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Elementary Algebra 2e

Chapter 3

Elementary Algebra 2eChapter 3
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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Chapter Review
      1. Key Terms
      2. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Chapter Review
      1. Key Terms
      2. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. 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
  13. Index

Be Prepared

3.1

2 x − 6 2 x − 6

3.2

x = 36 x = 36

3.2

x = 2 x = 2

3.3

0.045 0.045

3.4

60 % 60 %

3.5

0.88 0.88

3.6

10.71 10.71

3.7

n = 5 n = 5

3.8

12.55 12.55

3.9

3.5 3.5

3.10

x = 6 x = 6

3.11

d = q + 3 d = q + 3

3.12

3 h 3 h

3.13

l = w − 3 l = w − 3

3.14

b = 10 b = 10

3.15

12 12

3.16

210210 miles

3.17

x = 50 x = 50

3.18

1.51.5 hours

3.19

x ≥ 30 x ≥ 30

3.20

y > − 11 y > − 11

Try It

3.1

$180

3.2

40

3.3

2

3.4

7

3.5

25

3.6

4

3.7

3

3.8

6

3.9

9, 15

3.10

27, 31

3.11

−15 , −8 −15 , −8

3.12

−29 , 11 −29 , 11

3.13

−4 , 0 −4 , 0

3.14

−3 , −2 −3 , −2

3.15

47, 48

3.16

−16 , −15 −16 , −15

3.17

−33 , −32 , −31 −33 , −32 , −31

3.18

−13 , −12 , −11 −13 , −12 , −11

3.19

32, 34, 36

3.20

−10 , −8 , −6 −10 , −8 , −6

3.21

$5,000

3.22

$19,300

3.23

36

3.24

33

3.25

$26

3.26

$36

3.27

125%

3.28

175%

3.29

$14.67

3.30

$2.16

3.31

25 grams

3.32

2,375 mg

3.33

26%

3.34

40%

3.35

8.8%

3.36

50%

3.37

6.3%

3.38

10%

3.39

$142.50

3.40

$7,020

3.41

6%

3.42

4%

3.43

$11,450

3.44

$9,600

3.45

ⓐ $11.60 ⓑ $17.40

3.46

ⓐ $256.75 ⓑ $138.25

3.47

ⓐ $184.80 ⓑ 33%

3.48

ⓐ $60 ⓑ 15%

3.49

ⓐ $600 ⓑ $1,800

3.50

ⓐ $2,975 ⓑ $11,475

3.51

9 nickels, 16 dimes

3.52

17 nickels, 5 quarters

3.53

42 nickels, 21 dimes

3.54

51 dimes, 17 quarters

3.55

41 nickels, 18 quarters

3.56

22 nickels, 59 dimes

3.57

330 day passes, 367 tournament passes

3.58

112 adult tickets, 199 senior/child tickets

3.59

84 adult tickets, 31 student tickets

3.60

26 full-fare, 14 reduced fare

3.61

32 at $0.41, 12 at $0.02

3.62

26 at $0.41, 10 at $0.20

3.63

5 pounds cereal squares, 25 pounds nuts

3.64

21 gallons of fruit punch, 7 gallons of soda

3.65

$4,200 at 4%, $9,800 at 7%

3.66

$2,500 at 3.2%, $5,500 at 8%

3.67

21 degrees

3.68

56 degrees

3.69

8 feet

3.70

6 feet

3.71

14 inches

3.72

6 feet

3.73

34 ° 34 °

3.74

45 ° 45 °

3.75

20 ° , 70 ° , 90 ° 20 ° , 70 ° , 90 °

3.76

30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °

3.77

c = 10 c = 10

3.78

c = 13 c = 13

3.79

8

3.80

12

3.81

12 feet

3.82

8 feet

3.83

340 yards

3.84

220 feet

3.85

26 feet

3.86

29 meters

3.87

15

3.88

9

3.89

18 meters, 11 meters

3.90

19 feet, 11 feet

3.91

24, 8

3.92

5, 4

3.93

70 feet, 30 feet

3.94

90 yards, 60 yards

3.95

Wayne 21 mph, Dennis 28 mph

3.96

Jeromy 80 mph, mother 60 mph

3.97

Carina 50 mph, brother 65 mph

3.98

parents 55 mph, Ashley 62 mph

3.99

3 hours

3.100

2.2 hours

3.101

uphill 1.8 mph, downhill three mph

3.102

upstream 8 mph, downstream 12 mph

3.103

biking 16 mph, running 10 mph

3.104

uphill 12 mph, flat street 20 mph

3.105

There can be no more than 20 boxes.

3.106

A maximum of 14 people can safely ride in the elevator.

3.107

seven packs

3.108

11 people

3.109

at least $4,000,000

3.110

at least $1,200,000

3.111

no more than 106 text messages

3.112

no more than 76 therms

3.113

at least 96 hours

3.114

at least 1,380 invitations

3.115

at least 23 hours

3.116

at least 20 driveways

Section 3.1 Exercises

1.

Answers will vary

3.

30

5.

125

7.

6

9.

58

11.

$750

13.

$13,500

15.

4

17.

15

19.

5

21.

12

23.

−5 −5

25.

18, 24

27.

8, 12

29.

−18 , −27 −18 , −27

31.

−111 , −205 −111 , −205

33.

32, 46

35.

23, 28

37.

−2 , −3 −2 , −3

39.

4, 10

41.

38, 39

43.

−11 , −12 −11 , −12

45.

25, 26, 27

47.

−11 , −12 , −13 −11 , −12 , −13

49.

84, 86, 88

51.

55, 57, 59

53.

−10 , −12 , −14 −10 , −12 , −14

55.

−69 , −71 , −73 −69 , −71 , −73

57.

$45

59.

$1.25

61.

$1080

63.

answers will vary

65.

Consecutive odd integers are odd numbers that immediately follow each other. An example of three consecutive odd integers between 50 and 60 would be 51, 53, and 55.

Section 3.2 Exercises

67.

54

69.

26.88

71.

162.5

73.

18,000

75.

112

77.

108

79.

$35

81.

$940

83.

30%

85.

36%

87.

150%

89.

175%

91.

$11.88

93.

$259.80

95.

24.2 g

97.

2407 mg

99.

175 lb.

101.

$120

103.

18%

105.

45%

107.

25%

109.

12%

111.

200%

113.

72.7%

115.

2.5%

117.

11%

119.

5.5%

121.

$116

123.

$4,836

125.

3%

127.

3.75%

129.

$35,000

131.

$3,345

133.

$139

135.

$125

137.

ⓐ $26.97 ⓑ $17.98

139.

ⓐ $128.37 ⓑ $260.63

141.

ⓐ $332.48 ⓑ $617.47

143.

ⓐ $576 ⓑ 30%

145.

ⓐ $53.25 ⓑ 15%

147.

ⓐ $370 ⓑ 43.5%

149.

ⓐ $7.20 ⓑ $23.20

151.

ⓐ $0.20 ⓑ $0.80

153.

ⓐ $258.75 ⓑ $373.75

155.

21.2%

157.

The number should be greater than 44. Since 80% equals 0.8 in decimal form, 0.8 is less than one, and we must multiply the number by 0.8 to get 44, the number must be greater than 44.

159.

He meant that he should have packed half the shorts and twice the shirts.

Section 3.3 Exercises

161.

8 nickels, 22 dimes

163.

15 dimes, 8 quarters

165.

10 at $1, 7 at $5

167.

18 quarters, 36 nickels

169.

30 pennies, 90 dimes

171.

10 at $10, 5 at $5

173.

12 dimes and 27 nickels

175.

63 dimes, 20 quarters

177.

16 nickels, 12 dimes, 7 quarters

179.

30 child tickets, 50 adult tickets

181.

110 child tickets, 50 adult tickets

183.

34 general, 61 youth

185.

114 general, 246 student

187.

40 postcards, 100 stamps

189.

30 at $0.41, 10 at $0.02

191.

15 $10 shares, 5 $12 shares

193.

5 liters champagne, 10 liters orange juice

195.

7.5 lbs Maui beans, 17.5 Kona beans

197.

800 at $1.50, 200 at $9.00

199.

$8000 at 4%, $17,000 at 9%

201.

$10,000 in CD, $30,000 in mutual fund

203.

9.1%

205.

9 girls, 3 adults

207.

Answers will vary.

209.

Answers will vary.

Section 3.4 Exercises

211.

56 degrees

213.

44 degrees

215.

11 feet

217.

8 feet

219.

0.75 sq. ft.

221.

23 inches

223.

57

225.

67.5

227.

13 ft., 12 ft., 14 ft.

229.

3 ft., 6 ft., 8 ft.

231.

45 ° , 45 ° , 90 ° 45 ° , 45 ° , 90 °

233.

30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °

235.

15

237.

25

239.

8

241.

12

243.

10.2

245.

9.8

247.

5 feet

249.

14.1 feet

251.

260 feet

253.

58 feet

255.

23 meters

257.

26 inches

259.

24

261.

4.9

263.

16 in., 7 in.

265.

17 m, 12 m

267.

13.5 m length, 12.8 m width

269.

50 ft., 25 ft.

271.

7 m width, 11 m length

273.

160 yd., 120 yd.

275.

85 ft., 40 ft.

277.

240 feet

279.

area; answers will vary

281.

ⓐ Answers will vary.
 ⓑ Answers will vary.
 ⓒ Answers will vary.
 ⓓ The areas are the same.
 ⓔ The 2x8 rectangle has a larger perimeter than the 4x4 square.

Section 3.5 Exercises

283.

Mason 75 mph, train 60 mph

285.

express bus 75mph, local 50 mph

287.

Saul 82 mph, Erwin 74 mph

289.

Helen 57.2 mph, Anne 53.2 mph

291.

Aletheia 2.4 mph, Elvira 3 mph

293.

3 hours

295.

3.5 hours

297.

walking 3 mph, jogging 4.5 mph

299.

upstream 6 mph, downstream 9 mph

301.

skateboarding 7.2 mph, walking 2.9 mph

303.

heavy traffic 30 mph, light traffic 70 mph

305.

ⓐ 36 mph ⓑ 25 mph ⓒ 3.05 hours ⓓ 29.5 mph

307.

Answers will vary.

Section 3.6 Exercises

309.

15 children

311.

12 people

313.

five drinks

315.

31 aprons

317.

$15,000

319.

$400,000

321.

16 ccf

323.

nine movies

325.

48 cut & styles

327.

44 meals

329.

49 cars

331.

9 cars

333.

91 students

335.

169 guests

337.

Answers will vary.

Review Exercises

339.

answers will vary

341.

116

343.

38

345.

−18 , −9 −18 , −9

347.

−3 , −10 −3 , −10

349.

−48 , −47 , −46 −48 , −47 , −46

351.

15, 17, 19

353.

167.5

355.

160

357.

120%

359.

$3.89

361.

$875

363.

2.5%

365.

$428.22

367.

$1,900

369.

$63

371.

ⓐ $55.20 ⓑ $82.80

373.

ⓐ $70 ⓑ 15.6%

375.

ⓐ $175 ⓑ $225

377.

16 dimes, 11 quarters

379.

six $5 bills, 11 $10 bills

381.

35 adults, 82 children

383.

57 students, 68 adults

385.

three $0.26 stamps, eight $0.41 stamps

387.

2.2 lb. of raisins, 7.8 lb. of nuts

389.

$12,500 at 4.5%, $2,500 at 1.8%

391.

73 ° 73 °

393.

600 square inches

395.

30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °

397.

22.5 ° , 67.5 ° , 90 ° 22.5 ° , 67.5 ° , 90 °

399.

26

401.

8

403.

8.1

405.

6 ′ 6 ′

407.

ⓐ 110 ft. ⓑ 684 sq. ft.

409.

62 m

411.

24.5 cm, 12.5 cm

413.

Gabe 70 mph, Elsa 77 mph

415.

2.5 hours

417.

flat road 11 mph, uphill 8 mph

419.

$33 per day

421.

at least $300,000

423.

at least 112 jobs

Practice Test

425.

15

427.

−49 , −47 −49 , −47

429.

8%

431.

ⓐ $208.50 ⓑ 30%

433.

140 adult, 85 children

435.

41.5 ° , 55.5 ° , 83 ° 41.5 ° , 55.5 ° , 83 °

437.

10

439.

127.3 ft.

441.

2.5 hours

443.

at most $44.44 per costume

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