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Prealgebra 2e

Chapter 9

Prealgebra 2eChapter 9
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Table of contents
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

Be Prepared

9.1

2 x − 6 2 x − 6

9.2

36 36

9.3

2 2

9.4

3.5 3.5

9.5

20 + 5 n 20 + 5 n

9.6

6 6

9.7

x = 2 x = 2

9.8

60 60

9.9

10 10

9.10

w − 3 w − 3

9.11

3 h 3 h

9.12

6 6

9.13

25 25

9.14

(a) 50.24in.50.24in.; (b) 200.96sq.in200.96sq.in.

9.15

0 .196 0 .196

9.16

125 125

9.17

32 32

9.18

77 2 77 2

9.19

35   miles 1   gallon 35   miles 1   gallon

9.20

12 12

9.21

$200 $200

Try It

9.1

$180

9.2

40

9.3

2

9.4

7

9.5

$950

9.6

$4,200

9.7

25

9.8

4

9.9

3

9.10

6

9.11

9, 15

9.12

27, 31

9.13

−8, −15

9.14

−29, 11

9.15

−4, 0

9.16

−2, −3

9.17

47, 48

9.18

−15, −16

9.19

31, 32, 33

9.20

−11, −12, −13

9.21

9 nickels, 16 dimes

9.22

17 nickels, 5 quarters

9.23

42 nickels, 21 dimes

9.24

51 dimes, 17 quarters

9.25

41 nickels, 18 quarters

9.26

22 nickels, 59 dimes

9.27

330 day passes, 367 tournament passes

9.28

112 adult tickets, 199 senior/child tickets

9.29

32 at 49 cents, 12 at 8 cents

9.30

26 at 49 cents, 10 at 21 cents

9.31
  1. ⓐ 155°
  2. ⓑ 65°
9.32
  1. ⓐ 103°
  2. ⓑ 13°
9.33

40°, 140°

9.34

25°, 65°

9.35

21°

9.36

56°

9.37

34°

9.38

45°

9.39

20°, 70°, 90°

9.40

30°, 60°, 90°

9.41

8

9.42

22.5

9.43

10

9.44

17

9.45

8

9.46

12

9.47

12 feet

9.48

8 feet

9.49
  1. ⓐ cubic
  2. ⓑ linear
  3. ⓒ square
  4. ⓓ linear
  5. ⓔ square
  6. ⓕ cubic
9.50
  1. ⓐ cubic
  2. ⓑ square
  3. ⓒ cubic
  4. ⓓ linear
  5. ⓔ square
  6. ⓕ linear
9.51
  1. ⓐ 8 inches
  2. ⓑ 3 sq. inches
9.52
  1. ⓐ 8 centimeters
  2. ⓑ 4 sq. centimeters
9.53
  1. ⓐ 340 yd
  2. ⓑ 6000 sq. yd
9.54
  1. ⓐ 220 ft
  2. ⓑ 2976 sq. ft
9.55

15 in.

9.56

9 yd

9.57

18 m, 11 m

9.58

11 ft , 19 ft

9.59

8 ft, 24 ft

9.60

5 cm, 4 cm

9.61

26 ft

9.62

29 m

9.63

30 ft, 70 ft

9.64

60 yd, 90 yd

9.65

13 sq. in.

9.66

49 sq. in.

9.67

8 ft

9.68

6 ft

9.69

14 in.

9.70

6 ft

9.71

13 in.

9.72

17 cm

9.73

14 ft

9.74

7 m

9.75

161 sq. yd

9.76

225 sq. cm

9.77

42 sq. cm

9.78

63 sq. m

9.79

40.25 sq. yd

9.80

240 sq. ft

9.81
  1. ⓐ 31.4 in.
  2. ⓑ 78.5 sq. in.
9.82
  1. ⓐ 28.26 ft
  2. ⓑ 63.585 sq. ft
9.83

17.27 ft

9.84

37.68 ft

9.85

30 cm

9.86

110 ft

9.87

28 sq. units

9.88

110 sq. units

9.89

36.5 sq. units

9.90

70 sq. units

9.91

103.2 sq. units

9.92

38.24 sq. units

9.93
  1. ⓐ 792 cu. ft
  2. ⓑ 518 sq. ft
9.94
  1. ⓐ 1,440 cu. ft
  2. ⓑ 792 sq. ft
9.95
  1. ⓐ 216 cu. ft
  2. ⓑ 228 sq. ft
9.96
  1. ⓐ 2,772 cu. in.
  2. ⓑ 1,264 sq. in.
9.97
  1. ⓐ 91.125 cu. m
  2. ⓑ 121.5 sq. m
9.98
  1. ⓐ 389.017 cu. yd.
  2. ⓑ 319.74 sq. yd.
9.99
  1. ⓐ 64 cu. ft
  2. ⓑ 96 sq. ft
9.100
  1. ⓐ 4,096 cu. in.
  2. ⓑ 1536 sq. in.
9.101
  1. ⓐ 113.04 cu. cm
  2. ⓑ 113.04 sq. cm
9.102
  1. ⓐ 4.19 cu. ft
  2. ⓑ 12.56 sq. ft
9.103
  1. ⓐ 3052.08 cu. in.
  2. ⓑ 1017.36 sq. in.
9.104
  1. ⓐ 14.13 cu. ft
  2. ⓑ 28.26 sq. ft
9.105
  1. ⓐ 351.68 cu. cm
  2. ⓑ 276.32 sq. cm
9.106
  1. ⓐ 100.48 cu. ft
  2. ⓑ 125.6 sq. ft
9.107
  1. ⓐ 3,818.24 cu. cm
  2. ⓑ 1,356.48 sq. cm
9.108
  1. ⓐ 91.5624 cu. ft
  2. ⓑ 113.6052 sq. ft
9.109

65.94 cu. in.

9.110

235.5 cu. cm

9.111

678.24 cu. in.

9.112

128.2 cu. in.

9.113

330 mi

9.114

7 mi

9.115

11 hours

9.116

56 mph

9.117
  1. ⓐ r=45r=45
  2. ⓑ r=dtr=dt
9.118
  1. ⓐ r=65r=65
  2. ⓑ r=dtr=dt
9.119

ⓐ h=20h=20 ⓑ h=2Abh=2Ab

9.120
  1. ⓐ b=4b=4
  2. ⓑ b=2Ahb=2Ah
9.121
  1. ⓐ t=3 yearst=3 years
  2. ⓑ t=IPrt=IPr
9.122
  1. ⓐ r=0.12=12%r=0.12=12%
  2. ⓑ r=IPtr=IPt
9.123
  1. ⓐ y=1y=1
  2. ⓑ y=10−3x4y=10−3x4
9.124
  1. ⓐ y=−1y=−1
  2. ⓑ y=18−5x2y=18−5x2
9.125

b = P − a − c

9.126

c = P − a − b

9.127

y = 11 − 7x

9.128

y = 8 − 11x

9.129

y = 9 − 4 x 7 y = 9 − 4 x 7

9.130

y = 1 − 5 x 8 y = 1 − 5 x 8

Section 9.1 Exercises

1.

There are 30 children in the class.

3.

Zachary has 125 CDs.

5.

There are 6 boys in the club.

7.

There are 17 glasses.

9.

Lisa's original weight was 175 pounds.

11.

18%

13.

The original price was $120.

15.

4

17.

15

19.

5

21.

12

23.

−5

25.

18, 24

27.

8, 12

29.

−2, −3

31.

4, 10

33.

32, 46

35.

38, 39

37.

−11, −12

39.

25, 26, 27

41.

−11, −12, −13

43.

The original price was $45.

45.

Each sticker book cost $1.25.

47.

The price of the refrigerator before tax was $1,080.

49.

Answers will vary.

Section 9.2 Exercises

51.

8 nickels, 22 dimes

53.

15 dimes, 8 quarters

55.

12 dimes and 27 nickels

57.

63 dimes, 20 quarters

59.

10 of the $1 bills, 7 of the $5 bills

61.

10 of the $10 bills, 5 of the $5 bills

63.

16 nickels, 12 dimes, 7 quarters

65.

30 child tickets, 50 adult tickets

67.

110 child tickets, 50 adult tickets

69.

40 postcards, 100 stamps

71.

30 at 49 cents, 10 at 21 cents

73.

15 at $10 shares, 5 at $12 shares

75.

9 girls, 3 adults

77.

Answers will vary.

79.

Answers will vary.

Section 9.3 Exercises

81.
  1. ⓐ 127°
  2. ⓑ 37°
83.
  1. ⓐ 151°
  2. ⓑ 61°
85.

45°

87.

62.5°

89.

62°, 118°

91.

62°, 28°

93.

56°

95.

44°

97.

57°

99.

67.5°

101.

45°, 45°, 90°

103.

30°, 60°, 90°

105.

12

107.

351 miles

109.

15

111.

25

113.

8

115.

12

117.

10.2

119.

8

121.

5 feet

123.

14.1 feet

125.

2.9 feet

127.

Answers will vary.

Section 9.4 Exercises

129.

cubic

131.

square

133.

linear

135.
  1. ⓐ 10 cm
  2. ⓑ 4 sq. cm
137.
  1. ⓐ 8 cm
  2. ⓑ 3 sq. cm
139.
  1. ⓐ 10 cm
  2. ⓑ 5 sq. cm
141.
  1. ⓐ 260 ft
  2. ⓑ 3825 sq. ft
143.
  1. ⓐ 58 ft
  2. ⓑ 210 sq. ft
145.

24 inches

147.

27 meters

149.

23 m

151.

7 in., 16 in.

153.

17 m, 12 m

155.

13.5 m, 12.8 m

157.

25 ft, 50 ft

159.

7 m, 11 m

161.

26 in.

163.

55 m

165.

35 ft, 45 ft

167.

76 in., 36 in.

169.

30 sq. in.

171.

25.315 sq. m

173.

0.75 sq. ft

175.

8 ft

177.

23 in.

179.

11 yd

181.

28 cm

183.

17 yd

185.

6 m

187.

15 ft

189.

24 in.

191.

27.5 in.

193.

12 ft, 13 ft, 14 ft

195.

3 ft, 6 ft, 8 ft

197.

144 sq. ft

199.

2805 sq. m

201.

231 sq. cm

203.

28.56 sq. m

205.

13.5 sq. ft

207.

1036 sq. in.

209.

15 ft

211.

$240

213.

Answers will vary.

215.

Answers will vary.

Section 9.5 Exercises

217.
  1. ⓐ 43.96 in.
  2. ⓑ 153.86 sq. in.
219.
  1. ⓐ 53.38 ft
  2. ⓑ 226.865 sq. ft
221.

62.8 ft

223.

37.68 in.

225.

6.908 ft

227.

52 in.

229.

5.5 m

231.

24 ft

233.

6.5 mi

235.

16 sq. units

237.

30 sq. units

239.

57.5 sq. units

241.

12 sq. units

243.

67.5 sq. units

245.

89 sq. units

247.

44.81 sq. units

249.

41.12 sq. units

251.

35.13 sq. units

253.

95.625 sq. units

255.

187,500 sq. ft

257.

9400 sq. ft

259.
  1. ⓐ 6.5325 sq. ft
  2. ⓑ 10.065 sq. ft
261.

Answers will vary.

Section 9.6 Exercises

263.
  1. ⓐ 9 cu. m
  2. ⓑ 27 sq. m
265.
  1. ⓐ 17.64 cu. yd.
  2. ⓑ 41.58 sq. yd.
267.
  1. ⓐ 1,024 cu. ft
  2. ⓑ 640 sq. ft
269.
  1. ⓐ 3,350.49 cu. cm
  2. ⓑ 1,622.42 sq. cm
271.
  1. ⓐ 125 cu. cm
  2. ⓑ 150 sq. cm
273.
  1. ⓐ 1124.864 cu. ft.
  2. ⓑ 648.96 sq. ft
275.
  1. ⓐ 262,144 cu. ft
  2. ⓑ 24,576 sq. ft
277.
  1. ⓐ 21.952 cu. m
  2. ⓑ 47.04 sq. m
279.
  1. ⓐ 113.04 cu. cm
  2. ⓑ 113.04 sq. cm
281.
  1. ⓐ 1,766.25 cu. ft
  2. ⓑ 706.5 sq. ft
283.
  1. ⓐ 14,130 cu. in.
  2. ⓑ 2,826 sq. in.
285.
  1. ⓐ 381.51 cu. cm
  2. ⓑ 254.34 sq. cm
287.
  1. ⓐ 254.34 cu. ft
  2. ⓑ 226.08 sq. ft
289.
  1. ⓐ 29.673 cu. m
  2. ⓑ 53.694 sq. m
291.
  1. ⓐ 1,020.5 cu. cm
  2. ⓑ 565.2 sq. cm
293.
  1. ⓐ 678.24 cu. in.
  2. ⓑ 508.68 sq. in.
295.

37.68 cu. ft

297.

324.47 cu. cm

299.

261.67 cu. ft

301.

64,108.33 cu. ft

303.
  1. ⓐ 31.4 cu. ft
  2. ⓑ 2.6 cu. ft
  3. ⓒ 28.8 cu. ft
305.

Answers will vary.

Section 9.7 Exercises

307.

612 mi

309.

7 mi

311.

6.5 hours

313.

3.6 hours

315.

60 mph

317.

80 mph

319.
  1. ⓐ t=5t=5
  2. ⓑ t=drt=dr
321.
  1. ⓐ t=8.5t=8.5
  2. ⓑ t=drt=dr
323.
  1. ⓐ r=68r=68
  2. ⓑ r=dtr=dt
325.
  1. ⓐ r=64r=64
  2. ⓑ r=dtr=dt
327.
  1. ⓐ b=14b=14
  2. ⓑ b=2Ahb=2Ah
329.
  1. ⓐ h=30h=30
  2. ⓑ h=2Abh=2Ab
331.
  1. ⓐ P=$19,571.43P=$19,571.43
  2. ⓑ P=IrtP=Irt
333.
  1. ⓐ t=6yearst=6years
  2. ⓑ t=IPrt=IPr
335.
  1. ⓐ y=2y=2
  2. ⓑ y=12−2x3y=12−2x3
337.
  1. ⓐ y = 13
  2. ⓑ y = 7 − 3x
339.
  1. ⓐ b = 90 − a
  2. ⓑ a = 90 − b
341.

a = 180 − b − c

343.

y = 15 − 8x

345.

y = −6 + 4x

347.

y = 7 − 4 x 3 y = 7 − 4 x 3

349.

y = 4 + x

351.

L = P − 2 W 2 L = P − 2 W 2

353.

d = C π d = C π

355.

L = V W H L = V W H

357.

104° F

359.

Answers will vary

Review Exercises

361.

Answers will vary.

363.

There are 116 people at the concert.

365.

His original weight was 180 pounds.

367.

38

369.

18, 9

371.

16 dimes, 11 quarters

373.

6 of $5 bills, 11 of $10 bills

375.

35 adults, 82 children

377.

3 of 26 -cent stamps, 8 of 41 -cent stamps

379.

132°

381.

33°, 57°

383.

73°

385.

30°, 60°, 90°

387.

15

389.

26

391.

8

393.

8.1

395.

6 feet

397.

cubic

399.

square

401.
  1. ⓐ 8 units
  2. ⓑ 3 sq. units
403.
  1. ⓐ 140 m
  2. ⓑ 1176 sq. m
405.
  1. ⓐ 98 ft.
  2. ⓑ 180 sq. ft.
407.

25 cm

409.

62 m

411.

24.5 cm., 12.5 cm.

413.

135 sq. in.

415.

600 sq. in.

417.

7 in., 7 in.

419.

17 ft., 20 ft., 22 ft.

421.

100 sq. ft.

423.

675 sq. m

425.
  1. ⓐ 18.84 m
  2. ⓑ 28.26 sq. m
427.

48 in.

429.

30 sq. units

431.

300 sq. units

433.

199.25 sq. units

435.
  1. ⓐ 630 cu. cm
  2. ⓑ 496 sq. cm
437.
  1. ⓐ 15.625 cu. in.
  2. ⓑ 37.5 sq. in.
439.
  1. ⓐ 267.95 cu. yd.
  2. ⓑ 200.96 sq. yd.
441.
  1. ⓐ 12.76 cu. in.
  2. ⓑ 26.41 sq. in.
443.
  1. ⓐ 75.36 cu. yd.
  2. ⓑ 100.48 sq. yd.
445.
  1. ⓐ 753.6 cu. cm
  2. ⓑ 477.28 sq. cm
447.

5.233 cu. m

449.

4.599 cu. in.

451.

1520 miles

453.

1.6 hours

455.
  1. ⓐ t=6.2t=6.2
  2. ⓑ t=drt=dr
457.
  1. ⓐ b=26b=26
  2. ⓑ b=2Ahb=2Ah
459.
  1. ⓐ P=$6000P=$6000
  2. ⓑ P=I(r⋅t)P=I(r⋅t)
461.
  1. ⓐ y=4y=4
  2. ⓑ y=20−6x5y=20−6x5
463.

a = 90 − b

465.

y = 17 − 4x

467.

W = P − 2 L 2 W = P − 2 L 2

Practice Test

471.

−16

473.

7 quarters, 12 dimes

475.

38°

477.

48.3

479.

10

481.

127.3 ft

483.

2200 square centimeters

485.

282.6 inches

487.

1440

489.

31,400 cubic inches

491.

14.7 miles per hour

493.
  1. ⓐ height=52height=52
  2. ⓑ h=2Abh=2Ab
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