Homework Helper Answer Key
Lesson 4-1
11. a. 3.9 cm b. She did not square the length of the given leg. 12. 9.2 ft 13. 36.5 cm 14. a. B b. 35.0 cm 15. Biking 16. 27.4 mm
The Pythagorean Theorem 1. 26 2. 17.464 in. 3. 17.1 ft 4. 28.7 m 5. 68 6. a. 37 ft b. Answers will vary. 7. a. 27.7 cm b. D 8. 708.5 ft
Lesson 4-3 The Converse of the Pythagorean Theorem
9. "10
1. Yes 2. No 3. II only 4. a. A b. Answers will vary. 5. B 6. a. Student 1 and Student 3 are incorrect.
10. a. 39.6 ft b. Answers will vary. 11. 306.5 ft 12. a. A b. 39 13. a. B b. 34 in. 14. a. 37.0 m b. go through the park
b. They used the equation a b c, not a2 b2 c2. 7. Triangle 2 and Triangle 3 are right triangles. 8. Triangle 1, Triangle 3 9. No 10. a. A b. Answers will vary. 11. D 12. a. Decide which side length to substitute for the hypotenuse length. b. No 13. a. The sides of the triangle satisfy the equation a2 b2 c2. b. Triangle 1, Triangle 2, Triangle 3 14. a. Triangle 1 and Triangle 2 only b. Answers will vary.
Lesson 4-2 Finding Unknown Leg Lengths 1. 12 2. 400 ft 3. 17.7 yd 4. a. D b. 9.8 ft 5. 48 in. 6. 92.3 in. 7. 33.6 ft 8. a. 125 ft b. Answers will vary. 9. a. 36.8 ft b. Answers will vary. 10. a. 39.6 ft b. Answers will vary.
digits Texas
13
Grade 8
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Unit C
Homework Helper Answer Key
Lesson 4-4
10. a. 5,096 in.2 b. Answers will vary. 11. (5, 5) (3, 5) 12. a. A b. 26.7 in.
Distance in the Coordinate Plane 1. 5 mi 2. 3.9 3. scalene 4. a. You are closer to the school. b. Answers will vary.
13. 1,800 cm2 14. a. 24.7 in. b. Answers will vary.
5. a. The triangle formed by the points H, P, and L is a right triangle. The distance from the library to your home is the length of the hypotenuse, HL. b. 6 miles 6. 5 yd 7. 86.0 ft 8. 6.2 9. a. Find PR by finding the difference of the x-coordinates. Then use the Pythagorean Theorem to find PQ and QR. b. Isosceles 10. B
Lesson 5-1 Surface Areas of Prisms 1. 368 in.2 2. 666 in.2 3. 297 in.2 4. 5,152 cm2 5. 283.36 m2 6. a. 1,522 cm2 b. Check students’ work. Answers will vary. 7. Answers will vary; 2 : 3 8. 4,007.66 cm2 9. a. 335.8 cm2 b. C 10. a. 28.32 cm2 b. Answers will vary. 11. a. B b. 777.12 in.2 12. a. A b. 265.2 cm2 13. a. 2,494.6 in.2 b. 3,136 in.2
Lesson 4-5 Additional Problem Solving 1. (10, 10), (10, 8) 2. a. (5, 10), (5, 14) b. (5, 8), (5, 16) 3. 9,680 ft3 4. 19.6 cm 5. a. B, C b. 20.7 cm 6. a. (7, 3), (7, 5) b. D 7. a. 360 in.2 b. Yes 8. (4, 4), (4, 4) 9. a. A b. 8 mm c. 2,400 mm3
digits Texas
14
Grade 8
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Unit C
Homework Helper Answer Key
Lesson 5-2
8. a. 96p ft3 b. 6,144p ft3 c. 64 9. 773.6 cm3 10. 25,143p in.3 11. 4 m 12. a. A b. 147p yd3 13. a. Use the height of the original can to find the height of the new can. b. 261.0 cm3 14. 34.0 lb 15. 1.8 in.
Surface Areas of Cylinders 1. 150.7 cm2 2. 1,758.8 mm2 3. 2,179.5 ft2 4. 950.8 in.2 5. 725.3 cm2 6. a. 228.3 m2 b. Answers will vary. 7. a. 620.7 in.2 b. Answers will vary. 8. a. A b. 432.5 in.2 9. a. 494.6 in.2 b. She forgot to include the lateral area.
Lesson 5-4 Volumes of Cones 1. 12p 2. Cone 1, Cone 3, Cone 2
10. a. 742.6 ft2 b. 11 gal 11. a. D b. 52.1 in.2 12. 2,628.2 cm2 13. a. 111p in.2 b. 6.25 in.2
3. 759.88 m3 4. a. B b. 190.76 5. $12,057.60 6. 7 yd 7. 3.9 feet 8. 7 feet 9. a. B, C b. 2.17 yd 10. a. 75p b. Answers will vary. 11. a. 16 b. Answers will vary. 12. a. 4 b. C
Lesson 5-3 Volumes of Cylinders 1. a. 48p in.3 b. 96p in.3 2. 91.4 in.3 3. 1,055.04 in.3 4. 2.0 cm 5. a. 4.9 in. b. Answers will vary. 6. a. 800p m3 b. Answers will vary. 7. a. 36.0 in.3 b. No c. He found the volume of the rectangular container instead of the cylinder.
digits Texas
13. a. 871.87 m3 b. A 14. a. 508.68 in.3 b. 1,526.04 in.3 15. 3 cm
15
Grade 8
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Unit C
Homework Helper Answer Key Lesson 5-6
16. 296 packages 17. a. Cone 1: 3,072p Cone 2: 6,000p 64 b. 125 or 125 64
Additional Problem Solving 1. 523 cm3 2. a. 1,611 in.3 b. A 3. 46 cm3
Lesson 5-5 Volumes of Spheres
4. a. 54,937 m3 b. Check students’ drawings. 5. 910 gallons 6. a. B 8,574 in.3 7. 915.8 in.3
1. 2,143.57 in.3 2. 113 ft3 3. 268 in.3 4. 4,187 ft3 5. a. 0.47 in.3 b. Answers will vary. 6. 16 cm 7. 12 cm 8. Radius: 7 mm Diameter: 14 mm 9. a. B b. 33 in.3 10. a. 44,579.63 in.3 b. Answers will vary. 11. a. 4.4 in. b. Answers will vary.
Lesson 6-1 Solving Two-Step Equations 1. 84 2. 4018 3. a. D b. 123.32 mi 4. a. B b. 8 5. a. D b. $5.38 6. x 8
12. a. 82.41 m3 b. B 13. 9,412.01 in.3 14. a. 7,234.56 cm3 b. 24 minutes
7. z 3114 8. $30 per ft2 9. a. y 15 b. Answers will vary. 10. a. D b. 227 11. a. D b. 8 mi 12. a. D b. B; 1 13. a. C b. y 60 14. a. B b. A c. 255.01 5 15. h 2916
15. 163 yd3 16. a. 7.6 cm b. 229.73 cm3 17. a. B b. 555.36 cm3 18. 575 in.3 19. a. 8513p in.3 b. 4223p in.3 c. 3 in.
digits Texas
16
Grade 8
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Unit C
Homework Helper Answer Key
Lesson 6-2
8. a. A b. Answers will vary. c. x 3; answers will vary.
Writing and Solving Equations with Variables on Both Sides 1. 4 2. 8 3. a. Answers will vary. b. 1 4. 2 5. 4 6. a. 43,425 125x 200x 45,000 150x b. 7 months 7. a. 2 b. Answers will vary. 8. a. D b. Answers will vary. 9. a. x; all real numbers b. Answers will vary. 10. 20 11. a. 6 b. C 12. a. D b. 2 13. 2.9 hours 14. a. A b. Answers will vary.
9. a. A b. D; x 1.1 10. a. A b. Answers will vary. 11. D; 2
Lesson 6-4 Additional Problem Solving 1. 520 2. 27 in. 3. $643.51 4. a. 50 hr b. Answers will vary. 5. a. 9 lb b. Answers will vary. 6. 3 hr 7. 15 8. a. D b. 10 9. a. 12 yd b. 24 yd 10. a. B b. 28 11. a. C b. 9 months 12. 3 hr 13. 27 14. a. 90 b. 280 c. 560
Lesson 6-3 Writing and Solving Inequalities with Variables on Both Sides 1. x 6 2. After 1.5 hours. 3. a. B b. Answers will vary. 4. After 11 months. 5. x 16 6. a. C b. A; x 4.5 c. B 7. a. C b. After 2 hours.
Lesson 7-1 Angles, Lines, and Transversals 1. B 2. mu 32 3. m2 157 4. 75.8
digits Texas
17
Grade 8
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Unit C
Homework Helper Answer Key
5. a. 3 and 6, 2 and 7 b. Answers will vary. 6. a. mw 79 b. Jacob thought that w and y are corresponding angles, when actually w and t are corresponding angles and have the same measure. 7. m1 27 8. a. m12 127 b. Answers will vary. 9. 148° 10. a. Find the measure of the corresponding angle, 2, by subtracting m1 from 180. b. 101 11. a. D b. 32 12. a. m3 86 and m6 129 b. Ball A
11. a. The value of x must equal the value of y. b. 73
Lesson 7-3 Interior Angles of Triangles 1. 37 2. 50 3. 41 4. 30 5. 50 6. x 36, mQ 126 7. a. 61 b. Answers will vary. 8. a. 51 b. Answers will vary. 9. a. 35 b. D 10. 45 11. a. D b. 52.8 12. mA 40 13. mB 93.5 14. a. D b. 36.2 15. a. C b. mA 19.3 mB 77.2 mC 83.5 16. mA 93 mB 31 mC 56
Lesson 7-2 Reasoning and Parallel Lines 1. D 2. 142 3. a. Yes, because corresponding angles are 27 each. b. Yes, because alternate interior angles are 81 each. 4. D 5. m 7 n 6. a. 72 b. Your friend found the supplement of 72. 7. a. C b. Answers will vary. 8. D 9. a. 2x 54 86 b. 16 c. Answers will vary. 10. a. 2x 20 86 b. 53
Lesson 7-4 Exterior Angles of Triangles 1. B 2. a. D b. B, D 3. a. C b. A, C 4. m1 62
digits Texas
18
Grade 8
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Unit C
Homework Helper Answer Key
5. m1 32 m2 36 6. a. m1 116 b. Answers will vary. 7. a. m1 58 b. Answers will vary. 8. a. m1 54 m2 68 b. B 9. m1 30 10. m1 145 11. m1 120 m2 35 12. a. A b. 73 13. a. C b. 97
3. B 4. a. First use vertical angles to find m5. Then use corresponding angles to find m3. Finally, use alternate interior angles to find m2. b. m2 55 c. Answers will vary. 5. a. m4 129 b. A 6. m4 136, m3 44 7. m2 78 8. a. Yes b. Each triangle has angle measures of 30, 59, and 91. 9. a. C b. 117 10. a. m1 m2 m3 b. 36 11. m1 23 m2 49 m3 108 m4 72 12. A
Lesson 7-5 Angle-Angle Triangle Similarity 1. Yes 2. No 3. B, C 4. a. Yes b. Answers will vary. 5. a. A, B, C b. Anchil did not give all the similar triangles. 6. No 7. Yes 8. A, B, C 9. a. If two angles of WSR are congruent to two angles of ZSP b. No 10. a. A, C, D b. A, B, D 11. B, D, E, F
Lesson 8-1 What Are Simultaneous Linear Equations in Two Variables? 1. C, D, F 2. Answers will vary. 3. Yes 4. B 5. a. C b. Answers will vary. 6. a. A b. Answers will vary. 7. a. n 16 4w n 42 11w b. Answers will vary. 8. a. d 58 d 3t 53 b. Lake 2
Lesson 7-6 Additional Problem Solving 1. m3 49 2. m3 150
digits Texas
19
Grade 8
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Unit C
Homework Helper Answer Key Lesson 8-3
9. a. Answers will vary. b. No 10. C 11. C, E 12. B 13. a. C b. c 25 0.35m c 13 0.4m 14. a. c 42 c 10 8t b. Shop N
Solving Simultaneous Linear Equations by Graphing 1. a. Check students’ graphs. b. (4, 3) 2. a. Check students’ graphs. b. A 3. a. A b. Check students’ graphs. c. 4 hours 4. a. c 10 c 0.6n 1 b. Check students’ graphs. c. 15 5. a. Check students’ graphs. b. (3, 3) c. Answers will vary. 6. a. c 5 c 2 0.2n b. Check students’ graphs. c. 15 copies d. Store Z; Store W; answers will vary. 7. a. Answers will vary. b. (3, 3) 8. a. Check students’ graphs. b. D c. Answers will vary. 9. a. A b. Answers will vary. 10. a. Check students’ graphs. b. (7, 3) 11. a. c 12.75n 12 c 15.75n b. Check students’ graphs. 12. a. Check students’ graphs. b. (0.5, 3.75) c. Answers will vary.
Lesson 8-2 Estimating Solutions of Simultaneous Linear Equations by Inspection 1. one solution 2. one solution 3. no solution 4. one solution 5. infinitely many solutions 6. a. no solution b. Answers will vary. 7. A 8. C 9. a. one solution b. D 10. a. infinitely many solutions b. Answers will vary. 11. a. A b. one solution 12. infinitely many solutions 13. a. A b. A 14. a. A b. infinitely many solutions 15. a. infinitely many solutions b. Answers will vary. 16. no solution
digits Texas
20
Grade 8
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Unit C
Unit C
Homework Helper Answer Key
Lesson 8-4
6. a. 20 b. 70 7. a. 45 b. 21 8. a. C 0.7m 24 C 1.5m b. A c. 30 miles d. Taxicab 9. a. 9 minutes; 22,500 feet b. Answers will vary.
Solving Simultaneous Linear Equations Using Substitution 1. (4, 2) 2. (4, 6) 3. Pedro: 1,471; Ricky: 1,195 4. River C: 2,800 miles; River D: 2,700 5. a. length: 160 ft; width: 50 ft b. Answers will vary.
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6. a. Q1, 58 R b. Answers will vary. 7. a. (4, 9) b. C 8. 217 children; 264 adults 9. a. (3, 4) b. Answers will vary. 10. a. (2, 1) b. Answers will vary. 11. Speed of plane: 323.9 mph Speed of wind: 26.1 mph 12. 90 more acres 13. a. B b. (5, 2) 14. (4, 2); 48 15. a. A b. 40 dimes, 30 nickels 16. a. 100 adult tickets, 400 student tickets b. $10 below goal
Lesson 8-5 Additional Problem Solving 1. W 28 ft, L 30 2. a. (80, 70) b. D c. y 70.8 d. C 3. W 370 ft, L 780 ft 4. a. 500; $55 b. Plan B 5. Leslie: 584, Jackie: 626
digits Texas
21
Grade 8