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Prealgebra 2e

Chapter 4

Prealgebra 2eChapter 4
  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. Key Terms
    8. Key Concepts
    9. 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. Key Terms
    8. Key Concepts
    9. 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. Key Terms
    8. Key Concepts
    9. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    8. Key Concepts
    9. 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. Key Terms
    8. Key Concepts
    9. 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. Key Terms
    7. Key Concepts
    8. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    9. Key Concepts
    10. 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. Key Terms
    7. Key Concepts
    8. 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

4.1

1111

4.2

2>52>5

4.3

2222322223

4.4

4.5

Answers may vary. Acceptable answers include 1012,1518,5060,1012,1518,5060, etc.

4.6

33

4.7

112112

4.8

135135

4.9

5x+55x+5

4.11

5656

4.12

1012,15181012,1518

4.13

22

4.15

234234

4.16

7272

4.17

11

4.18

y=6y=6

4.19

2525

Try It

4.1
  1. 3838
  2. 4949
4.2
  1. 3535
  2. 3434
4.3


A circle is shown divided into 8 pieces, of which 6 are shaded.
4.4


A rectangle is divided into 5 sections, of which 2 are shaded.
4.5


A circle is shown. It is divided into 3 equal pieces. All 3 pieces are shaded.
4.6


A circle is divided into 8 sections, of which all are shaded.
4.7


Two circles are shown. Each is divided into three sections. All of the first circle is shaded. 2 out of 3 sections of the second circle are shaded.
4.8


Three circles are shown. Each is divided into two sections. The first two circles are completely shaded. Half of the third circle is shaded.
4.9

53=12353=123

4.10

138=158138=158

4.13

127127

4.14

134134

4.15

118118

4.16

116116

4.17

167.167.

4.18

159159

4.19

327327

4.20

44114411

4.21

267267

4.22

238238

4.23

50115011

4.24

343343

4.25

2

4.26

3

4.27

Correct answers include 610,915,and1220.610,915,and1220.

4.28

Correct answers include 810,1215,and1620.810,1215,and1620.

4.29

18211821

4.30

3010030100

4.35
  1. >
  2. >
  3. <
  4. <
4.36
  1. >
  2. <
  3. >
  4. <
4.37

2323

4.38

3434

4.39

3434

4.40

2323

4.41

9797

4.42

9595

4.43

23402340

4.44

5858

4.45

xyxy

4.46

abab

4.47

310310

A rectangle is shown, divided vertically into five equal pieces. Three of the pieces are shaded. The first three pieces of the rectangle are divided by a horizontal line, creating six equal pieces. Three of the six pieces are darkly shaded.
4.48

512512

A rectangle is shown, divided vertically into six equal pieces. Five of the pieces are shaded.
4.49

215215

4.50

21402140

4.51

514514

4.52

14271427

4.53

421421

4.54

316316

4.55
  1. 9
  2. −33a
4.56
  1. 2424
  2. 44x344x3
4.57
  1. 7575
  2. −8−8
  3. 411411
  4. 114114
4.58
  1. 7373
  2. 1212
  3. 914914
  4. 121121
4.61

2


A rectangle is shown, labeled as one third. Below it is an identical rectangle split into two equal pieces, each labeled as one sixth.
4.62

2


A rectangle is shown, labeled as one half. Below it is an identical rectangle split into two equal pieces, each labeled as one fourth.
4.63

6


Two rectangles are shown, each labeled as 1. Below it are two identical rectangle, each split into three pieces. Each of the six pieces is labeled as one third.
4.64

6


Three rectangles are shown, each labeled as 1. Below are three identical rectangles, each split into 2 equal pieces. Each of these six pieces is labeled as one half.
4.65

914914

4.66

10211021

4.67

215p215p

4.68

158q158q

4.69

4545

4.70

5454

4.71

415415

4.72

2323

4.73

2

4.74

9494

4.75

−15

4.76

856856

4.77

5858

4.78

7878

4.79

2

4.80

5252

4.81

9s149s14

4.82

5y65y6

4.83

abcdabcd

4.84

p+qrp+qr

4.85

4545

4.86

11141114

4.87

2727

4.88

103103

4.89

34b34b

4.90

4q4q

4.91

2549.2549.

4.92

1212

4.93

35,3−535,3−5

4.94

−27,2−7−27,2−7

4.95

109109

4.96

1212

4.97

−34−34

4.98

2323

4.99

2929

4.100

8585

4.101

4

4.102

2

4.103

5858

A circle divided into 8 sections, 5 of which are shaded.
4.104

5656

A circle divided into 6 sections, 5 of which are shaded.
4.105

5656

4.106

1

4.107

x+34x+34

4.108

y+58y+58

4.109

1d1d

4.110

3m3m

4.111

9p89p8

4.112

9q59q5

4.113

2323

4.114

2323

4.115

3838, models may differ.

4.116

1616, models may differ

4.117

3737

4.118

1212

4.119

x27x27

4.120

y1314y1314

4.121

16x16x

4.122

22a22a

4.123

−1

4.124

2323

4.125

60

4.126

15

4.127

96

4.128

224

4.129

912,1012912,1012

4.130

3560,44603560,4460

4.131

5296,51965296,5196

4.132

72224,18922472224,189224

4.133

712712

4.134

710710

4.135

5858

4.136

1212

4.137

79607960

4.138

1036010360

4.139

196196

4.140

7522475224

4.141

3721037210

4.142

25962596

4.143

3y+14183y+1418

4.144

5x+14305x+1430

4.145
  1. 11121112
  2. 1818
4.146
  1. 103103
  2. 13121312
4.147
  1. (27a32)36(27a32)36
  2. 2a32a3
4.148
  1. (24k+25)30(24k+25)30
  2. 24k2524k25
4.149

190190

4.150

272

4.151

2

4.152

2727

4.153
  1. −1−1
  2. 1212
4.154
  1. 7676
  2. 1414
4.155

3434

4.156

238238

4.157

1212

4.158

2323

4.159

5252

4.160

3232

4.161

5

The figure shows five circles. The last one is divided into five equal sections.
4.162

5

The figure shows five circles. The last one is divided into six equal sections.
4.163

423423

The figure shows five circles. The last two are divided into six equal sections. Two sections of the last circle are white.
4.164

312312

The figure shows four circles. The last two are divided into eight equal sections. Four sections of the last circle are white.
4.165

567567

4.166

79117911

4.167

16121612

4.168

15131513

4.169

913913

4.170

635635

4.171

3434

No alt text
4.172

4545

No alt text
4.173

9595

No alt text
4.174

5353

No alt text
4.175

2323

No alt text
4.176

3434

No alt text
4.177

2323

A circle divided into three sections, two of which are shaded.
4.178

2525

A circle divided into 5 sections, 2 of which are shaded.
4.179

223223

4.180

157157

4.181

223223

4.182

157157

4.183

67126712

4.184

1231012310

4.185

47104710

4.186

2111221112

4.187

418418

4.188

7576375763

4.189
  1. no
  2. yes
  3. no
4.190
  1. no
  2. no
  3. yes
4.191

1212

4.192

415415

4.193

−1

4.194

6767

4.195

193193

4.196

232232

4.197

−125

4.198

−243

4.199

245

4.200

132

4.201

−48

4.202

23

4.203

35

4.204

18

4.205

−91

4.206

−108

4.207

n7=−21;n=−147n7=−21;n=−147

4.208

n8=−56;n=−448n8=−56;n=−448

4.209

q−8=72;q=−576q−8=72;q=−576

4.210

p−9=81;p=−729p−9=81;p=−729

4.211

25f=16;f=4025f=16;f=40

4.212

34f=21;f=2834f=21;f=28

4.213

n23=512;n=518n23=512;n=518

4.214

c38=49;c=16c38=49;c=16

4.215

58+x=14;x=3858+x=14;x=38

4.216

134x=56;x=1112134x=56;x=1112

Section 4.1 Exercises

1.
  1. 1414
  2. 3434
  3. 3838
  4. 5858
3.


A circle is shown. It is divided into 2 equal pieces. 1 piece is shaded.
5.


A circle is shown. It is divided into 4 equal pieces. 3 pieces are shaded.
7.


A circle is shown. It is divided into 6 equal pieces. 5 pieces are shaded.
9.


A circle is shown. It is divided into 8 equal pieces. 5 pieces are shaded.
11.


A circle is shown. It is divided into 3 equal pieces. All 3 pieces are shaded.
13.


Two circles are shown. Each is divided into 6 equal pieces. All 6 pieces are shaded in the circle on the left. 1 piece is shaded in the circle on the right.
15.


Two circles are shown. Each is divided into 5 equal pieces. All 5 pieces are shaded in the circle on the left. 2 pieces are shaded in the circle on the right.
17.
  1. 54=11454=114
  2. 74=13474=134
  3. 118=138118=138
19.
  1. 114=234114=234
  2. 198=238198=238
21.


A circle is shown. It is divided into 4 equal pieces. All 4 pieces are shaded.
23.


Two circles are shown. Each is divided into 3 equal pieces. All 3 pieces are shaded in the circle on the left. 2 pieces are shaded in the circle on the right.
25.


Two circles are shown. Each is divided into 8 equal pieces. All 8 pieces are shaded in the circle on the left. 5 pieces are shaded in the circle on the right.
27.


Three circles are shown. Each is divided into 4 equal pieces. All 4 pieces are shaded in the two circles on the left. 1 piece is shaded in the circle on the right.
29.

123123

31.

235235

33.

319319

35.

32153215

37.

7575

39.

176176

41.

197197

43.

329329

45.

4

47.

9

49.

9

51.

Answers may vary. Correct answers include 26,39,412.26,39,412.

53.

Answers may vary. Correct answers include 1012,1518,2024.1012,1518,2024.

55.

Answers may vary. Correct answers include 1018,1527,2036.1018,1527,2036.

57.


A number line is shown. The numbers 0, 1, 2, 3, 4, 5, and 6 are labeled. Between 0 and 1, 1 third is labeled and shown with a red dot. Between 1 and 2, 7 fourths is labeled and shown with a red dot. Between 2 and 3, 13 fifths is labeled and shown with a red dot.
59.


A number line is shown. The numbers 0, 1, 2, 3, 4, 5, and 6 are labeled. Between 0 and 1, 7 tenths is labeled and shown with a red dot. Between 1 and 2, 13 eighths is labeled and shown with a red dot. Between 2 and 3, 5 halves is labeled and shown with a red dot. 3 is labeled and shown with a red dot.
61.


A number line is shown. The numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4 are labeled. Between negative 3 and negative 2, negative 2 and 1 third is labeled and shown with a red dot. Between 2 and 3, 2 and 1 third is labeled and shown with a red dot.
63.


A number line is shown. The numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4 are labeled. Between negative 3 and negative 2, negative 8 thirds is labeled and shown with a red dot. Between negative 2 and negative 1, negative 1 and 3 fourths is labeled and shown with a red dot. Between negative 1 and 0, negative 2 fifths is labeled and shown with a red dot. Between 0 and 1, 2 fifths is labeled and shown with a red dot. Between 1 and 2, 1 and 3 fourths is labeled and shown with a red dot. Between 2 and 3, 8 thirds is labeled and shown with a red dot.
65.

<

67.

>

69.

<

71.

<

73.
  1. 2
  2. 614614
75.

Answers will vary.

Section 4.2 Exercises

77.

1313

79.

3434

81.

511511

83.

127127

85.

10211021

87.

7878

89.

xyxy

91.

x4yx4y

93.

2x23y2x23y

95.

1313

No alt text
97.

518518

No alt text
99.

215215

101.

27402740

103.

1414

105.

1616

107.

2929

109.

21502150

111.

11301130

113.

20112011

115.

9n

117.

7p

119.

−34

121.

3838

123.

827827

125.

12966251296625

127.

4343

129.

175175

131.

811811

133.

119119

135.

1

136.


No alt text
137.


A table is shown with four columns and five rows. The first row reads Number, Opposite, Absolute Value, and Reciprocal. The second row reads negative three thirteenths, three thirteenths, three thirteenths, negative thirteen thirds. The third row reads nine fourteenths, negative nine fourteenths, nine fourteenths, and fourteen ninths. The fourth row reads fifteen sevenths, negative fifteen sevenths, fifteen sevenths, and seven fifteenths. The last row reads negative nine, nine, nine, negative one ninth.
139.

4

No alt text
141.

12

No alt text
143.

4

145.

16151615

147.

5454

149.

1

151.

185y185y

153.

252c252c

155.

3434

157.

2929

159.

14r15s14r15s

161.

−12

163.

125125

165.

9

167.

8787

169.
  • 4·23cups=83cups=223cups4·23cups=83cups=223cups
  • Answers will vary.
171.

18yard18yard

173.

Answers will vary.

175.

Answers will vary.

Section 4.3 Exercises

177.

44214421

179.

358358

181.

163163

183.

63166316

185.

3232

187.

4343

189.

2

191.

5

193.

7v137v13

195.

abab

197.

A3BA3B

199.

3232

201.

15221522

203.

310310

205.

1616

207.

3r5s3r5s

209.

92y92y

211.

28

213.

118118

215.

−49,49−49,49

217.

13−6,−13613−6,−136

219.

127127

221.

5252

223.

234234

225.

1313

227.

4545

229.

1212

231.

2

233.

5656

235.

26252625

237.

116116

239.

5252

241.

−10

243.

−2

245.

51205120

247.

187187

249.
  1. 43=113cups43=113cups
  2. 803=2623cups803=2623cups
251.

Answers will vary.

253.

Answers will vary.

Section 4.4 Exercises

255.


A circle is divided into 10 equal pieces. 7 of the pieces are shaded.


710710

257.


A circle is divided into 8 equal pieces. 6 of the pieces are shaded.


3434

259.

7979

261.

16151615

263.

y+23y+23

265.

14q14q

267.

9a79a7

269.

−4x5−4x5

271.

3434

273.

7878

275.

819819

277.

13121312

279.


A circle is divided into eight sections, three of which are shaded.


1212

281.

1515

283.

513513

285.

1616

287.

8383

289.

x819x819

291.

11z81311z813

293.

14c14c

295.

55v55v

297.

3d113d11

299.

14s314s3

301.

2727

303.

311311

305.

1818

307.

6s116s11

309.

2929

311.

49274927

313.

14cup14cup

315.

No, adding up the number of pieces gives 13121312, which is greater than 1. (Answers may vary.)

Section 4.5 Exercises

317.

20

319.

48

321.

240

323.

245

325.

60

327.

520,420520,420

329.

1424,15241424,1524

331.

3348,20483348,2048

333.

2060,4560,36602060,4560,3660

335.

920920

337.

11241124

339.

3838

341.

2323

343.

23202320

345.

19241924

347.

148148

349.

124124

351.

112112

353.

760760

355.

53805380

357.

291245291245

359.

120120

361.

11401140

363.

116116

365.

710710

367.

3y+463y+46

369.

4x5204x520

371.
  1. 5656
  2. 44
373.
  1. 37403740
  2. 110110
375.
  1. 9a149a14
  2. 9a14249a1424
377.
  1. 4q274q27
  2. 4q7515q4q7515q
381.

11241124

383.

718718

385.

215215

387.

−338x88−338x88

389.

16391639

391.

181181

393.

32

395.

36253625

397.

607607

399.

152152

401.

313313

403.

19301930

405.

−9

407.

91609160

409.

11401140

411.

5656

413.

1

415.

227227

417.
  1. 1212
  2. −1−1
419.
  1. 0 0
  2. 1616
421.
  1. 1313
  2. −1−1
423.
  1. 1616
  2. 2323
425.

415415

427.

916916

429.

−2

431.

3

433.

She needs238cupsShe needs238cups

435.

Answers will vary.

Section 4.6 Exercises

437.


Four circles are shown. The first three are shaded. The last circle is divided into 3 equal parts. 2 parts are shaded.


323323

439.


Four circles are shown. The first three are shaded. The last circle is divided into 3 equal parts. 2 parts are shaded.


323323

441.

759759

443.

11

445.

11131113

447.

11131113

449.


A circle is shown. It is divided into 8 equal pieces. 4 pieces are shaded.


1212

451.

116116

453.

625625

455.

179179

457.

5656

459.

7111271112

461.

16161616

463.

5112051120

465.

−11124−11124

467.

6171861718

469.

7979

471.

23

473.

834834

475.

415415

477.

535535

479.

116116

481.

1311313113

483.

71307130

485.

10271027

487.

27452745

489.

17241724

491.

712yards712yards

493.

1314inches1314inches

495.

Answers will vary.

497.

Answers will vary.

Section 4.7 Exercises

499.
  1. no
  2. yes
  3. no
501.
  1. no
  2. yes
  3. no
503.

m=12m=12

505.

h=23h=23

507.

c = −1

509.

z = −1

511.

p=3740p=3740

513.

k=715k=715

515.

k=187k=187

517.

v=113v=113

519.

b = −27

521.

x = −256

523.

q = 160

525.

s = 45

527.

y = −42

529.

k=1720k=1720

531.

p = 100

533.

m = −16

535.

b = −21

537.

v = 36

539.

y = 0

541.

g=19g=19

543.

q=34q=34

545.

n=145n=145

547.

y=2524y=2524

549.

d=815d=815

551.

n6=−24;n=−144n6=−24;n=−144

553.

m−7=−8;m=56m−7=−8;m=56

555.

f−4=−20;f=80f−4=−20;f=80

557.

g9=14;g=126g9=14;g=126

559.

25q=20;q=5025q=20;q=50

561.

49p=−28;p=−6349p=−28;p=−63

563.

h2=43;h=86h2=43;h=86

565.

a23=34;a=12a23=34;a=12

567.

34+x=18;x=5834+x=18;x=58

569.

y13=16;y=16y13=16;y=16

571.

30 inches

573.

Answers will vary.

Review Exercises

575.

5959

577.

32=11232=112

579.

58115811

581.

495495

583.

Answers may vary.

585.


A number line is shown. Integers from negative 4 to 4 are labeled. Between negative 4 and negative 3, negative 7 halves is labeled and marked with a red dot. Between negative 2 and negative 1, negative 1 and 1 third is labeled and marked with a red dot. Between negative 1 and 0, negative 1 fourth is labeled and marked with a red dot. Between 0 and 1, 1 fourth is labeled and marked with a red dot. Between 1 and 2, 1 and 1 third is labeled and marked with a red dot. Between 3 and 4, 7 halves is labeled and marked with a red dot.
587.

>

589.

3434

591.

xyxy

593.

4747

595.

24m1124m11

597.

6

599.

415415

601.

−4

603.

4

605.

415415

607.

52b52b

609.

2681126811

611.

8

613.

Vh6Vh6

615.

2929

617.

22

619.

736736

621.

5858

623.

3535

625.

x+710x+710

627.

1212

629.

19151915

631.

815815

633.

15

635.

60

637.

924and2024924and2024

639.

2060,4560and48602060,4560and4860

641.

1414

643.

77907790

645.

3y10303y1030

647.

14d1114d11

649.

256225256225

651.
  1. 8585
  2. 11201120
653.

13231323

655.

81118111

657.

51105110

659.

113113

661.
  1. no
  2. yes
  3. no
663.

n=511n=511

665.

h=5140h=5140

667.

z = −23

669.

q110=12;q=35q110=12;q=35

671.

38y=24;y=6438y=24;y=64

Practice Test

673.

237237

675.

1414

677.

1414

679.

16u

681.

−2

683.

12251225

685.

5

687.

5p2q5p2q

689.

13

691.

713713

693.

−1

695.

94x94x

697.

3

699.

y=45y=45

701.

f=1312f=1312

703.

c = −27

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