Download Lesson Lesson Warm Up 1 1. Venn diagram 2. 0. − 2 3. 4.375 4. 5. 5

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.
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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%
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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
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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
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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
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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
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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
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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
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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.
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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%
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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°
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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