4 24. (-2, -4) 2 -4 -2 25. 8 years x O 116 2 4 -2 26. $1492.32 16. -3.7574, -12.2426 17. 120 18. no solution; 27. because b is negative; Sample: The range values are not all positive or all negative. For example, f(2) = 16 and f(3) = -32. y 28. a. Divide each term 3. by √ √ 3 b. _ 2 -4 -2 x O 2 4 -2 9 29. x = 2, (2, -10) 19. C 20. Sample: The discriminant tells how many times the graph of a quadratic equation crosses or touches the x-axis. 30. f(x) is exponential decay, g(x) is quadratic, h(x) is exponential growth, and j(x) is linear. 21. no solution 22. x < -1.5 OR x > 3; -4 -2 0 2 4 6 23. x = 81 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 116–3 Saxon Algebra 1 Lesson Warm Up 117 117 g. ∠A ≈ 32.28°; ∠B ≈ 57.72° 1. division h. 66.42° 2. 15 in. 21 in. or ≈ 13.75 in. 3. 3 √ 4. yes 5. no Lesson Practice 117 5 12 _ , cos A = , a. sin A = _ 13 13 12 tan A = _ 5 3 4 _ , cos B = , b. sin B = _ 5 5 5 4 , csc B = _ , tan B = _ sec B = 3 5 _ , 3 cot B = 4 3 _ 4 c. sin 49° ≈ 0.7547, cos 49° ≈ 0.6561, tan 49° ≈ 1.1504 d. csc 67° ≈ 1.0864, sec 67° ≈ 2.5593, cot 67° ≈ 0.4245 e. x ≈ 29.06 f. x ≈ 12.63; y ≈ 11.38 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 117–1 Saxon Algebra 1 Lesson Practice 117 20 21 _ , cos A = , 1. sin A = _ 29 29 20 tan A = _ 2. 21 15 , sin A = _ 17 15 tan A = _ 8 8 cos A = _ , 17 1 x 3. y = _ 8 117 11. Sample: The opposite leg is the leg of a right triangle that is opposite the acute angle and the adjacent leg is the leg that is next to the acute angle, but not the hypotenuse. 12. Student B; Sample: Student A found the interest earned, not the account’s value. 4. sin 77° ≈ 0.9744, cos 77° ≈ 0.2250, tan 77° ≈ 4.3315 5. Student A; Sample: The tangent ratio is the opposite leg over the adjacent leg and Student B used adjacent over opposite. 13. 10% for 10 years earns $10.54 more. 14. ;y=3 y 8 4 x O -4 -2 2 4 -4 6. 45°; 3.54 cm 7. a. 250 feet b. 16.26° 8. 25 feet tall 9. $198 10. about 0.41 miles below the water’s surface 15. Student B; Sample: Student A graphed the parent function. 16. x = 3 17. x = 3 or x = 1.5 18. 1320 19. x = ±2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 117–2 Saxon Algebra 1 Lesson 20. 63 (-2, _94 ) and (-7, _ 8 ) 117 27. f(0) = 15, f(1) = 12, 3 f(2) = 9_ 5 21. d = 12; two real solutions y 16 22. B 12 23. Sample: The graph + 4 can of f(x) = √x be rewritten in the - c by form f(x) = √x changing + 4 to -(-4). The function is now y = √x - (-4) , which is a translation 4 units left of the parent function. 24. -0.75 < x < 0.25 -1 -0.5 0 0.5 1 25. a. x and x + 2 b. x2 + (x + 2)2 = 74 c. 5 and 7 or -5 and -7 26. csc 81° ≈ 1.0125, sec 81° ≈ 6.3925, cot 81° ≈ 0.1584 8 4 x 4 8 12 28. Sample: In the second system, the points on the boundary line are solutions to the system, and the boundary lines, which intersect, are solid. In the first system, the boundary line is dashed because the points on that line are not solutions. They do not intersect. 29. A half-life is the amount of time it takes for half of a substance to remain; 6 half-lives 30. a. y = 2 b. x = 0 c. 12 rackets © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 117–3 Saxon Algebra 1 Lesson 118 Warm Up 118 1. permutation 2. 5040 3. 30 4. 210 5. 3024 Lesson Practice 118 a. 20 permutations b. 10 combinations c. 70 d. 497,420 1 e. _ 3060 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 118–1 Saxon Algebra 1 Lesson Practice 118 118 1. 1365 11. a. 2,042,975 1 b. _ 2. 330 24 7 _ , cos A = , 12. sin A = _ 25 25 735,471 3. 36 25 24 _ tan A = _ , csc A = , 7 24 4. 792 25 7 , cot A = _ sec A = _ 7 24 13. a. 16 feet 5. Sample: With permutations order matters, but with combinations, order does not matter. b. 36.87° 14. 53.13°; 6 4 2 8! =_ 3!(8 - 3)! 0 8! 1 =_ ·_ 3! (8 - 3)! 8P3 = __ number of ways to order 3 items 10. 28 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. 2 4 6 8 16. $6764.51 (8 - 3)! =_ 3! 9. 5(3x - 2) C x A 15. $10,580 8! _ 8. 120 B 8 6. Sample: 8C3 7. A y 17. Student A; Sample: Student B used interest compounded annually, not quarterly. 18. 30,240 3-8 19. -4 √ 20. (-1, -4) and (5, 20) LSN 118–2 Saxon Algebra 1 Lesson 118 21. Use the equation 45 = -16t 2 + 75t + 2. Then 0 = -16t 2 + 75t - 43 and the discriminant is 2873, so the ball will reach a height of 45 feet. b. No; Sample: There is no ordered pair with 15 teachers that is in the solution set. 29. -2z3(r + 11)(r + 4) 22. y ≈ 1.6 30. 6 half-lives; 5 mg 28. 1 and -11 23. A 24. y = x3 25. x ≈ ±6.708 26. a. 312,500 ( ) n-1 3 b. a 4 _ 4 c. about 254,533 1 ⎧3x + _ y ≥ 200 2 ; 27. a. ⎨ x + y ≤ 250 ⎩ y Students 220 176 132 88 44 0 x 60 120 180 240 Teachers © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 118–3 Saxon Algebra 1 Lesson 119 Warm Up 119 1. vertex 2. x = -2 3. m = 0.5; b = -3.5 4. m = 4; b = 5 5. B Lesson Practice 119 a. linear b. quadratic c. exponential d. linear e. quadratic f. linear g. quadratic h. exponential i. quadratic j. exponential k. linear © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 119–1 Saxon Algebra 1 Lesson Practice 119 1. Student A; Sample: Student B wrote an equation that does not 2 have an x term in it. 119 13. a. 7315 1 b. _ 7315 14. sin 14° ≈ 0.2419, cos 14° ≈ 0.9703, tan 14° ≈ 0.2493 2. exponential 3. quadratic 4. Sample: Graph the parent function and then graph a series of transformations of it. 5. quadratic; f(x) = x 2 6. Student A; Sample: Student B used the formula for permutations. 15. Student B; Sample: The cosine ratio is the adjacent leg over the hypotenuse and x represents the adjacent leg. 16. about 41,927 feet 17. no solution. 4 2 -4 7. a. linear b. f(x) = 1.5x + 16 y -2 O x 4 -4 18. d = 0; one real solution 8. linear 9. C 10. quadratic 11. linear 19. n ≥ 0; Sample: The domain is n ≥ -30, but in the context of the problem the number of cards cannot be negative. 12. exponential © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 119–2 Saxon Algebra 1 Lesson 20. 8 ; y c. 4 -4 O -2 4 119 y 2 x 2 O 4 x 8 12 -2 -8 -4 y = -2 27. exponential 21. Sample: The amount for simple interest results in I = 500(0.06)(3) = 90 for an account balance of $590, but compound interest is A = 500(1.06)3 = 595.51 for an account balance of $595.51. 28. Sample: It can be easily factored so the quadratic formula would be unnecessary work. 29. 6P2 6! 6! _ =_ = 4! (6 - 2)! 6·5·4·3·2·1 = __ 4·3·2·1 = 6 · 5 = 30 22. D 30. parabola; line; parabola; horizontal line 23. 56 3 √7 9 √ 5 -_ 24. - _ 19 19 25. m = -1 or m = -5 26. a. x = 20 b. Sample: To isolate the radical, both sides of the equation must be multiplied by -1. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 119–3 Saxon Algebra 1 Lesson 120 Warm Up 120 1. complement 1 2. _ 4 1 3. _ 3 4. 125 sq in. 5. 12.56 sq in. Lesson Practice 120 1 a. _ 75 9 b. _ 25 4 ≈ 0.92 c. 1 - _ 16π 15 = 0.9 d. 1 - _ 150 11 e. _ 12 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 120–1 Saxon Algebra 1 Lesson Practice 120 120 12. -9.317 15 1. _ 64 13. ≈ 0.21 2. Sample: using geometric formulas to calculate the favorable and total outcomes. 14. Student B; Sample: Student A found the probability of landing on the triangle. 3. The system has no solution. 15. Sample: Using A = s2, the area of the square is 49 square centimeters. The radius of the circle is half the diameter or 3 centimeters. Using A = πr2, the area of the circle is 9π. Find the probability of not landing in the circle by finding the complement of the probability of landing in the circle. The 9π formula is 1 - _ which 49 4. Sample: 1 _ ·8·8 2 1- _ 8·8 32 32 1 _ _ =1-_ = = 64 64 2 5. 21 6. 125 cubic centimeters 7. B 8. 125,970 1 36 - _ (4)(5) 2 ≈ 0.13 9. _ 64π 10. Any right triangle with sides that are similar to a 3-4-5 right triangle is valid where the shorter leg is opposite angle A. is approximately 0.42. 2 16. _ 3 4 17. _ 15 3 18. a. _ 4 b. 196 square millimeters 11. x ≥ 0 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 120–2 Saxon Algebra 1 Lesson 19. Student B; Sample: A linear function must have a constant rate of change. Student A’s graph does not have a constant rate of change; it gets steeper as x increases. 120 30. a. 720 1 b. _ 720 20. a. quadratic; Sample: The graph is a parabola. b. 14 feet 21. quadratic 22. Student A; Sample: Student B made order count. 23. d = 8; two real solutions 24. ≈ 0.42 25. $4056 26. f(x) = |x + 2| + 3 27. A 28. x = 0.5 or x = -3.5 29. ≈ 0.99 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved. LSN 120–3 Saxon Algebra 1