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CHAPTER 1
28.
Number of Pages
page 724
Chapter
250
200
150
100
50
0 1 2 3 4 5
Cover Price($)
positive correlation
29. mean ≠ 39.375
median ≠ 38
mode ≠ 35
30. mean ≠ 0.943
median ≠ 0.9
mode ≠ none
31. mean ≠ 6.3
median ≠ 6
mode ≠ 5, 8
Extra Practice: Skills and Word Problems
1
Extra Practice
Lesson 1-1 Define variables and write an equation to model each situation.
1. The total length of the edges of a cube is 12 times the length of an edge. s ≠ side length; < ≠ 12s
2. The total cost of lunch is $5.50 times the number of people at the table. n ≠ number of people; c ≠ 5.50n
3. The area of a rectangle is 12 cm times the length of the rectangle. e ≠ length of rectangle; a ≠ 12e
4. The cost of a telephone call is 75 cents plus 25 cents times the number of minutes. t ≠ time in minutes;
c ≠ 75 ± 25t
Lesson 1-2 Simplify each expression.
5. 4 + 3 ? 8 28
9.
42
6. 2 ? 3 2 - 7 11
+ 8 4 2 20
13. 2 + 6 ? 8 4 4 14
7. 6 ? (5 - 2) - 9 9
8. 2 - 12 4 3 –2
10. 12 4 43 38
11. -6 ? 4.2 - 5 4 2 –27.7 12. 9 - (3 + 1)2 –7
14. 6 + 8 4 2 - 3 7
15. 10 4 5 ? 2 + 6 10
16. 5 + 4 ? (8 - 6)2 21
Lesson 1-3 Use <, ≠, or S to compare.
17. 0.45 j 0.54 R
18. -1.08 j -1.008 R
21. 0.444 c j 49 ≠
4 j 4 S
22. 13
15
11 R
19. 73 j 25
20. 1.4 j 18
11 R
22
1
23. 0.101101110 c j 9 R 24. p j 7 R
Lesson 1-4 The relationships in the tables are functions. Write a function rule
for each.
25. Ears of
Corn
1
26.
Total
Cost
Time
(hours)
Cost of
Canoe Rental
1
$0.20
2
$0.40
3
$0.60
4
$0.80
c ≠ 0.20E
27.
Number
of Tickets
Total
Cost
$12
1
$9
2
$19
2
$18
3
$26
3
$27
4
$33
4
$36
c ≠ 5 ± 7t
c ≠ 9n
Lesson 1-5
28. Make a scatter plot of the data. Describe the trend of the data. See margin.
Cover Price and Number of Pages of Some Magazines
Cover Price
Number of Pages
$2.25
$2.50
$3.75
$3.00
$4.95
$1.95
$2.95
$2.50
208
68
122
124
234
72
90
90
32a. 1 8
1 7
1 6
1 5
1 4
1 3
1|4
8
7
6
5
4
Lesson 1-6 Find the mean, median, and mode for each set of data. 29–31. See margin.
29. 36, 42, 35, 40, 35, 51, 41, 35
30. 1.2, 0.9, 0.7, 1.1, 0.8, 1.3, 0.6
32. A student surveyed the members of the drama club. She
included a question about age. Her results are shown at
the right.
a. Make a stem-and-leaf plot for the data.
b. What is the median age of the drama club members? 15
a. See above right.
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Chapter 1 Extra Practice: Skills and Word Problems
31. 5, 8, 6, 8, 3, 5, 8, 6, 5, 9
Ages of Drama Club Members
14 18 16 15 17 14 15 18 15
13 14 15 18 14 17 16 14 16
8
6
5 5
4 4 4
means 14
33. The total cost of gas is the number of gallons times $2.25.
34. The length of the trip is 35 minutes plus extra time spent in traffic.
35. The number of tickets available is 4200 minus the number of tickets sold.
b 1 b
Lesson 1-2 Use the formula for the area of a trapezoid A = h Q 1 2 2 R , where A is
area, b1 and b2 are the length of the bases and h is the height, to answer each
question.
36. What is the area of a trapezoidal pool with and a height of 15 yd and bases of
14 yd and 26 yd? 300 yd2
37. How many square feet of grass are there on a trapezoidal field with a height of
75 ft and bases of 125 ft and 81 ft? 7725 ft2
Lesson 1-3 Is each statement true or false? If the statement is false, give a
counterexample. 38–39. See margin.
34. < ≠ length of trip
t ≠ time in traffic
< ≠ 35 + t
35. a ≠ available tickets
s ≠ tickets sold
a ≠ 4200 - s
45. no correlation; The
length of a town’s name
is not likely to affect its
population.
46. positive; The hotter the
weather, the more
water athletes should
drink.
39. The quotient of two integers is an integer.
47. negative; the lower the
price, the more likely
people are to buy it.
40. The sum of two rational numbers is a rational number. true
48.
38. The product of a rational number and an integer is not an integer.
Lesson 1-4 Identify the independent and dependent quantity in each situation.
41. A museum charges $10 admission for each person. number of people; total charge
6
7
8
9
2
2
1
1
8
2
2
3
Extra Skills and Word Problems
Extra Skills and Word Problems
Lesson 1-1 Define variables and write an equation for each phrase. 33–35. See margin.
33. c ≠ cost of gas
g ≠ gallons
c ≠ 2.25g
8
5 5 6 8 8
8 8 8 8
5
42. Marta is reimbursed $.20 for each mile that she drives on company business. miles driven; reimbursement
43. Each acre of cropland takes a farmer 90 minutes to plow. acres plowed; time
7 5 means 75
44. Tom earns $12 for each lawn he cuts. He can cut up to seven lawns working on
Saturday and Sunday. Identify the independent and dependent quantities for
this situation. Then find reasonable domain and range values.
lawns cut; earnings; 1 to 7 lawns; $12 to $84
79.9, 78.8
49.
Lesson 1-5 Would you expect a positive correlation, a negative correlation, or no
correlation between the two data sets? Explain why. 45–47. See margin.
0 2 3 4 5 6 9 9
1 0 1 1 2 4 6
45. the population of a town and the length of its name
0 4 means 0.4
46. the temperature during a lacrosse game and the amount of water the players
need to drink
0.86, 0.9, 0.9
47. the number of computers sold and the price of the computer
Lesson 1-6 Make a stem-and-leaf plot for each set of data. Then find the mean,
median, and mode. 48–49. See margin.
48. Students’ grades on a test:
95, 62, 68, 72, 88, 75, 78, 81, 88, 91, 72, 68, 75, 78, 82, 88, 88, 76, 93
49. Amount of precipitation for the past 12 months in inches:
0.4, 0.6, 1.2, 1.0, 0.9, 1.4, 1.6, 1.1, 0.9, 1.1, 0.2, 0.3, 0.5
Chapter 1 Extra Practice: Skills and Word Problems
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Chapter
2
Extra Practice: Skills and Word Problems
Lessons 2-1 to 2-3 Simplify each expression.
1. 22 + (-33) –11
2. 45 + (-54) –9
4 - 4 0
4. 13
13
7. -(-(11 - 22)) –11
5. Δ12 - 21« 9
3. 2 43 - 45 –32
15
6. Δ12« - Δ-21« –9
8. P 23 + 45 P 22
15
2
11. -3 –9
12. Q 32 R Q 2 22
33 R –1
2
13. 33 98
2
2
14. 25 2 –1
15. 81 4 (-9) –9
2
16. 42 16
5 25
?314 5
17. 22(3
1 4) 7
2
19. Q 57 R 25
49
20. 23 4 49 32
1
10
7
2 1 13
23
0
24 6
27 6
21. c
d + c
d c
d
3 8
11 25
28 13
10. (-3)2 9
22. c
9. (-2)(44) –88
(25)
6 12
8 26
22 18
d - c
d c
d
224 7
29 7
15
0
18. 1 1
23. c
4.2 0.6
5.8 23.5 10
22.9
d
d + c
d c
1.9 14.4
1.7 9.5
0.2
4.9
Lessons 2-4 and 2-5 Simplify each expression.
26. 5 + 6(m + 1) 6m ± 11
27. 94(18 - 9t) 8 – 4t
25. -12 Q 43 x 2 1 R –16x ± 12
28. 1 + 3 + 5 + 7 16
30. -3(7w) + 7(3w) 0
31. 2(1 - d) - (2d + 1) 1 – 4d
32. 6c + 2(4c - 3) 14c – 6
33 5(2 - j) + (2j - 3) 7 – 3j
34. 13 (12 - 6r) 4 – 2r
35. 6 Q 12 2 23 y R 3 – 4y
24. -4(a + 3) –4a – 12
29. 1 - 3 + 5 - 7 –4
Lesson 2-6 The results of rolling a number cube 54 times are at the
right. Use the results to find each probability.
6 3 4 5 1 1 5 5 3632133321
2 3 6 3 3 4 5 1 2263365453
2 5 1 4 5 2 6 2 5212532463
5
37. P(4) 54
14
36. P(3) 54
40. P(even number)
23
54
41. P(not 1)
38. P(not 5) 44
54
47
54
42. P(1)
39. P(7) 0
43. P(odd number) 31
54
7
54
Lesson 2-7 You roll a blue number cube and a red number cube. Find
each probability.
1
46. P(blue 5 and red less than 4) 12
1
44. P(blue 3 and red 2) 36
1
45. P(blue odd and red 6) 12
47. P(same number) 16
48. P(both numbers less than three) 91 49. P(both numbers greater than 5)
You have 3 green marbles, 5 red marbles, and 1 yellow marble in a bag. You pick two
marbles from the bag. You pick the second one without replacing the first one. Find
each probability.
5
50. P(red then green) 24
726
726
5
51. P(yellow then red) 72
Chapter 2 Extra Practice: Skills and Word Problems
1
52. P(two greens) 12
1
36
53. A pot of water has a temperature of 25°C. How many degrees should you raise
the temperature to boil the water at 100°C? 75° C
54. Romana is 68 in. tall and Sophie is 73 in. tall. How much taller is Sophie than
Romana? 5 in.
55. Your goal is to save $50. So far, you have saved $34. How much more do you
need to save? $16
56. A company buys 1500 small items from a manufacturer for $.02 apiece. What is
the total cost of the items? $30
57. If 36 people are at a pizza party, how many eight-piece pizzas need to be
ordered so each person can get two pieces of pizza? 9 pizzas
58. Your parents drove the family car 462 miles on 14 gallons of gas. On average,
how many miles did the car travel on each gallon of gas? 33 mi
Extra Skills and Word Problems
Extra Skills and Word Problems
Lessons 2-1 to 2-3 Use addition, subtraction, multiplication, or division to answer
each question.
Lesson 2-4 Use the Distributive Property to find each price.
59. Cereal is on sale for $3.95 per box. What is the cost of seven boxes? $27.65
60. The school drama club is putting on a play. If there will be five shows and the
auditorium holds 480 people, how many people can see the show? 2400 people
61. What is the total cost of four CDs on sale for $12.15 each? $48.60
Lesson 2-5 Identify the property of real numbers shown in each situation.
62. The cost of one item sold for $14.50 is $14.50. Ident. Prop. of Mult.
63. You can find the cost of fish by multiplying the price per pound by the amount
or by multiplying the amount by the price per pound. Comm. Prop. of Mult.
64. To find total time spent doing homework in a week, you add the amount from
each day. You find that the total is the same no matter what order you use.
Comm. Prop. of Add.
Lesson 2-6 Find the theoretical probability of each event.
65. What is the probability of rolling an even number on a number cube? 12
66. Tiles with the letters from the word PROBABILITY are placed in a bag.
4
What is the probability of selecting a vowel at random? 11
67. A spinner has four equal sections. Two are red, one is blue, and one is yellow.
What is the probability of spinning yellow? 14
Lesson 2-7 A bag contains 5 green marbles, 15 purple marbles, and 10 yellow
marbles.
68. What is the probability of selecting a green marble, replacing it, and then
1
selecting another green marble? 36
69. What is the probability of selecting a yellow marble, not replacing it, and then
5
selecting a green marble? 87
Chapter 2 Extra Practice: Skills and Word Problems
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Chapter
3
Extra Practice: Skills and Word Problems
Lessons 3-1 to 3-2 Solve each equation.
1. 8p - 3 = 13 2
2. 8j - 5 + j = 67 8
3. -n + 8.5 = 14.2 –5.7
5. m - 9 = 11 20
6. 12 (s 1 5) = 7.5 10
7. 7h + 2h - 3 = 15 2
9. 3r - 8 = -32 –8
10. 8g - 10g = 4 –2
11. -3(5 - t) = 18 11
4. 6(t + 5) = -36 –11
7 x = 3 18
8. 12
14 49
12. 3(c - 4) = -9 1
Define a variable and write an equation for each situation. Then solve.
13. Your test scores for the semester are 87, 84, and 85. Can you raise your test
average to 90 with your next test? t ≠ test score; 87 1 84 41 85 1 t ≠ 90; no
14. You spend 12 of your allowance each week on school lunches. Each lunch costs
$1.25. How much is your weekly allowance? a ≠ allowance; 12a ≠ 5(1.25); $12.50
Lesson 3-3 Solve each equation. If the equation is an identity, write identity. If it
has no solution, write no solution.
15. 4h + 5 = 9h 1
18. m + 3m = 4 1
21. 10z - 5 + 3z = 8 - z
13
14
16. 2(3x - 6) = 3(2x - 4) identity
17. 7t = 80 + 9t –40
19. -b + 4b = 8b - b 0
20. 6p + 1 = 3(2p + 1) no solution
22. 3(g - 1) + 7 = 3g + 4 identity
23. 17 - 20q = (-13 - 5q)4
no solution
Lessons 3-4 and 3-5 Solve each proportion.
24. 43 = 26
m –8
3 1
25. 7t = 21
3 48
26. j = 16
w
27. 25 = 65
26
s = 4 4
28. 15
45 3
x 45
29. 94 = 10
2
8 155
30. 10
q = 62 2
31. 32 = 18
y 12
9
32. The scale on a map is 1 in. : 15 mi. The distance between two cities is
25 mi. Find the distance in inches between the cities on the map. about 1.7 in.
Lesson 3-6
33. Transportation A bus traveling 40 mi/h and a car traveling 50 mi/h cover the
same distance. The bus travels 1 h more than the car. How many hours did
each travel? bus: 5 h; car: 4 h
Lesson 3-7 Find each percent of change. Describe each as a percent of increase or
decrease. Round to the nearest percent.
34. $4.50 to $5.00 11% increase
35. 56 in. to 65 in. 16% increase
36. 18 oz to 12 oz 33% decrease
37. 1 s to 3 s 200% increase
38. 8 lb to 5 lb 38% decrease
39. 6 km to 6.5 km 8% increase
Lesson 3-8 Find the square roots of each number.
40. 25 w5
41. 49 w23
42. 64 w8
5
43. 25
36 w6
44. 0.81 w0.9
45. 900 w30
Lesson 3-9 Determine whether the given lengths are sides of a right triangle.
46. 15, 36, 39
47. 3, 7, 10
48. 8, 15, 17
yes; 152 ± 362 ≠ 392
no; 3 2 ± 7 2 u 102
yes; 82 ± 152 ≠ 172
For the values given, a and b are legs of a right triangle. Find the length of the
hypotenuse. If necessary, round to the nearest tenth.
50. a = 6, b = 8 10
728
728
51. a = 5, b = 9 10.3
Chapter 3 Extra Practice: Skills and Word Problems
52. a = 4, b = 10 10.8
49. !3, !4, !5
no; 3 ± 4 u 5
53. a = 9, b = 1 9.1
54. A DVD club charges a monthly membership fee of $4.95 and $11.95 for each
DVD purchased. If a customer’s bill for the month was $64.70, how many
DVDs did the customer purchase? 5 DVDs
55. A lawyer charges $100 per month to be put on retainer for a client. The lawyer
also charges an hourly rate of $75 for work done. How many hours does the
lawyer have to work for a client, in one month, to charge $625? 7 h
56. A rectangular pool is twice as long as it is wide. What are the dimensions of the
pool if the perimeter is 42 yd? 7 yd by 14 yd
57. Two friends rent an apartment together. They agree that one person will pay
1.5 times what the other person pays. If the rent is $850, how much will each
friend pay? $340; $150
58. A shopper’s discount club charges a monthly fee of $15 and sells gasoline for
$2.05 per gallon. The gas station across the street sells gasoline for $2.35 per
gallon and charges no fee. How many gallons of gasoline would you have to
buy in one month to spend the same amount at either store? 50 gallons
Extra Skills and Word Problems
Extra Skills and Word Problems
Lessons 3-1 to 3-3 Write an equation to model each situation. Then solve.
59. Michael and Kevin are running. Kevin gets a 3-mile head start and runs at a
rate of 5.5 mi/h. Michael runs at a rate of 7 mi/h. How many hours will it take
Michael to catch up with Kevin? 2 h
Lessons 3-4 and 3-5
about
60. A 12-ounce can of green beans is sold for $1.45. What is the price per pound? $1.93/lb
61. A sailboat is traveling at a speed of 10 nautical miles per hour. If 1 nautical
mile is 6076 ft, what is the speed of the sailboat in feet per second? about 16.9 ft/sec
62. A 40 : 1 scale model of an airplane is being used to conduct wind-tunnel tests.
If the model is 4.5 feet long, how long is the actual airplane? 180 ft
Lesson 3-6
63. Joe and Gayna live 3 miles apart. They both leave their houses at the same time
and walk to meet each other. Joe walks at 2.5 mi/h and Gayna walks at 3.5 mi/h.
How far will Joe walk before he meets Gayna? 1.25 mi
Lesson 3-7 Find the percent of change. Describe the percent of change as an
increase or decrease.
64. A $1500 computer is on sale for $1275. 15% decrease
65. The value of a stamp collection increases from $160 to $180 in one year.
12.5% increase
Lesson 3-8
66. What is the length of each side of a square garden with an area of 70 ft2?
about 8.4 ft
Lesson 3-9 Use the Pythagorean Theorem to answer each question.
67. A 20-ft ladder is placed 5 ft from the base of a building. How high on the
building will the ladder reach? about 19.4 ft
68. A soccer field is 80 yd long and 35 yd wide. What is the diagonal distance across
the field? about 87.3 ft
Chapter 3 Extra Practice: Skills and Word Problems
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Chapter
CHAPTER 4
page 730
1.
4
Extra Practice
4 3 2 1 0 1
2.
Lessons 4-1 to 4-4 Solve each inequality. Graph and check your solution. 1–24. See margin for graphs.
8 4 0 4 8 12
3.
4.
4 3 2 1 0 1
8 4 0 4
128 4 0 4 8
7.
12 0
8.
9.
1
2
1
3. 4r . -1 r S –4
4. 7y + 2 # -8 y K –10
7
5. t - 5 $ -13 t L –8
6. 9h . -108 h S –12
8. 6s # 3 s K 18
9. 6c
5 $ -12 c L –10
–14
10. -8O + 3.7 # 31.7 < L –3.5
11. 9 - t # 4 t L 5
12. m + 4 $ 8 m L 4
13. y + 3 , 16 y R 13
14. n - 6 # 8.5 n K 14.5
15. 12b - 5 . -29 b S –2
16. 4 - a . 15 a R –11
17. 4 - x # 3 x L 1
18. 1 - 4d $ 4 - d d K –1
19. n + 7 # 3n - 1 n L 4
20. 2s + 1 , s + 2 s S –2
22. 8r - 6r . 16 - 8 r S –1
23. 1.4 + 2.4x , 0.6 x R –31
21. 3 - 2x
3 . 5 x R –3
24. x - 2 , 3x - 4 x S 1
26. You earn $7.50 per hour and need to earn $35. Write and solve an inequality to
find how many hours you must work. 7.5h L 35, 4 23 h
10 5 0 5
4 3 2 1 0 1
11.
2. 9 + p # 17 p K 8
25. The booster club raised $102 in their car wash. They want to buy $18 soccer
balls for the soccer team. Write and solve an inequality to find how many
soccer balls they can buy. 18x K 102, 5 balls
126 0 6 12 18
10.
1. -8w , 24 w S –3
7. 8w + 7 . 5 w S
4 2 0 2 4
5.
6.
Extra Practice: Skills and Word Problems
Lesson 4-5 Solve each compound inequality.
27. 8 , w + 3 , 10 5 R w R 7
29. 6m - 15 # 9 or 10m . 84
m K 4 or m S 8.4
30. 9j - 5j $ 20 and 8j . -36 j L 5 31. 37 , 3c + 7 , 43 10 R c R 12 32. 3 , 5 + 6h , 10 –13 R h R 56
0 2 4 6
12.
28. -6 , t - 1 , 6 –5 R t R 7
33. 1 + t , 4 , 2 + t 2 R t R 3
34. 2 + 3w , -1 , 3w + 5
35. 2x - 3 # x and 2x + 1 $ x + 3
–2 R w R –1
2KxK3
36. 3n - 7 . n + 1 or 4n - 5 , 3n - 3 n R 2 or n S 4
0 2 4 6
13.
0 6 12 18
14.
0 6 12 18
37. all real numbers less than 2 units from 0 »x… R 2
15.
16.
Lesson 4-6 Choose a variable and write an absolute value inequality that
represents each set of numbers.
3 21 0 1
38. all real numbers more than 0.5 units from 4.5 »x 2 4.5… S 0.5
39. all real numbers less than 1 unit from -4 »x 1 4… R 1
1284 0 4 8
40. all real numbers 3 or more units from -1 »x 1 1… L 3
17.
41. all real numbers less than or equal to 5 units from 3 »x 2 3… K 5
0 1 2 3 4
18.
Solve each inequality. Graph and check your solution. 42–50. See margin for graphs.
4 2 0 2
19.
0 4 8 12
20.
21.
22.
23.
4 2 0 2
42. Δx« , 5 –5 R x R 5
43. Δt« . 1 t R –1 or t S 1
45. Δ-6m + 2« . 20
46. Δ3c« - 1 $ 11 c K –4 or c L 4 47. Δ8 - w« # 8 0 K w K 16
48. Δ2b + 3« , 7 –5 R b R 2
49. Δc - 5« # 6 –1 K c K 11
51. Write an absolute value inequality that has numbers between 2 and 3 as
the solutions. »x 2 2.5… R 0.5
6 4 2 0
44. Δt« - 5 # 3 –8 K t K 8
50. Δn« + 4 # 5 –1 K n K 1
45. m R –3 or m S 11
3
52. Holes with radius 3 cm must be drilled in sheets of metal. The radius must have
an error no more than 0.01 cm. Write an absolute value inequality whose
solutions are acceptable radii. »x 2 3… K 0.01
4 2 0 2
2 1 0 1
730
24.
Chapter 4 Extra Practice: Skills and Word Problems
0 2 4 6
42.
43.
8 4 0 4 8
44.
730
4 2 0 2 4
16 8 0 8 16
45.
46.
8 4 0 4 8
8 4 0 4 8
47.
48.
8 0 8 16 24
8 4 0 4
49.
50.
5 0 5 10 15
4 2 0 2 4
54. No more than 425 tickets to a musical will be sold.
55. You must be at least 18 years old to vote.
56. The party store sold more than 720 balloons in July.
Lessons 4-2 to 4-4 Write and solve an inequality for each situation.
57. Suppose you are trying to increase your coin collection to at least 500 coins.
How many more coins do you need if you already have a collection of
375 coins?
375 ± c L 500
c L 125
58. Janet has a balance of $125 on a credit card. On her next statement, she
wants to reduce her balance to no more than $60. How much does she need
to pay off?
125 – p K 60
65 K p
54. t is the number of
tickets; t K 425
55. y is age in years;
y L 18
56. b is the number of
ballons; b S 720
66. »d - 105» K 0.175;
104.875 K d K 105.175
67. »r - 4.25» K 0.005;
4.245 K r K 4.255
68. »w - 175» K 0.35;
174.65 K w K 4175.35
Extra Skills and Word Problems
Extra Skills and Word Problems
Lesson 4-1 Define a variable and write an inequality for each situation. 53–68. Choice of
variable may vary.
53. A car dealership sells at least 35 cars each week. 53–56. See margin.
53. c is the number of cars
sold; c L 35
59. A homeroom class with 25 students is holding a fund-raiser to support school 25c L 200
cL8
sports. Their goal is to raise at least $200. On average, how much money does
each student need to contribute to meet or exceed the goal?
19
n
60. You are reading a book with 19 chapters. How many chapters should you
read each week if you want to finish the book in 5 weeks or less?
K5 4Kn
61. The sophomore class is putting on a variety show to raise money. It costs $700 15n – 700 L 1000
n L 114
to rent the banquet hall they are going to use. If they charge $15 for each
ticket, how many tickets do they need to sell in order to raise at least $1000?
35h ± 10 R 100
h R 2.5
62. A technical-support company charges $10 per month plus $35 per hour of
phone support. If you need to spend less than $100 per month on support,
how many hours can you get?
Lesson 4-5 Write a compound inequality for each situation. Graph your solution. 63–65. See margin
for graphs.
63. Water will not be in liquid form when it is colder than 32°F or warmer than
212°F. 32 K t K 212
64. The width of a parking space needs to be at least 8 feet and no more than
11 feet. 8 K w K 11
65. A car salesman has been told to sell a particular car for more than $14,500 and
up to the sticker price of $15,755. 14,500 R p K 15,755
Lesson 4-6 Write and solve an absolute value inequality for each situation. 66–68. See margin.
66. The ideal diameter of an aircraft tire is 105 inches. The acceptable error for
each tire is 0.175 inches. Find the range of acceptable tire diameters.
67. A tractor crankshaft is designed to have a radius of 4.25 cm. The acceptable
error for the radius is 0.005 cm. Find the range of acceptable radii for the
crankshaft.
68. The ideal weight of an exercise ball is 175 ounces. Each ball can have an error
of 0.35 ounces. What is the range of acceptable weights?
Chapter 4 Extra Practice: Skills and Word Problems
63.
100
64.
0
100
200
300
0
731
65.
2
4
6
8
10 12
0
2
4
6
8
10 12
731
Chapter
CHAPTER 5
page 732
Extra Practice: Skills and Word Problems
5
Extra Practice
Number of Apples
1.
Lesson 5-1 Sketch a graph to describe each situation. Label each section of the graph. 1–4. See margin.
1. the number of apples on a tree over one year
2. the amount of milk in your bowl as you eat cereal
3. the energy you use in a 24-h period
4. your distance from home plate after your home run
Time (1 year)
Lesson 5-2 Find the range of each function when the domain is {–4, –1, 0, 3}.
Ea
r
Ce
Pouring M
ilk
g
tin
5. y = 6x - 5 {–29, –11, –5, 13}
6. y = Δx« - 2 {2, –1, –2, 1}
8. y = 12x + 8 {6, 7.5, 8, 9.5}
9. y = -x 2 - x {–12, 0}
l
ng
ini
Dra owl
B
After
School
Energy Used
Breakfast
Lunch
Gym
3.
12. {(5, 2), (1, 3), (4, 7), (5, 6), (0, 4)} no
13. {(3.4, 2), (5.6, 2), (0.1, 2), (2.8, 2)} yes
14. {(6, 7), (5, 2), (7, 7), (4, 3), (0, 0)} yes
Distance from Home Plate
To
1B
16. y = 4 - x
18.
x
3
1
1
3
19.
f(x)
1
1
3
5
f(x) ≠ x ± 2
x
0
3
6
9
20.
f(x)
0
6
12
18
f(x) ≠ 2x
To
To
2B
22. (5, 4)
3B
23. (7, 7)
21.
f(x)
14
18
22
26
x
8
6
4
2
f(x)
4
3
2
1
f(x) ≠ 12 x
f(x) ≠ x – 7
To
P.
H.
27. y = 10 when x = 7 70
26. (-2, 9)
28. y = -8 when x = 12 –96
29. y = 0.2 when x = 4 0.8
30. (5.4, 3) and (2, y) 8.1
31. (x, 4) and (5, 6) 7.5
32. (3, 6) and (9, y) 2
33. (100, 2) and (x, 25) 8
34. (6, 1) and (x, -2) –3
35. (8, y) and (-2, 4) –1
Lesson 5-7 Find the second and fifth terms of each sequence.
x
2
2
36. A(n) = 22 + (n - 1)11 33, 66
37. A(n) = -2 + (n - 1)(-2) –4, –10
38. A(n) = -2 + (n - 1) –1, 2
39. A(n) = 1 + 4(n - 1) 5, 17
4
y
732
4
Chapter 5 Extra Practice: Skills and Word Problems
17.
2
y
1
x
2
25. (4, -8)
Each pair of points is on the graph of an inverse variation. Find the missing value.
y
2 O
24. (-3, -10)
Lesson 5-6 Find the constant of variation k for each inverse variation.
2
4
3
O
3
732
x
21
25
29
33
Lesson 5-5 Graph the direct variation that includes the given point.
Write the equation of the line. 22–26. See back of book.
Time
O
17. y = Δx« - 3
Lesson 5-4 Write a function rule for each table.
Time (1 day)
16.
{–38 , –23 , 0, 2}
11. {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)} yes
15. y = 2x + 1
15.
10. y = 23 x
Lesson 5-3 Graph each function. 15–17. See margin.
Time
4.
7. y = x 2 + 3x + 1 {5, –1, 1, 19}
Use a mapping diagram to determine whether each relation is a function.
ea
Amount of Milk
2.
1
x
Extra Skills and Word Problems
Extra Skills and Word Problems
Lesson 5-1 Sketch a graph to represent each situation. 40–42. See margin.
40. the speed of a bus as it makes its last stop to pick up students and then
continues until it arrives at school
41. the temperature of a lake from January through December
42. the height of a roller coaster during a ride
Lesson 5-2 Evaluate each function rule to find the range for the domain {1, 4, 9}.
43. The function f(x) 20 x represents the amount of change you receive after
paying for an item that costs x dollars with a $20 bill. {19, 16, 11}
44. The function f(x) x2 represents the area of a square with a side length of x. {1, 16, 81}
45. The function f(x) 8x represents the number of pieces of pizza from x
eight-piece pizzas. {8, 32, 72}
46. The function f(x) 175 x represents the amount of money in a savings
account that started with $175 after a deposit of x dollars.
40.
47. The function f(x) 4x represents the perimeter of a square with side length x.
Speed of bus
Lesson 5-3 Make a table of values and graph each function. 46–47. See back of book.
Lesson 5-4 Write a function rule for each situation.
48. the circumference of a circle C(r) when you know the radius r C(r) ≠ 2pr
49. the area of a 100-yard-long field A(w) when you know the width w A(w) ≠ 100w
50. the distance run in feet D(m) when you know the distance in miles m D(m) ≠ 5280m
0
n
51. the number of pounds P(n) when you know the number of ounces n P(n) ≠ 16
School
Time
41.
Temperature of lake
Lessons 5-5 and 5-6 Write a direct or inverse variation to model each situation.
Then answer the question.
52. After 30 minutes a car moving at a constant speed has traveled 25 miles.
Moving at the same speed, how far will it travel in 140 minutes? 50t ≠ d
about 117 mi
53. The perimeter of a square depends on the length of a side of the square. What
is the perimeter of a square with side length 13.4 in.? P ≠ 4s
53.6 in.
54. Two rectangular fields have the same area. One measures 75 yd by 60 yd. If the
other has a length of 72 yd, what is its width? Ow ≠ 4500
62.5 yd
55. Kevin is training to run in a half marathon. Initially, he could run 6 miles per
hour for 2 hours. Two months later he ran the same distance in 1 hour and
45 minutes. What is his new speed? rt ≠ 12
about 6.9 mi/h
0
Time (1 year)
Height of Roller Coaster
42.
Lesson 5-7 Use inductive reasoning to answer the question.
56. A train arrives at a subway station at 9:05 A.M. Another train arrives at
9:12 A.M. and a third arrives at 9:19 A.M. If the trains keep running on the
same schedule, at what times will each of the next three trains arrive?
9:26 A.M., 9:33 A.M., 9:40 A.M.
57. The balance of a car loan starts at $9,200 and decreases by $180 each month.
What will the balance be at the end of the next three months?
$9020, $8840, $8660
0
Chapter 5 Extra Practice: Skills and Word Problems
Last
Stop
Time
733
733
21.
Chapter
y
4
6
x
O
4
22.
8
Extra Practice: Skills and Word Problems
Lesson 6-1 Find the rate of change for each situation.
y
1. growing from 1.4 m to 1.6 m in one year 0.2 m/yr
3
2. bicycling 3 mi in 15 min and 7 mi in 55 min 0.1 mi/min
3. growing 22.4 mm in 14 s 1.6 mm/s
x
2
1
O
4. reading 8 pages in 9 min and 22 pages in 30 min 23 pages per minute
3
Lessons 6-2 and 6-3 Find the slope and y-intercept. 5–8. See margin.
23.
y
2
5. y = 6x + 8
6. 3x + 4y = -24
8. y = 23
4 x-8
7. 2y = 8
x
2
O
Graph each equation. 9–12. See back of book.
2
9. y = 2x - 3
2
10. y = 23 x - 4
12. y = -54 x
11. y = 12 x + 4
Lessons 6-4 and 6-5 Find the x- and y-intercepts for each equation. 13–16. See margin.
24.
y
13. 6x + y = 12
x
2
O
4
15. y = 12 x + 3
14. y = -7x
16. -2y = 5x - 12
2
Write the equation in point-slope form for the line through the given point with
the given slope. 17–20. See margin.
4
17. (4, 6); m = -5
25.
2
Graph each equation. 21–26. See margin.
y
x
2
20. (0, -6); m = 34
19. (8, 5); m = 12
18. (3, -1); m = 1
O
2
2
21. x + 4y = 8
22. y - 5 = -2(x + 1)
23. x + 3 = 0
24. 4x - 3y = 12
25. y = -1
26. y + 1 = 2 12(x + 2)
A line passes through the given points. Write an equation for the line in
slope-intercept form. 27–30. See margin.
26.
y
x
2 O
4
27. y ≠ 23 x ± 2
28. y ≠ –12 x ± 621
2
27. (2, 5) and (4, 8)
28. (1, 6) and (7, 3)
29. (-2, 4) and (3, 9)
30. (1, 6) and (9, -4)
31. (0, -7) and (-1, 0)
32. (7, 0) and (3, -4)
33. (0, 0) and (-7, 1)
34. (10, 0) and (0, 7)
7
y ≠ –7x – 7
y≠x–7
y ≠ –71 x
y ≠ –10
x±7
Lesson 6-5 Write an equation in standard form that satisfies the given conditions. 35–40. See back of book.
35. parallel to y = 4x + 1, through (-3, 5)
36. perpendicular to y = -x - 3, through (0, 0)
37. perpendicular to 3x + 4y = 12, through (7, 1)
38. parallel to 2x - y = 6, through (-6, -9)
39. parallel to the x-axis and through (4, -1)
40. through (4, 44) and parallel to the y-axis
29. y ≠ x ± 6
Lesson 6-6
30. y ≠ –54 x ± 714
41. a. Graph the (ages, grades) data of some
students in a school at the right. a–c. See back
of book.
b. Draw a trend line.
c. Find the equation of the line of best fit.
(10, 6), (16, 10), (15, 10), (18, 12), (17, 11),
(17, 12), (19, 12), (16, 11), (11, 7), (15, 9), (13, 8)
Lesson 6-7 Graph each equation by translating y ≠ »x… or y ≠ –»x…. 42–49. See back of book.
42. y = Δx« + 1
43. y = Δx + 2«
44. y = Δx - 2«
45. y = -Δx - 1«
46. y = -Δx + 1«
47. y = -Δx« + 1
48. y = Δx + 0.5«
49. y = Δx« - 4
734
Chapter 6 Extra Practice: Skills and Word Problems
CHAPTER 6
page 734
Practice
734
Extra
5. slope ≠ 6,
y-intercept ≠ 8
6. slope ≠ –43 ,
y-intercept ≠ –6
y-intercept ≠ 12
y-intercept ≠ 6
7. slope ≠ 0,
y-intercept ≠ 4
14. x-intercept ≠ 0,
y-intercept ≠ 0
17. y – 6 ≠ –5(x – 4)
8. slope ≠ –34 ,
y-intercept ≠ –8
15. x-intercept ≠ –6,
y-intercept ≠ 3
19. y – 5 ≠ 12 (x – 8)
20. y ± 6 ≠ 43 x
13. x-intercept ≠ 2,
16. x-intercept ≠ 12
5 ,
18. y ± 1 ≠ x – 3
50. The cost of four movie tickets is $30 and the cost of seven tickets is $52.50. $7.50/ticket
51. Five seconds after jumping out of the plane, a sky diver is 10,000 ft above the
ground. After 30 seconds, the sky diver is 3,750 ft above the ground. –250 ft/s
Lesson 6-2 Write an equation in slope-intercept form for each situation.
5
52. A skateboard ramp is 5 ft high and 12 ft long from end to end. y ≠ –12
x±2
53. An airplane with no fuel weighs 2575 lbs. Each gallon of gasoline added to
the fuel tanks weighs 6 lbs. y ≠ 6x ± 2
Lesson 6-3 Write a function for each situation and then determine a reasonable
range for the function.
C ≠ 3.75n
54. You plan to buy no more than three gallons of milk. Each gallon costs $3.75. $3.75 to $11.25
55. The amount of time spent in line at a grocery store depends on how many
people are in line ahead of you. Each person takes about two minutes to
check out at the cash register. t ≠ 2n; even whole numbers
61. False; the slope of
perpendicular lines have
a product of -/, so one
must be positive and the
other must be negative.
Extra Skills and Word Problems
Extra Skills and Word Problems
Lesson 6-1 Find the rate of change for each situation.
60. True; the same rate of
travel means that slopes
of the graphs are the
same, so the lines are
parallel.
Lesson 6-4 Write an equation in standard form for each situation.
56. Juan can ride his bike at 12 mi/h and walk at 4 mi/h. Write an equation that
relates the amount of time he can spend riding or walking combined, to
travel 20 miles. 12b ± 4w ≠ 20
57. You have $25 to buy supplies for a class party. Juice costs $3 per bottle and
chips cost $2 per bag. Write an equation that relates the amount of juice and
chips you can buy using $25. 3j ± 2c ≠ 25
Lesson 6-5 Write an equation in point-slope form for each situation.
58. A train travels at a rate of 70 mi/h. Two hours after leaving the station it
was 210 miles from its destination. y – 210 ≠ 70(x – 2)
59. An escalator has a slope of 34. After traveling forward 32 feet, the escalator is
24 feet above the floor. y – 24 ≠ 3 (x – 32)
4
Lesson 6-6 Tell whether each statement is true or false. Explain your choice. 60–61. See margin.
60. Two airplanes traveling at the same rate leave an airport 1 hour apart.
The graphs of the distance each plane travels will be parallel.
61. Two lines with negative slopes can be perpendicular.
Lesson 6-7
62. Use a calculator to find a line of best fit for the data.
Find the value of the correlation coefficient r.
Let x = 0 correspond to 1960. y ≠ 0.11x ± 7.3; 0.8466
Total U.S. Vehicle Production (millions)
1960
1970
1980
1990
2000
7.9
8.8
8.0
9.8
12.8
Lesson 6-8
63. A car traveling at a rate of 50 mi/h passes a rest area 30 minutes after the
beginning of the trip. Write an absolute value equation that represents the car’s
distance from the rest area. y ≠ 50»x – 0.5»
Chapter 6 Extra Practice: Skills and Word Problems
735
735
Chapter
CHAPTER 7
page 736
Extra Practice: Skills and Word Problems
7
Extra Practice
1. (4, –3);
y
Lesson 7-1 Solve each system by graphing. 1–3. See margin.
3x 2y 6
2
1. x - y = 7
x
4
2 O
4. x - y = 13
5. 3x - y = 4 x ≠ 1, y ≠ –1
infinite number
y - x = -13 of solutions
xy7
6. x + y = 4 x ≠ 0, y ≠ 4
x + 5y = -4
y = 7x + 4
Lesson 7-3 Solve each system by elimination.
2. (–2, –1);
y
7. x + y = 19 x ≠ 6, y ≠ 13
y 2x 3
2
2
-3x + 2y = -30
11. 4x - 9y = 61 x ≠ 4, y ≠ –5
y - x = -8
4
9. 3x + y = 3 x ≠ 4, y ≠ –9
3x + 2y = -17
10. 6x + y = 13 x ≠ 3, y ≠ –5
x
O
8. -3x + 4y = 29 x ≠ –7, y ≠ 2
x - y = -7
2
12. 4x - y = 105 x ≠ 25, y ≠ –5
10x + 3y = 25
x + 7y = -10
Lesson 7-4 Write a system of equations to model each problem and solve.
y 23 x 4
13. Suppose you have 12 coins that total 32 cents. Some of the coins are nickels and
the rest are pennies. How many of each coin do you have? x ± y ≠ 12, 5x ± y ≠ 32; 5 nickels, 7 pennies
3. (0, 6);
14. Claire bought three bars of soap and five sponges for $2.31. Steve bought five 3x ± 5y ≠ 2.31, 5x ± 3y ≠ 3.05;
soap: $.52, sponges: $.15
bars of soap and three sponges for $3.05. Find the cost of each item.
y
15. The perimeter of a rectangular lot is 74 feet. The cost of fencing along the two 2x ± 2y ≠ 74, 7x ± 2y ≠ 159;
lengths is $1 per foot, and the cost of fencing along the two widths is $3.50 per length: 20 ft, width: 17 ft
foot. Find the dimensions of the lot if the total cost of the fencing is $159.
3x 4y 24
4
16. A chemist wants to make a 10% solution of fertilizer. How much water
and how much of a 30% solution should the chemist mix to get 30 L of a
10% solution? x ± y ≠ 30, x ± 0.7y ≠ 0.9(30); water: 20 L, 30% solution: 10 L
2
y 2x 6
2 O
2
4
x
17. Fruit drink A consists of 6% pure fruit juice and drink B consists of 15% pure fruit
juice. How much of each kind of drink should you mix together to get 4 L of a 10%
concentration of fruit juice? x ± y ≠ 4, 0.06x ± 0.15y ≠ 0.1(4); A: 2 92 L, B: 1 79 L
y
x
O
2
20.
3x + 4y = 24
Lesson 7-2 Solve each system by using substitution.
4
19.
3. y = -2x + 6
y = 2 32 x - 4
3x + 2y = 6
4
2
4
2. y = 2x + 3
18. A motor boat traveled 12 miles with the current, turned around, and returned
12 miles against the current to its starting point. The trip with the current took
2 hours and the trip against the current took 3 hours. Find the speed of the boat
and the speed of the current. (x ± y)2 ≠ 12, (x – y)3 ≠ 12; boat: 5 mph, current: 1 mph
2
y
O
1 2 3
Lesson 7-5 Graph each linear inequality. 19–24. See margin.
x
2
3
4
21.
19. y , x
20. y , x - 4
21. y . -6x + 5
22. y # 14 - x
23. y $ 14 x - 3
24. 2x + 3y # 6
Lesson 7-6 Solve each system by graphing. 25–30. See margin.
y
25. y # 5x + 1
26. y . 4x + 3
y.x-3
2
O
736
y
8
4
8 4
8
12
23.
x
O
4 8
2
4
30. y # 5x - 2
y $ -x + 1
y.3
Chapter 7 Extra Practice: Skills and Word Problems
24.
y
O
y.x-4
29. y # 5
y . -2x - 3
22.
736
y $ -2x - 1
28. y , -2x + 1
x
27. y . -x + 2
2
4
3
25.
y
26.
y
y
3
1
x
1
1
x
O
1 2 3
O
1
x
x
O
5
2
1 2
2
32. Suppose that you have $75 in your savings account and you save an additional
$5 per week. Your friend has $30 in his savings account and saves an additional
$10 per week. In how many weeks will you both have the same amount of
money in your accounts?
Lesson 7-2 Write and solve a system of equations by substitution.
33. A farmer grows corn and soybeans on her 300-acre farm. She wants to plant c ± s ≠ 300
110 more acres of soybeans than corn. How many acres of each crop does she s ≠ c ± 110
need to plant? corn: 95 acres; soybeans: 205 acres
34. The perimeter of a rectangle is 34 cm. The length is 1 cm longer than the width. 2 / ± 2w ≠ 34
What are the dimensions of the rectangle? 9 cm by 8 cm
/≠w±1
39. 3a + b K 10
12
8
4
0
1
2
3
Apples (lbs)
Answers may vary. Sample:
1 lb of apples and 3 lbs of
bananas, or 2 lbs of apples
and 2 lbs of bananas, or 1 lb
of apples and 4 lbs of
bananas
Lesson 7-3 Write and solve a system of equations using elimination.
4h ± 7c ≠ 34.50
8h ± 3c ≠ 30.50
$2.50, $3.50
35. Two groups of people order food at a restaurant. One group orders 4
hamburgers and 7 chicken sandwiches for $34.50. The other group orders 8
hamburgers and 3 chicken sandwiches for $30.50. Find the cost of each item.
32. y = 75 + 5x
y = 30 + 10x
9 weeks
Bananas (lbs)
31. One calling card has a $.50 connection fee and charges $.02 per minute.
Another card has a $.25 connection fee and charges $.03 per minute. After how
many minutes would a call cost the same amount using either card?
Extra Skills and Word Problems
Extra Skills and Word Problems
Lesson 7-1 Write and solve a system of equations by graphing. 31–32. See margin.
31. y = 0.5 + 0.02x
y = 0.25 + 0.03x
25 minutes
36. The sum of two numbers is 25. Their difference is 9. What are the x ± y ≠ 25
x–y≠9
two numbers?
17, 8
Lesson 7-4 Write and solve a system of equations for each situation by any
method. Explain why you chose the method.
40. 2< + 2w K 40
20
Width (ft)
b ≠ 45 g; b ± g ≠ 3321
37. The ratio of boys to girls at a college is 4 : 5. How many boys and girls are there 1476 boys, 1845 girls
if the total number of students is 3321?
38. A boat travels 18 miles downstream in 1.5 hours. It then takes the boat 3 hours (b ± c)(1.5) ≠ 18
to travel upstream the same distance. Find the speed of the boat in still water (b – c)(3) ≠ 18
boat: 9mi/h; current: 3 mi/h
and the speed of the current.
15
10
5
Lesson 7-5 Write and graph a linear inequality for each situation. 39–40. See margin.
0
39. Suppose you can spend up to $10 on bananas and apples. Apples cost $3 per
pound and bananas cost $1 per pound. List three possible combinations of
apples and bananas you can buy.
5
10 15 20
Length (ft)
Answers may vary. Sample:
5 ft by 10 ft, 8 ft by 7 ft,
2 ft by 11 ft.
40. Trenton is going to make a rectangular garden in his yard. He wants the
perimeter to be no larger than 40 ft. What are three possible sets of dimensions
that the garden can have?
41. 17d + 14c K 60
d+cL2
Lesson 7-6
4
DVDs
41. Hideo plans to spend no more than $60 at an entertainment store on DVDs
and CDs. DVDs cost $17 each and CDs cost $14 each. He wants to buy at least
two items. Write and graph a system of linear inequalities that describes the
situation. What are three possible combinations of CDs and DVDs that he can
buy? Write and graph a system of inequalities that describes the situation.
See margin.
2
0
737
Chapter 7 Extra Practice: Skills and Word Problems
27.
28.
y
29.
y
x
1
2 O
3
1
5
x
2
30.
y
4
2
4
y
4
2
CDs
4
Answers may vary. Sample:
He can buy 3 CD’s and 1 DVD,
or 1 CD and 2 DVD’s, or 2 CD’s
amd 1 DVD.
2
2
O
2
O
x
x
2
737
Chapter
CHAPTER 8
page 738
41. 1.5; 40.5, 60.75
42. 0.5; 0.25, 0.125
Extra Practice: Skills and Word Problems
8
Extra Practice
Lessons 8-1 to 8-5 Simplify each expression. Use only positive exponents.
43. 0.2; –0.008, –0.0016
1. (2t)-6
2. 5m5m-8 53
44. 2; –16, –32
5.
6.
45. 3; 54, 162
9.
46. –0.5; –0.15, 0.075
50.
51.
52.
53.
decrease
{
}
–1, –4, –16 ;
decrease
55.
{ 15, 3,
}; decrease
{12 , 1, 2, 4}; increase
{23 , 2, 6, 18}; increase
16
{45 , 1, 45 , 25
}; decrease
{52 , 1, 52 , 254 }; increase
{–20, –4, –54 , –254 };
57.
58.
59.
60.
r 5g3
c6
a3b10
m
A w-2j-4 B -3 A j7j3 B
w 6 j 22
1 a4
10. 24
14.
4t 8t21
4. A m7t-5 B 2 m10
7. A t 6 B 3(m)2 t18m2
8.
11.
a
A 2t 5 B 3
3. (4.5)4(4.5)-2 (4.5)2
2t 8
w7
w26
14
t
A 3n4 B 2 9n8
6 6t 4
12. 24
w13
t
6 23
15. Q a 7 R
a3
5 23 22 1
16. Q c c24 R
12
a
c
c
Evaluate each expression for m ≠ 2, t ≠ –3, w ≠ 4, and z ≠ 0.
17. t m 9
21. A w z B m 1
18. t-m 19
19. (w ? t)m 144
22. w m w z 16
20. wm ? t m 144
23. z-t A m t B z 0
24. w-t t t –64
27
27. 1500 1.5 3 10 3
28. 0.0002 2 3 10–4
Write each number in scientific notation.
25. 34,000,000 3.4 3 10 7
26. 0.00063 6.3 3 10–4
29. 360,000 3.6 3 10 5
30. 6,200,000,000 6.2 3 10 9 31. 0.05 5 3 10–2
32. 0.000000000891
8.91 3 10–10
Write each number in standard notation.
54.
56.
g
a b c
{ 13 , 1, 3, 9}; increase
{ 34 , 1, 34 , 169 }; decrease
{ 32 , 1, 32 , 49 }; increase
{ 16 , 12 , 32 , 29 }; increase
{ –37 , –3, –21, –147};
–41 ,
r5
23
2 27c 4
13. a 5b 3 22
10
47. 31; 10
9 , 27
48. 4; –144, –576
49.
1
64t 6
2
A x 2 n 4 B A n-8 B x 4
n
3 3
5 , 25
increase
61. exponential growth;
growth factor ≠ 8
62. exponential growth;
growth factor ≠ 2
33. 8.05 3 10 6 8,050,000
34. 3.2 3 10-7 0.00000032 35. 9.0 3 10 8 900,000,000 36. 4.25 3 10 -4 0.000425
37. 2.35 3 10 2 235
38. 6.3 3 104 63,000
39. 2.001 3 10 -5
40. 5.2956 3 103 5295.6
0.00002001
Lesson 8-6 Find the common ratio of each sequence. Then find the next two terms. 41–48. See margin.
41. 12, 18, 27, c
45. 2, 6, 18, c
42. 2, 1, 0.5, c
43. -1, -0.2, -0.04, c
44. -2, -4, -8, c
46. 1.2, -0.6, 0.3, c
47. 30, 10, 10
3,c
48. -2.25, -9, -36, c
Lesson 8-7 Evaluate each function for the domain {–1, 0, 1, 2}. As the values of the domain increase, do the values
of the function increase or decrease? 49–60. See margin.
49. y = 3 x
50. y = Q 34 R
53. y = -3 ? 7 x
54. y = -(4)x
55. y = 3 ? Q 15 R
57. y = 2 ? 3x
58. y = (0.8)x
59. y = 2.5x
x
52. y = 12 ? 3x
51. y = 1.5 x
x
56. y = 2x
60. y = -4 ? (0.2)x
Lesson 8-8 Identify each function as exponential growth or exponential decay.
Then identify the growth factor or decay factor. 61–68. See margin.
61. y = 8 x
63. y = 9 ? Q 12 R
x
64. y = 4 ? 9 x
63. exponential decay; decay
factor ≠ 12
62. y = 34 ? 2 x
65. y = 0.65 x
66. y = 3 ? 1.5 x
67. y = 25 ? Q 14 R
x
68. y = 0.1 ? 0.9 x
64. exponential growth;
growth factor ≠ 9
Write an exponential function to model each situation. Find each amount after the
specified time.
65. exponential decay; decay
factor ≠ 0.65
69. $200 principal, 4% compounded annually for 5 years y ≠ 200(1.04)x; $243.33
66. exponential growth;
growth factor ≠ 1.5
67. exponential decay; decay
factor ≠ 14
68. exponential decay; decay
factor ≠ 0.9
738
70. $1000 principal, 3.6% compounded monthly for 10 years y ≠ 1000(1.003)x; $1432.56
71. $3000 investment, 8% loss each year for 3 years y ≠ 3000(0.92)x; $2336.06
738
Chapter 8 Extra Practice: Skills and Word Problems
72. Suppose an investment doubles in value every 5 years. This year the investment
is worth $12,480. How much will it be worth 10 years from now? How much
was it worth 5 years ago? $49,920; $6240
Lesson 8-2 Write each number in scientific notation.
73. A bacteria culture has a population of approximately 7,500,000,000. 7.5 3 10 9
74. The diameter of a blood cell is about 0.0000082 m. 8.2 3 10 –6 m
Lessons 8-3 and 8-4 Write each answer in scientific notation.
75. A light-year is the distance light travels in one year. If the speed of light is
about 3 105 km/s, how long is a light-year in kilometers? (Use 365 days for
the length of a year). about 9.5 3 1012 km
76. The radius of Earth is approximately 6.4 106 m. Use the formula V = 43 pr 3 to
find the volume of Earth. about 1.1 3 1021 m3
Extra Skills and Word Problems
Extra Skills and Word Problems
Lesson 8-1
77. A spherical cell has a radius of 2.75 10–6 m. Use the formula for the
surface area of a sphere S.A. = 4pr 3to find the surface area of a cell. about 9.5 3 10–11 m2
Lesson 8-5
64
78. What is the volume of a cube with a side length of 45 m? 125
m3
79. The speed of sound is approximately 1.2 103 km/h. How long does it take for
sound to travel 7.2 102 km? Write your answer in minutes. 36 min
Lesson 8-6 Write a rule and find the given term in each geometric sequence
described below.
80. What is the ninth term when the first term is 4 and the common ratio is 6? A(n) 5 4 ? (26)n 2 1; 6,720,000
81. What is the sixth term when the first term is 60 and the common ratio is 0.4? A(n) 5 60 ? (0.4)n 2 1; 0.6144
Lesson 8-7 Write and solve an exponential equation to answer each question.
82. Suppose an investment of $5,000 doubles every 12 years. How much is the f(x) 5 5000 ? 2x
$40,000, $80,000
investment worth after 36 years? After 48 years?
83. Suppose 15 animals are taken to an island, and then their population triples f(x) 5 15 ? 3x
every 8 months. How many animals will there be in 4 years?
10,935 animals
Lesson 8-8 Find the balance in each account.
84. You deposit $2500 in a savings account with 3% interest compounded annually.
What is the balance in the account after 6 years? $2,985.13
85. You deposit $750 in an account with 7% interest compounded semiannually.
What is the balance in the account after 4 years? $987.61
86. You deposit $520 in an account with 4% interest compounded monthly. What is
the balance in the account after 5 years? $634.92
Chapter 8 Extra Practice: Skills and Word Problems
739
739
Chapter
CHAPTER 9
page 739
1.
±
2.
5x 2
– 2x
4x 2
– 11x ± 11
4.
–t 2
5.
–10c3
6.
–19v 3
± 10t ± 11
4. A 8t 2 + t + 10 B - A 9t 2 - 9t - 1 B
– 9c – 7
5. A -7c 3 + c 2 - 8c - 11 B - A 3c 3 + 2c 2 + c - 4 B
6. A 6v + 3v 2 - 9v 3 B + A 7v - 4v 2 - 10v 3 B
–
± 13v
7. A s 4 - s 3 - 5s 2 + 3s B - A 5s 4 + s 3 - 7s 2 - s B
8. A 9w - 4w 2 + 10 B + A 8w 2 + 7 + 5w B
± 3m – 2)
21. 4c 2(3c3 – c ± 4)
–2v 5(5v4
– 4v – 1)
23. n2(2n2 – 3n ± 6)
24.
3. A 4m 3 + 7m - 4 B + A 2m3 - 6m + 8 B
v2
19. t 2(t 4 – t 3 ± t 2 ± 1)
5r(4r 2
2. A x 2 + 3x - 2 B + A 4x 2 - 5x + 2 B
–
8. 4w2 ± 14w ± 17
22.
1. A 5x 3 + 3x 2 - 7x + 10 B - A 3x 3 - x 2 + 4x - 1 B
c2
7. –4s4 – 2s3 ± 2s2 ± 4s
20.
Extra Practice: Skills and Word Problems
Lesson 9-1 Simplify. Write each answer in standard form. 1–8. See margin.
3. 6m3 ± m ± 4
3(m2
9
Extra Practice
2x 3
± 3r ± 1)
25. x 5(4x2 ± 9x ± 5)
26.
–d 4(2d 6
27.
–5c 2
–
4d 4
– 7)
9. The sides of a rectangle are 4t - 1 and 5t + 9. Write an expression for the
perimeter of the rectangle. 18t ± 16
10. Three consecutive integers are n - 1, n, and n + 1. Write an expression for the
sum of the three integers. 3n
Lesson 9-2 Simplify each product.
11. 4b A b2 + 3 B 4b3 ± 12b
9c3 – 27c2 ± 45c
12. 9c A c 2 - 3c + 5 B
32m2 – 40m
13. 8m(4m - 5)
5k3 ± 40k2
14. 5k A k 2 + 8k B
15. 5r 2 A r 2 + 4r - 2 B
16. 2m 2 A m 3 + m - 2 B
17. -3x A x 2 + 3x - 1 B
5r 4 ± 20r 3 – 10r 2
2m5 ± 2m3 – 4m2
–3x 3 – 9x2 ± 3x
Find the GCF of the terms of each polynomial. Factor. 19–26. See margin.
18. -x A 1 + x + x 2 B
–x 3 – x2 – x
19. t 6 + t 4 - t 5 + t 2
20. 3m 2 - 6 + 9m
21. 16c 2 - 4c 3 + 12c 5
22. 8v 6 + 2v 5 - 10v 9
23. 6n2 - 3n 3 + 2n 4
24. 5r + 20r 3 + 15r 2
25. 9x 6 + 5x 5 + 4x 7
26. 4d 8 - 2d 10 + 7d 4
± 7c ± 6
28. 6t 2 ± t – 1
Lessons 9-3 and 9-4 Simplify each product. Write in standard form. 27–38. See margin.
29. w 3 ± 4w2 ± 3w – 2
27. (5c + 3)(-c + 2)
28. (3t - 1)(2t + 1)
29. (w + 2) A w 2 + 2w - 1 B
30. (3t + 5)(t + 1)
30. 3t 2 ± 8t ± 5
31. (2n - 3)(2n + 4)
32. (b + 3)(b + 7)
33. (3x + 1)2
34. (5t + 4)2
35. (w - 1) A w 2 + w + 1 B
36. (a + 4)(a - 4)
37. (3y - 2)(3y + 2)
38. A w 2 + 2 B A w 2 - 2 B
31. 4n2 ± 2n – 12
32. b2 ± 10b ± 21
33. 9x 2 ± 6x ± 1
34. 25t2 ± 40t ± 16
35. w 3 – 1
36. a 2 – 16
39. Geometry A rectangle has dimensions 3x - 1 and 2x + 5. Write an expression
for the area of the rectangle as a product and in standard form. (3x – 1)(2x ± 5), 6x 2 ± 13x – 5
40. Write an expression for the product of the two consecutive odd integers n - 1
and n + 1. (n – 1)(n ± 1) ≠ n2 – 1
Lessons 9-5 to 9-7 Factor each expression. 41–60. See margin.
41. x 2 - 4x + 3
42. 3x 2 - 4x + 1
43. v 2 + v - 2
44. 5t 2 - t - 18
45. m 2 + 9m - 22
46. x 2 - 2x - 15
47. 2n 2 + n - 3
48. 2h 2 - 5h - 3
49. m 2 - 25
50. 9y 2 - 1
51. 9y 2 + 6y + 1
52. p 2 + 2p + 1
41. (x – 3)(x – 1)
53. x 2 + 6x + 9
54. 25x 2 - 9
55. 4t 2 + t - 3
56. 9c 2 - 169
42. (3x – 1)(x – 1)
57. 4m 2 - 121
58. 3v 2 + 10v - 8
59. 4g 2 + 4g + 1
60. -w 2 + 5w - 4
43. (v – 1)(v ± 2)
61. 9t 2 + 12t + 4
62. 12m 2 - 5m - 2
63. 36s 2 - 1
(3m – 2)(4m ± 1)
(6s ± 1)(6s – 1)
(3t ± 2)2
Lesson 9-8 Factor each expression. 65–72. See margin.
64. c 2 - 10c + 25
(c – 5)2
65. 3y 3 + 9y 2 - y - 3
66. 3u 3 + u 2 - 6u - 2
67. w 3 - 3w 2 + 3w - 9
68. 4z 3 + 2z2 - 2z - 1
69. 3x 3 + 8x 2 - 3x
70. y 5 - 9y
71. 2p3 - 4p 2 + 2p - 4
72. 3y 3 - 3y 2 - 6y
37. 9y 2 – 4
38.
w4
–4
44. (t – 2)(5t ± 9)
45. (m – 2)(m ± 11)
46. (x – 5)(x ± 3)
47. (n – 1)(2n ± 3)
48. (h – 3)(2h ± 1)
49. (m – 5)(m ± 5)
50. (3y ± 1)(3y – 1)
51. (3y ± 1)2
52. ( p ± 1)2
53. (x ± 3)2
740
740
Chapter 9 Extra Practice: Skills and Word Problems
54. (5x ± 3)(5x – 3)
59. (2g ± 1)2
68. (2 z ± 1)(2z 2 – 1)
55. (t ± 1)(4t – 3)
60. –(w – 4)(w – 1)
69. x(x ± 3)(3x – 1)
56. (3c – 13)(3c ± 13)
3)(3y2
65. (y ±
– 1)
70. y(y2 – 3)(y 2 ± 3)
57. (2m ± 11)(2m – 11)
66. (3u ± 1)(u2 – 2)
71. 2(p – 2)(p2 ± 1)
58. (v ± 4)(3v – 2)
67. (w – 3)(w2 ± 3)
72. 3y(y – 2)(y ± 1)
73. A rectangle has side lengths 4k 3 and 2k 2. 12k – 2
74. A triangle has side lengths 2t2, 4t 3, and 10 2t. 2t2 ± 2t – 13
75. A rhombus has two sides 3d3 2d long and two sides d2 5 long. 6d 3 ± 2d 2 – 4d ± 10
Lesson 9-2
76. A rectangular roof has a length of 13g and a width of 4g 7. Write an
expression for the area of the roof. 52g2 ± 91g
77. A cylinder has a volume of 12w3 20w and a height of 4w. Find an expression
for the area of the base. 3w2 ± 5
Lesson 9-3
78. A circular pool has a radius of 5p 3 m. Write an expression for area
the pool. 25p2π – 30pπ ± 9π
Extra Skills and Word Problems
Extra Skills and Word Problems
Lesson 9-1 Find an expression for the perimeter of each figure.
79. An office building has a rectangular base with side lengths of 12y 7 and
22y 4. Write an expression for the area of a floor in the office building.
264y2 ± 202y – 28
Lesson 9-4
80. Suppose you play a game with two number cubes. Let A represent rolling a
number less than 4 and B represent rolling a number greater than 4. The
probability of A is 21 . The probability of B is 13.
a. Find Q 21A + 13B R 2 41 A2 ± 31 AB ± 19 B2
b. What is the probability that both cubes show a number less than 4? 14
c. What is the probability that one cube shows a number less than 4 and the
other cube shows a number greater than 4? 13
81. Suppose there are two squares with side lengths of 4x 3 and 2x 4. Write an
expression for the area of each square. Find the area of each square if x 6 cm.
16x2 – 24x ± 9, 4x2 ± 16x ± 16; 441 cm2, 256 cm2
Lesson 9-5
82. Write an expression for the side length of a square that has an area of
h2 12h 36. h – 6
83. Write an expression for the radius of a circular flower garden with an area of
pm2 14pm 49p. m ± 7
Lessons 9-6 to 9-8 Use factoring to find expressions for possible dimensions of
each figure.
84. A rectangular parking lot has an area of 10w2 9w 40. (5w ± 8) by (2w – 5)
85. A rectangular door has an area of 12d2 31d 14 (12d – 7) by (d – 2).
86. A circular window has an area of 49pv2 84pv 36p. radius: (7v ± 6)
87. A rectangular field has an area of 64m2 169n2. (8m – 13n) by (8m ± 13n)
88. A rectangular prism has a volume of 6t3 44t2 70t. 2t by (13t ± 7) by (t ± 5)
89. A rectangular field has an area of 10k3 25k2 6k 15. (5k2 – 3) by (2k ± 5)
Chapter 9 Extra Practice: Skills and Word Problems
741
741
18.
Chapter
y
2
10
x
1
O
Extra Practice: Skills and Word Problems
2
Lesson 10-1 Without graphing, describe how each graph differs from the graph of
y ≠ x 2. 1–8. See margin.
y
19.
6
4
1. y = 3x 2
2. y = -4x 2
3. y = -0.5x 2
4. y = 0.2x 2
5. y = x 2 - 4
6. y = x 2 + 1
7. y = 2x 2 + 5
8. y = -0.3x 2 - 7
Lesson 10-2 Identify the axis of symmetry and the vertex of each function.
9. y = 3x 2 x ≠ 0, (0, 0)
2
x
2 O
12. y = -x 2 + 2x + 1 x ≠ 1, (1, 2)
2
10. y = -2x 2 + 1 x ≠ 0, (0, 1)
11. y = 0.5x 2 - 3 x ≠ 0, (0, –3)
13. y = 3x 2 + 6x x ≠ –1, (–1, –3)
14. y = 34 x 2 x ≠ 0, (0, 0)
15. y = 2x 2 - 9 x ≠ 0, (0, –9)
20.
16. y = -5x 2 + x + 4
17. y = x 2 - 8x x ≠ 4, (4, –16)
1
1 81
x ≠ 10
, ( 10
, 20 )
Graph each quadratic inequality. 18–20. See margin.
y
2
1
3
18. y . x 2 - 4
x
O
Lessons 10-3 and 10-4 Solve each equation. If the equation has no solution,
write no solution.
55. quadratic
y
4
x
23. c 2 - 100 = 0 10, –10
24. 9d 2 = 25 35 , –53
25. (x - 4)2 = 100 14, –6
26. 3x 2 = 27 3, –3
27. 2x 2 - 54 = 284 13, –13
28. 7n 2 = 63 3, –3
29. h2 + 4 = 0 no solution
33. 2x 2 - 4x + 1 = 0 2 w2"2
36. x 2 + 8x + 4 = 0 –4 w 2 "3
y
6
4
2
x
O
22. x 2 + x - 2 = 0 1, –2
30. x 2 + 6x - 2 = 0 –3 w "11
4
56. linear
8
21. x 2 = 36 6, –6
Lessons 10-5 and 10-6 Solve each equation. If the equation has no solution,
write no solution.
2
2
2
20. y # x 2 + x - 2
2 3
3
O
19. y , 2x 2 + x
4
6
8
31. x 2 - 5x = 7 5 w 2"53
32. x 2 - 10x + 3 = 0 5 w "22
34. 3x 2 + x + 5 = 0 no solution
35. 12 x 2 - 3x - 8 = 0 8, –2
37. x 2 - 2x - 6 = 0 1 w "7
39. x 2 + 5x + 6 = 0 –2, –3
40. d 2 - 144 = 0 12, –12
42. x 2 + 4x = 2x 2 - x + 6 3, 2
43. 3x 2 + 2x - 12 = x 2 2, –3
38. -3x 2 + x - 7 = 0 no solution
41. c 2 + 6 = 2 - 4c –2
44. r 2 + 4r + 1 = r 23 w2 "5
45. d 2 + 2d + 10 = 2d + 100
46. 3c 2 + c - 10 = c 2 - 5 21 w4"41 47. t 2 - 3t - 10 = 0 5, –2
w3 "10
48. Agriculture You are planting a rectangular garden. It is 5 feet longer than
3 times its width. The area of the garden is 250 ft2. Find the dimensions of
the garden. 25
3 ft by 30 ft
57. exponential
Lesson 10-7 Find the number of solutions of each equation.
y
6
4
50. 5x 2 - 4x = -6 0
51. x 2 - 20x + 101 = 1 1
52. 2x 2 - 8x + 9 = 4 2
53. 4x 2 - 5x + 6 = 0 0
54. x 2 - 2x + 7 = 0 0
Lesson 10-8 Graph each set of data. Which model is most appropriate for
each set? 55–57. See margin.
2
x
O
49. 3x 2 + 4x - 7 = 0 2
2
4
55. (2, 4), (4, 4), (1, 2), (5, 1.5)
742
Extra Practice
1. narrower
742
57. (0, 7), (1, 3), (3, 0.5), (2, 1)
Chapter 10 Extra Practice: Skills and Word Problems
CHAPTER 10
page 742
56. (3, 8), (4, 6), (5, 5), (6, 4), (7, 3)
2. narrower and reflected
over the x-axis
3. wider and reflected over
the x-axis
7. narrower and translated
up 5 units
4. wider
8. wider, reflected over the
x-axis, and translated
down 7 units
5. translated down 4 units
6. translated up 1 unit
58. Water from melting snow drips from a roof at a height of 40 ft. The function
h 16t2 40 gives the approximate height h in feet of a drop of water
t seconds after it falls. Graph the function. See margin.
Lesson 10-2 The formula h = 16t2 vt c describes the height of an object
thrown into the air, where h is the height, t is the time in seconds, v is the initial
velocity, and c is the initial height. Use the formula to answer each question.
59. A football is thrown with an upward velocity of 15 ft/s from an initial height
of 5 feet. How long will it take for the football to reach its maximum height? 0.46875 s
60. A ball is thrown from the top of a 50-ft building with an upward velocity of
24 ft/s. When will it reach its maximum height? How far above the ground will
it be? 0.75 s; 59 ft
Lesson 10-3 Model each problem with a quadratic equation. Then solve. If
necessary, round to the nearest tenth.
40
Height (ft)
Extra Skills and Word Problems
Lesson 10-1
30
20
10
0
1
2
Time (s)
Extra Skills and Word Problems
58.
61. Find the radius of a circular lid with an area of 12 in.2. 12 ≠ pr 2; 2.0 in.
62. Find the side length of a square sandbox with an area of 150 ft2. s2 ≠ 150; 12.2 ft
2
63. Find the diameter of a circular pond with an area of 300 m2. (D
2 ) p ≠ 300; 19.6 m
Lesson 10-4 Answer each question by factoring a quadratic equation.
64. The length of an open-top box is 4 cm longer than its width. The box was
made from a 480-cm2 rectangular sheet of material with 6 cm-by-6 cm squares
cut from each corner. The height of the box is 6 cm. Find the dimensions of
the box. 8 cm 12 cm 6 cm
65. Suppose you throw a rugby ball into the air with an initial upward velocity of
29 ft/s and an initial height of 6 ft. The formula h = 16t2 29t 6 gives the
ball’s height h in feet at time t seconds. Solve the equation for h = 0 to find
when the ball will hit the ground. 2 s
Lesson 10-5 Solve by completing the square.
66. A rectangular patio has a length of x 6 m, a width of x 8 m, and a total area
of 400 m2. Find the dimensions to the nearest tenth. 19.0 m, 21.0 m
Lessons 10-6 and 10-7
67. A tennis ball is hit with a vertical velocity of 40 ft/s from an initial height of 7 ft.
In how many seconds will the ball hit the ground? about 2.66 s
68. A ball is thrown from an initial height of 6 feet at a rate of 42 ft/s to someone
standing on a roof 30 feet above the ground. Use the discriminant to determine
if the ball will reach the person on the roof. yes
Lesson 10-8
69. Use a graphing calculator to determine what kind
of function best models the data. Let t 0
correspond to the year 2000. Write an equation
that models the data. quadratic;
y ≠ 1.786x2 – 24.043x ± 226.371
Bird Population in the Town Park
2000
2001
2002
2003
2004
225
207
185
168
160
Chapter 10 Extra Practice: Skills and Word Problems
743
743
Chapter
Extra Practice: Skills and Word Problems
11
Lesson 11-1 Simplify each radical expression.
1. !27 "33
!81
4. !72 65
!50
7.
4
44x 2x2
Ä 11
2.
Å
25 5
4 2
3.
13. 3 !300 + 2 !27 36 "3
"z3 z"5
!5z 5
1
19.
"2 – 1
!2 1 1
16.
50 5"2
3
9
5. !25 ? !4 10
6. !27 ? !3 9
2
8. "3c c3
9. !45 ? !18 9"10
!27
Lesson 11-2 Simplify each radical expression.
10. !75 - 4 !75 –15 "3
Å
11. !5A !20 2 !80 B –10
12. !6 A !6 2 3B 6 – 3"6
17. A !5 1 1BA !5 2 1B 4
18. A !3 1 !2 B 2 5 ± 2 "6
15. !8 - 4 !2 –2 "2
14. 5 !2 ? 3 !50 150
20.
21. !3 1 1 "6 ± "2 – "3 –1
2
–Q"2 ± 2R
!2 2 2
!2 1 1
Lesson 11-3 Solve each radical equation. Check your solution.
22. !3x 1 4 = 1 –1
23. 6 = !8x 2 4 5
24. 2x = !14x 2 6 12 , 3
28. !3x 2 2 = x 1, 2
29. !x 1 7 = x + 1 2
9 1, 6
30. !x 1 3 5 x 1
5
25. !2x 1 5 = !3x 1 1 4
26. 2x = !6x 1 4 2
27. !5x 1 11 = !7x 2 1 6
Lesson 11-4 Find the domain of each function. Then graph the function. 31–36. See back of book.
31. y = !x 1 5
34. y = !x - 4
32. y = !x - 2
33. y = !x 1 1
35. y = !x 2 3
36. y = !x + 6
Lesson 11-5 Use #ABC to find the value of each expression.
9
37. sin A 41
40
38. cos A 41
9
39. tan A 40
40. sin B 40
41
9
41. cos B 41
42. tan B 40
9
41
A
40
B
9
C
Find the value of each expression. Round to the nearest ten-thousandth.
43. sin 728 0.9511
44. cos 298 0.8746
45. tan 488 1.1106
46. tan 528 1.2799
47. sin 658 0.9063
48. cos 438 0.7314
Lesson 11-6
49. A forester is 50 m from the base of a tree and measures the angle between the
ground and the top of the tree. If the angle is 768, find the height of the tree.
Round your answer to the nearest meter. 201 m
50. A pilot is flying at an altitude of 25,000 ft. The angle of depression from her
position to the start of runway is 2°. How far is the airplane from the start of
the runway (in ground distance)? 715,906 ft (about 136 mi)
744
744
Chapter 11 Extra Practice: Skills and Word Problems
Extra Skills and Word Problems
Extra Skills and Word Problems
Lesson 11-1 Use the formula d ≠ !1.5h to estimate the distance d in miles to a
horizon when h is the height in feet of the viewer’s eyes above the ground.
Round your answer to the nearest mile.
51. Find the distance you can see to the horizon from the top of a building that is
355 ft high. 23 mi
52. Find the distance you can see to the horizon from an airplane that is 36,000 ft
above the ground. 232 mi
53. Find the distance you can see to the horizon from 15 ft above the ground. 5 mi
Lesson 11-2 Find an exact solution. Then find an approximate solution to the nearest tenth.
54. The ratio of the length of a painting to its width is (1 + !5) : 1. The length is 25 25A !5 2 1B ; 7.7 in.
4
in. What is the width?
55. The ratio of the length of a painting to its width is (1 + !3) : 1. The length is 40
cm. What is the width? –40(1–"3); 29.3 cm
Lesson 11-3 Write and solve a radical equation for each situation.
56. What is the diameter of a circular livestock pen if the area is 450 m2? 450 ≠ p Q D
2 R ; 23.9 m
57. On a roller coaster ride, your speed in a loop depends on the height h of the
preceding hill, and the radius of the loop in feet. The equation v = 8 !h 2 2r
gives the velocity v in feet per second of a car at the top of the loop. Suppose a
loop has a radius of 25 ft and you want the car to have a velocity of 25 ft/s at
the top of the loop. How high should the preceding hill be? about 60
2
Lesson 11-4 Write and graph a radical expression to answer each question.
58. Suppose a motorcycle company uses the function n = 30 !4t 1 90 to model
the sales volume n, as a function of time t, the number of months after the start
of the advertising camping.
a. Graph the function. See margin.
b. Use the graph to estimate when 200 motorcycles will be sold. about 3.5 months
58a
Sales Volume
200
Lessons 11-5 and 11-6 Use trigonometric ratios to answer each question.
59. A painter leans a 20-ft ladder up against the side of a house making a right
triangle. How far up the side of the house will the top of the ladder rest if the
ladder makes a 75° angle with the ground? about 19 ft
60. The length of a rectangular field is 100 yd and the diagonal across
the field forms an angle of 25° with the sideline. What is the length of the
diagonal line? about 110 ft
150
100
50
0
1
2
3
4
Time (months)
61. A pilot is flying a plane 6500 ft above the ground. The pilot begins a 3° descent
to an airport runway. Find the horizontal distance between the airplane and the
start of the runway? 124,027 ft (about 23 mi)
62. While hiking you see an 100-ft observation tower on top of a 1100-ft hill. The
angle of elevation to the top of the tower is 6°? How far away is the tower?
11,417 ft (about 2.2 mi)
Chapter 11 Extra Practice: Skills and Word Problems
745
745
CHAPTER 12
Chapter
page 746
Extra Practice
12
1. x ≠ 0, y ≠ 0;
Lesson 12-1 Identify the asymptotes of each function. Then graph the function. 1–8. See margin.
y
4
4
4
O
Extra Practice: Skills and Word Problems
x
4
1. y = x6
8
2 y=x1
2
3. y = x4 - 3
5 +3
4. y = x 1
1
5. y = x5 - 1
2
6. y = x 2
1
7. y = x3 + 4
2 -1
8. y = x 1
1
Lesson 12-2 Simplify each expression.
4
14. 4t 2
2 t –1
7
1
13. x2 1x 1
8x 1 7 x 1 1
2. x ≠ –2, y ≠ 0;
y
2 12
11. 4m
m23 4
1
10. c2 2 5 c 1
5
c 2 25
4t2 t
9. 16t
4
2
2a 2 3 a – 1
12. a 1
a13
2
6(b 1 7)
16. 6b 1 423m 1 10
2
2
1 2
15. m2 1 7m 1 10 m
m 1 8m 1 15 m 1 3
b
Lessons 12-3 to 12-5 Simplify each expression.
4
4 O
2
x
4
4t
18. 6t
5 + 5 2t
6 - 4 2
20. 3d
3d 3d
4
21. 5s 3 2s
10s
5
21
24. v3 ? 4v 2 4v
v
v
3y
9y
y
27.
4 2
2y 2 4y 6
4y 2 8
y
9b
8
26. 2
+ 4
m11
m 1 6m 1 5
2
Divide.
3b
3. x ≠ 0, y ≠ –3;
2 O
2
x
2
4
4
19. 6 + 42 6c 1
2
17. x4 - x3 1x
2
23. 8b 22 4b 4 2b 2 1 12
4(m 1 7)
(m 1 1)(m 1 5)
29. A 2x 3 - x 2 - 13x - 6 B 4 (x - 3) 2x 2 ± 5x ± 2
c
c
c
2 14 4
4n
22.
?
n
7 2n3
8(t 2 1)
5 + 3
25. t 1
4
t 2 4 t 2 2 16
28. 42 - 33 4d 23 3
d
d
d
6
30. A 3x 3 - 3 B 4 (x + 1) 3x 2 – 3x ± 3 – x 1
1
31. A 3x 3 + 5x 2 - 22x + 24 B 4 (x + 4) 3x 2 – 7x ± 6
32. A 3x 3 - 3 B 4 (x - 1) 3(x 2 ± x ± 1)
Lesson 12-6 Solve each equation. Check your answer.
4. x ≠ –1, y ≠ 3;
6
4 -3= 2 2
34. m
m 3
4 = 3 –3
36. x 2
1
x
37. n4 + 95 = 1 9
1 = 1 –1
35. b 2
3
4b
x 2 4 28
12
40. x
x 1 5 = x 1 4 –5
43. m 41 3 = m 62 3 –15
x = x 2 3 –3
38. x 1
2
x11
5
9
41. 51 - x1 = 21
15
4 +1=
44. t 1
6, –10
5
t2 2 25
Lessons 12-7 and 12-8 Simplify each expression.
O
4
33. 41 + x1 = 83 8
39. t - 8t = 17
5, –5
t
2
4
42. c 1 1 - c 2 1 = 3c2 1 6 –12
c 21
y
2 4
x
5. x ≠ 0, y ≠ –1;
45. 6 C 4 15
46. 7 P2 42
47. 10 C 5 252
48. 8C 7 8
49. 12 P6 665,280
50. 9 C 7 36
51. 10C 6 210
52. 10P6 151,200
53. How many four-letter groups can be made with the letters A, B, C, and D if no
letter can be repeated? 24
y
54. Two people are running for president, three are running for vice-president, and
two are running for speaker. How many election results are possible? 12
2
2 O
2
x
55. a. Suppose your bank assigns a four-digit personal identification number for
your bank card. The first digit cannot be zero. How many different numbers
are possible? 9000
1
b. What is the probability that the number you are given is 4861? 9000
2
6. x ≠ 1, y ≠ 0;
y
2
2
O
2
2
x
746
Chapter 12 Extra Practice: Skills and Word Problems
7. x ≠ 0, y ≠ 4;
8. x ≠ –1, y ≠ –1;
y
y
2
6
x
4
2
O
2
2
746
b
O
2
4
x
1
a light bulb with 350 watts. What is the intensity of light when you are 40 feet
away? 0.21875 lumens
57. The function s = 1500
2 gives the signal strength s of a radio signal at a distance d
d
miles from a transmitter. What is the signal strength when you are 25 miles
away? 2.4
Lesson 12-2 The expression 30rh gives the approximate baking time for bread in
r1h
minutes based on the radius r and the height h of the baked loaf in inches. Use this
expression to find the baking time for each loaf.
58. a roll that will have a radius of 2 in. and a height of 1.5 in. about 26 min
59. a loaf of Italian bread that will have a length of 18 in. and a radius of 4 in.
about 98 min
Lesson 12-3
60. Find an expression for the area of a rectangular field with a lengths of
m and a width of
y3 1 6
2(y3 1 6)
m.
3y 2 2 4
2y 2 1 5
4y 1 10
3y 2 2 4
m
Lesson 12-4
Intensity (lumens)
56. The function I = 350
gives the intensity I in lumens at a distance of x feet from
x2
6
4
2
0
10 20 30 40
Distance (ft)
57.
16
Signal strength
Extra Skills and Word Problems
Lesson 12-1 Graph a rational function to answer each question. 56–57. See margin for graphs.
12
8
4
0
61. What is the area of the base of a hexagonal prism with a volume of
15x3 - 26x2 + 43x - 14 m3 and a height of 5x - 2 m? 3x 2 – 4x ± 7 m2
Extra Skills and Word Problems
56.
10 20 30
Distance (ft)
Lesson 12-5
62. A canoe travels 5 miles downstream at rate r, and then 5 miles back upstream
at 70% of its downstream rate. Write and simplify a rational expression for the
5
total time of the trip. 5r ± 0.7r
N 12
r
63. Louis walks to get to his friend’s house 2 miles away. When he returns home he
jogs at a rate that is 160% of his walking rate r. Write and simplify a rational
2
expression for the total time of his trip. 2r ± 1.6r
≠ 3.25
r
Lesson 12-6
64. Suppose you can clean your kitchen in 30 minutes. Your friend can clean your
kitchen in 45 minutes. How long will it take you to clean the kitchen together? 18 min
65. One employee of a landscaping company can mow a lawn in 20 minutes.
Another employee can do it in 15 minutes. How long will it take them to mow
the lawn together? 8 47 min
Lessons 12-7 and 12-8 Find the number of possibilities for each situation.
66. Suppose you have nine different shirts. How many ways can you select five
shirts to wear in order? 15,120
67. How many different ways can four different officer positions be filled from a
school club with 35 members? 52,360
68. Suppose you have a summer reading list with 15 books and you have to read
three. How many different combinations of books can you read? 455
Chapter 12 Extra Practice: Skills and Word Problems
747
747