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CK-12 Middle School Math -Grade 8, Answer Key
CK-12 Foundation
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Printed: March 31, 2014
AUTHORCK-12 Foundation
iii
Contents www.ck12.org
Contents
1 Using Algebra, Answer Key 11.1 Analyzing Graphs, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Order of Operations, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Powers and Exponents, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Writing Expressions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Solving Equations, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.6 Using Formulas, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.7 A Problem Solving Plan, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.8 Problem Solving Strategies, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Using Rational Numbers, Answer Key 122.1 Adding and Subtracting Decimals, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Multiplying and Dividing Decimals, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Adding and Subtracting Fractions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4 Multiplying and Dividing Fractions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . 162.5 Adding and Subtracting Integers, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.6 Multiplying and Dividing Integers, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . 182.7 Rational Numbers, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.8 Number Properties, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Single Variable Equations and Inequalities, Answer Key 213.1 Solving Two Step Equations, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Solving Multi-Step Equations, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3 Solving Equations with the Variable on Both Sides, Answer Key . . . . . . . . . . . . . . . . . 243.4 Solving Equations with Rational Numbers, Answer Key . . . . . . . . . . . . . . . . . . . . . . 253.5 Solving Inequalities Using Addition or Subtraction, Answer Key . . . . . . . . . . . . . . . . . 263.6 Solving Inequalities Using Multiplication or Division, Answer Key . . . . . . . . . . . . . . . . 283.7 Solving Multi-Step Inequalities, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.8 Using Inequalities, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 Applying Proportions, Answer Key 314.1 Ratios and Rates, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.2 Writing and Solving Proportions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.3 Unit Scale and Scale Factor, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.4 Scale in Two Dimensions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.5 Scale in Three Dimensions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.6 Customary Units of Measure, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.7 Metric Units of Measure, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.8 Formulas and Unit Analysis, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5 Applying Percents, Answer Key 415.1 Fractions, Decimals and Percents, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
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5.2 Percents and Proportions, Answers Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.3 Using the Percent Equation, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.4 Percent Increase and Decrease, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.5 Consumer Percent, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.6 Percent and Statistics, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.7 Simple Interest, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.8 Compound Interest, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6 Geometry and Transformations, Answer Key 506.1 Angle Pairs, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.2 Triangles and Angles, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.3 Quadrilaterals and Angles, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.4 Polygons and Angles, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.5 Congruent Polygons, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.6 Reflections and Symmetry, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.7 Translations, Rotations and Tessellations, Answer Key . . . . . . . . . . . . . . . . . . . . . . . 576.8 Similarity and Dilations, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
7 Using Real Numbers and Right Triangles, Answer key 597.1 Radical Expressions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607.2 Rational and Irrational Numbers, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . 617.3 The Pythagorean Theorem, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627.4 Using the Pythagorean Theorem, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . 637.5 The Distance Formula, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647.6 Special Right Triangles, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.7 Exploring Trigonometric Ratios, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . 667.8 Using Trigonometric Ratios, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
8 Measurement, Area and Volume, Answer Key 688.1 Area of Polygons, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698.2 Area of Circles, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708.3 Solid Figures, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 718.4 Surface Area of Prisms and Cylinders, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . 728.5 Surface Area of Pyramids and Cones, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . 738.6 Volume of Prisms and Cylinders, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . 748.7 Volume of Pyramids and Cones, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . 758.8 Surface Area and Volume of Spheres, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . 76
9 Linear Functions and Graphs, Answer Key 779.1 Relations and Functions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 789.2 Linear Equations in Two Variables, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . 799.3 Using Intercepts, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 849.4 The Slope of a Line, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859.5 Slope-Intercept Form, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879.6 Linear Functions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889.7 Systems of Linear Functions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 899.8 Graphs of Linear Inequalities, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
10 Analyzing Data, Answer Key 9210.1 Measures of Central Tendency and Dispersion, Answer Key . . . . . . . . . . . . . . . . . . . . 9310.2 Stem-and-Leaf Plots and Histograms, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . 9510.3 Box-and-Whisker Plots and Outliers, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . 97
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10.4 Scatterplots, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9910.5 Misleading Statistics, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10210.6 Using Data Displays, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10510.7 Collecting Data, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10710.8 Interpreting Data, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
11 Using Probability, Answer Key 11011.1 Counting Methods, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11111.2 Permutations, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11211.3 Combinations, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11311.4 Theoretical and Experimental Probability, Answer Key . . . . . . . . . . . . . . . . . . . . . . 11411.5 Probability and Odds, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11611.6 Conditional Probability, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11711.7 Geometric Probability, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11811.8 Probability and Simulations, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
12 Polynomials, Answer key 12012.1 Polynomials, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12112.2 Adding and Subtracting Polynomials, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . 12212.3 Monomials and Powers, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12312.4 Multiplying Binomials, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12412.5 Exploring Parabolas, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12512.6 Quadratic Functions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12712.7 Exponential Functions, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13212.8 Sequences, Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
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www.ck12.org Chapter 1. Using Algebra, Answer Key
CHAPTER 1 Using Algebra, Answer KeyChapter Outline
1.1 ANALYZING GRAPHS, ANSWER KEY
1.2 ORDER OF OPERATIONS, ANSWER KEY
1.3 POWERS AND EXPONENTS, ANSWER KEY
1.4 WRITING EXPRESSIONS, ANSWER KEY
1.5 SOLVING EQUATIONS, ANSWER KEY
1.6 USING FORMULAS, ANSWER KEY
1.7 A PROBLEM SOLVING PLAN, ANSWER KEY
1.8 PROBLEM SOLVING STRATEGIES, ANSWER KEY
1
1.1. Analyzing Graphs, Answer Key www.ck12.org
1.1 Analyzing Graphs, Answer Key
1.
2.
3.4. Alaska and Hawaii5. 19596. North Dakota, South Dakota, Montana and Washington7. 1863 and 18838. 3
15 = 15 = 20%
9. 5
2
www.ck12.org Chapter 1. Using Algebra, Answer Key
10. 27%
11.
12.
13.14. Pug, Jack Russell Terrier, Dachshund, Corgi, Border Collie, English Springer Spaniel15. 6
1016. 60%17. Golden Retriever, Lab, Akita, Bull Mastiff18. 4
1019. 40%20. Bull Mastiff –145 pounds
3
1.1. Analyzing Graphs, Answer Key www.ck12.org
21.
22.
23.24. Largest on July 12th, smallest on Aug. 19th
25. 20%26. 4
1027. Oct. 1st
28. Aug. 10th and Sept. 2nd
4
www.ck12.org Chapter 1. Using Algebra, Answer Key
1.2 Order of Operations, Answer Key
1. 112. 83. 314. 135. 66. 237. 438. 319. 11
10. 2011. 2812. 3613. 1914. 1015. 4516. 617. 6118. 919. 2720. 2421. 022. 1623. 524. 3125. 1626. 1227. 2628. 16
5
1.3. Powers and Exponents, Answer Key www.ck12.org
1.3 Powers and Exponents, Answer Key
1. 272. 163. 164. 645. 1256. 647. 818. 649. 58
10. -911. 2012. 613. 7214. 9615. 216. 2217. 23018. 1619. -2820. 5721. 022. 623. 26624. 27,64825. 117
6
www.ck12.org Chapter 1. Using Algebra, Answer Key
1.4 Writing Expressions, Answer Key
1. 552. 143. 764. 45. 14.56. 857. 318. 889. 62
10. 78211. x+1212. x−813. 3x14. x2 +515. x
2 +716. 4(x+6)17. 2x
418. 6x+2x19. x2 +7−420. x
3 +1221. 2422. 423. 3624. 14925. 1326. 7227. 628. 9629. 14730. 16
7
1.5. Solving Equations, Answer Key www.ck12.org
1.5 Solving Equations, Answer Key
1. x = 182. y = 223. x = 594. x = 35. x = 66. x = 67. x = 98. y = 109. a = 40
10. b = 211. x = 412. y = 713. b = 614. y = 815. a = 316. x = 817. x = 1618. x = 219. a = 920. b = 621. There are three parts to this answer. Verbal Model: Heart Rate After Exercise –Resting Heart Rate = Difference
between the two Equation: x−75 = 30 Solution: 105 beats per minute22. There are three parts to this answer. Verbal Model: Total Number of Toothpicks = Three times the Number
of Rectangles One Toothpick Let “n” equal the number of rectangles Equation: 3n+1 Solution: 3(15)+1 =46 toothpicks
8
www.ck12.org Chapter 1. Using Algebra, Answer Key
1.6 Using Formulas, Answer Key
1. P = 20 in,A = 25 sq. in.2. P = 16 in,A = 15 sq. in3. P = 28 cm,A = 48 sq. cm.4. P = 44 f t,A = 121 sq. f t.5. P = 27 in,A = 40.5 sq. in.6. P = 28 f t,A = 49 f t.7. P = 46 m,A = 132 sq. m.8. P = 52 m,A = 169 sq. m.9. P = 46 f t,A = 120 sq. f t.
10. P = 50 f t,A = 156.25 sq. f t.11. 8 in12. 6 in13. 9 m14. 10 in15. 12 ft.16. 11 cm17. 2 mm18. 132 miles19. 330 miles20. 520 miles21. 600 miles22. 840 miles23. 630 miles24. 15 hours25. 50 mph26. 5 miles per minute27. 8 hours
9
1.7. A Problem Solving Plan, Answer Key www.ck12.org
1.7 A Problem Solving Plan, Answer Key
1. Working backwards2. Not comparing anything3. .12(20)4. 20(.12)+ .75+ .15+ .425. $3.726. Look for a pattern7. The number of weeks8. 25x+75 = 5009. x = 17 weeks
10. Use a proportion11. You are comparing costs12. $12.2913. $24.5714. $4.5015. $9.0016. $36.0017. Look for a pattern18. 45(4)19. 180 pounds20. 360 pounds
10
www.ck12.org Chapter 1. Using Algebra, Answer Key
1.8 Problem Solving Strategies, Answer Key
1. Look for a pattern2. Make a table3. 6 weeks4. Write an equation.5. $19.67 savings6. Original price = $78.67
11
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CHAPTER 2 Using Rational Numbers,Answer Key
Chapter Outline2.1 ADDING AND SUBTRACTING DECIMALS, ANSWER KEY
2.2 MULTIPLYING AND DIVIDING DECIMALS, ANSWER KEY
2.3 ADDING AND SUBTRACTING FRACTIONS, ANSWER KEY
2.4 MULTIPLYING AND DIVIDING FRACTIONS, ANSWER KEY
2.5 ADDING AND SUBTRACTING INTEGERS, ANSWER KEY
2.6 MULTIPLYING AND DIVIDING INTEGERS, ANSWER KEY
2.7 RATIONAL NUMBERS, ANSWER KEY
2.8 NUMBER PROPERTIES, ANSWER KEY
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www.ck12.org Chapter 2. Using Rational Numbers, Answer Key
2.1 Adding and Subtracting Decimals, AnswerKey
1. 19.722. 31.553. 35.7344. 14.55. 13.366. 91.347. 131.298. 136.159. 23.33
10. 64.7511. 75.6612. 217.813. 663.2314. 26.3615. 4916. 6117. 8718. 6719. 3220. 1021. 1822. 1523. 1924. 19.525. 12.926. 9.227. 22.3
13
2.2. Multiplying and Dividing Decimals, Answer Key www.ck12.org
2.2 Multiplying and Dividing Decimals, AnswerKey
1. 92. 323. 494. 805. 606. 307. 728. 409. 72
10. 14411. 1112. 413. 414. 215. 716. 617. 718. 519. 220. 221. 3.04522. 6.223. 3.524. 32.7625. 28.8126. .917727. 17.88628. 5.4229. 6.930. 7.45
14
www.ck12.org Chapter 2. Using Rational Numbers, Answer Key
2.3 Adding and Subtracting Fractions, AnswerKey
1. 23
2. 35
3. 710
4. 56
5. 58
6. 1320
7. 34
8. 13
9. 13
10. 15
11. 49
12. 35
13. 5 12
14. 6 35
15. 8 56
16. 7 35
17. 3 13
18. 7 34
19. 1120. 10 1
221. 1 3
1022. 123. 7
924. 2
925. 1
326. 1
2027. 7
1128. 1 7
2429. 1 2
1530. 9
10
15
2.4. Multiplying and Dividing Fractions, Answer Key www.ck12.org
2.4 Multiplying and Dividing Fractions, AnswerKey
1. 38
2. 58
3. 118
4. 2536
5. 724
6. 827
7. 411
8. 35
9. 27
10. 524
11. 1 12
12. 2 12
13. 1 79
14. 1 78
15. 2 23
16. 117. 118. 1 5
719. 2 1
220. 1 3
521. 7 1
222. 10 2
323. 12 1
224. 17 1
325. 1726. 327. 1 3
828. 2 2
15
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2.5 Adding and Subtracting Integers, AnswerKey
1. 132. -33. 04. -45. 66. 57. -218. -269. -23
10. -4811. -1412. -1513. -2014. -315. -516. 2317. 1618. 3219. -320. -321. -3422. 25623. -32124. -103225. -27726. -27627. -55928. -261
17
2.6. Multiplying and Dividing Integers, Answer Key www.ck12.org
2.6 Multiplying and Dividing Integers, AnswerKey
1. 482. -503. -124. -125. -726. -1087. -888. 459. 56
10. -14411. -612. 313. -214. 2015. 216. 717. -918. 519. -320. 3421. 6422. -50423. 9624. -72925. 4826. -8427. -8028. -70
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www.ck12.org Chapter 2. Using Rational Numbers, Answer Key
2.7 Rational Numbers, Answer Key
1. Yes, decimal2. Yes, fraction3. Yes, integer4. Yes, integer5. Yes, integer6. Yes, repeating decimal7. No, irrational8. Yes, terminating decimal9. Yes, decimal
10. Yes, fraction11. <12. >13. <14. <15. <16. >17. >18. >19. >20. <21. 1.522. 323. -5924. -425. 526. -20
19
2.8. Number Properties, Answer Key www.ck12.org
2.8 Number Properties, Answer Key
1. Sample equation: 64+ x = x+642. Sample equation: 712×0 = 03. Sample explanation: The additive identity is 0, and the multiplicative identity is 1.4. Multiplicative identity property5. $2106. $1387. 8 weeks8. 6 years old9. 7 hours
10. 88.7 cm
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www.ck12.org Chapter 3. Single Variable Equations and Inequalities, Answer Key
CHAPTER 3 Single Variable Equationsand Inequalities, Answer Key
Chapter Outline3.1 SOLVING TWO STEP EQUATIONS, ANSWER KEY
3.2 SOLVING MULTI-STEP EQUATIONS, ANSWER KEY
3.3 SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES, ANSWER KEY
3.4 SOLVING EQUATIONS WITH RATIONAL NUMBERS, ANSWER KEY
3.5 SOLVING INEQUALITIES USING ADDITION OR SUBTRACTION, ANSWER KEY
3.6 SOLVING INEQUALITIES USING MULTIPLICATION OR DIVISION, ANSWER KEY
3.7 SOLVING MULTI-STEP INEQUALITIES, ANSWER KEY
3.8 USING INEQUALITIES, ANSWER KEY
21
3.1. Solving Two Step Equations, Answer Key www.ck12.org
3.1 Solving Two Step Equations, Answer Key
1. x = 62. y = 33. x = 54. x = 25. y = 86. x = 37. y = 28. y = 59. x = 12
10. x = 1011. a = 3612. a = 23413. b = 7214. c = 10815. x = 9816. x = 7717. x = 8418. a = 2819. x = 420. y = 621. x = 622. y = 523. x = 624. y = 925. x = 6026. y = 6627. x = 11928. x = 12829. y = 11230. x = 88
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www.ck12.org Chapter 3. Single Variable Equations and Inequalities, Answer Key
3.2 Solving Multi-Step Equations, Answer Key
1. 11x+22. 2y+83. 15x−84. −8y+165. 9x−16. x = 27. y = 68. x =−59. y =−1
10. x = 211. a = 412. a = 613. x =−814. y =−515. x = 216. x = 117. x = 618. x = 519. x = 1320. y = 921. x = 422. y = 223. y = 224. y = 4
23
3.3. Solving Equations with the Variable on Both Sides, Answer Key www.ck12.org
3.3 Solving Equations with the Variable onBoth Sides, Answer Key
1. x = 42. y = 63. y =−64. x =−105. x = 86. y =−37. x = 28. y = 69. x =−10
10. y =−211. x =−212. x = 213. x = 314. x = 215. y =−216. x = 417. y =−1118. x =−1219. y = 120. x = 121. x = 122. x =−323. y =−424. x =−725. y = 526. x =−6
24
www.ck12.org Chapter 3. Single Variable Equations and Inequalities, Answer Key
3.4 Solving Equations with Rational Numbers,Answer Key
1. 22. 253. 5
364. 145. 2
36. 6 1
47. 208. 99. 28.8
10. 1 13
11. 3612. 62.213. 3014. 6815. 316. d− 1
2 d−6 = 917. $3018. $1519. 4.50+2.50(m−1) = 1220. 4 miles21. x+ 2
3 x+10 = 6022. $3023. $20
25
3.5. Solving Inequalities Using Addition or Subtraction, Answer Key www.ck12.org
3.5 Solving Inequalities Using Addition or Sub-traction, Answer Key
1. {12, 11, 10...}2. {6, 7, 8...}3. {1, 0, -1...}4. {-2, -1, 0...}5. {13, 14, 15...}6. {4, 3, 2...}7. {3, 4, 5...}8. {-3, -2, -1...}9. {-5, -6, -7...}
10. {11, 12, 13...}
11.
12.
13.
14.
15.
16.
26
www.ck12.org Chapter 3. Single Variable Equations and Inequalities, Answer Key
17.
18.
19.
20.21. x > 622. y < 3123. a <−124. b≥ 225. y≤−226. x≥−6
27
3.6. Solving Inequalities Using Multiplication or Division, Answer Key www.ck12.org
3.6 Solving Inequalities Using Multiplication orDivision, Answer Key
1. x < 302. x > 203. x < 1004. x > 5005. x≤ 406. x > 427. x≤ 188. x≥ 559. x < 6
10. x≥ 5611. x < 412. x > 1213. x < 1214. x > 915. x > 1116. x≤ 417. x≥ 318. x≤ 419. x > 320. x≤ 421. n < 1822. x >−923. n≤−724. x≥ 24225. b
5 ≥ 326. 15 brownies27. 9h > 11728. Yes. She could work 14 hours.
28
www.ck12.org Chapter 3. Single Variable Equations and Inequalities, Answer Key
3.7 Solving Multi-Step Inequalities, AnswerKey
1. x > 42. x < 33. y > 104. x≤−1
25. x≥ 26. x≤ 27. x > 128. x <−49. x >−60
10. x >−1011. k > 312. x≥−413. j < 614. b≥−415. n≤ 516. z <−717. h > 1018. t ≤ 6319. p≥ 520. y <−221. 8+ s+ s < 40 or an equivalent inequality22. Answers will vary, but should only include numbers less than 16, for example: 5, 10, and 15.5.23. 2(l +7)≥ 36 or an equivalent inequality24. Yes, because the solution to the inequivality in part a is l > 11. Since 12 is greater than 11, it could be a value
for l.
29
3.8. Using Inequalities, Answer Key www.ck12.org
3.8 Using Inequalities, Answer Key
1. x−2≥ 16 and x−2≤ 252. x≥ 18 and x≤ 273. 16 to 274. n
3 <−5, n3 > 3
5. n <−5,n > 96. -5 to 97. 7+2n <−5,7+2n≥ 98. n <−6,n≥ 19. -6 to 1
10. w+3 > 8 and w+3 < 1211. w > 5 and 2 < 912. No13. The cost of the sandwich is greater than $5 and less than $9.14. 3g≥ 30 and 3g≤ 10515. g≥ 10 and g≤ 3516. yes17. He buys between 10 and 30 gallons of gas per week, so it is possible for him to buy 30 gallons of gas.18. Answers will vary19. Answers will vary20. Answers will vary
30
www.ck12.org Chapter 4. Applying Proportions, Answer Key
CHAPTER 4 Applying Proportions,Answer Key
Chapter Outline4.1 RATIOS AND RATES, ANSWER KEY
4.2 WRITING AND SOLVING PROPORTIONS, ANSWER KEY
4.3 UNIT SCALE AND SCALE FACTOR, ANSWER KEY
4.4 SCALE IN TWO DIMENSIONS, ANSWER KEY
4.5 SCALE IN THREE DIMENSIONS, ANSWER KEY
4.6 CUSTOMARY UNITS OF MEASURE, ANSWER KEY
4.7 METRIC UNITS OF MEASURE, ANSWER KEY
4.8 FORMULAS AND UNIT ANALYSIS, ANSWER KEY
31
4.1. Ratios and Rates, Answer Key www.ck12.org
4.1 Ratios and Rates, Answer Key
1. 163 , 16 : 3
2. 4 : 5, 45
3. 14 , 1 to 4
4. 12 to 1, 12 : 15. 6
11 , 6 to 116. 33
100 , 33 : 1007. 4 to 9, 4 : 98. 3
4 , 3 : 49. 45 : 12, 45
1210. 12 to 12, 12
1211. 1
312. 1
413. 6
114. 1
215. 1
516. 4
717. 4
1118. 7
1119. The Gray building, by 19
6520. 56 miles per hour21. 240 books per hour22. $1.62 per pound23. $36.67 per day24. 825 words in 15 minutes25. 12 presents in 1.5 hours
32
www.ck12.org Chapter 4. Applying Proportions, Answer Key
4.2 Writing and Solving Proportions, AnswerKey
1. 92. 103. 144. 185. 556. 247. 908. 219. 49
10. 4211. 1.512. 2.913. 2.514. 17.115. 7.516. 5
3 = f480
17. 49 = 184
a18. 10
7 = c84
19. $15020. 14 miles21. 157.5 miles22. $10.7523. 218.75 minutes24. 214.29 minutes25. 212.5 points
33
4.3. Unit Scale and Scale Factor, Answer Key www.ck12.org
4.3 Unit Scale and Scale Factor, Answer Key
1.
1′′
2 f t=
x18 f t
x = 9′′
2.
1′′
5 f t=
x20 f t
x = 4′′
3.
12′′
2 f t=
y10 f t
x = 2.5′′
4.
1′′
12 f t=
y72 f t
x = 6′′
5.
3′′
4 f t=
x16 f t
x = 12′′
6. 87. 128. 189. 24
10. 2811. 812. 1213. 1614. 2415. 4816. 1
417. 1
418. 1
419. 1
320. 1
221. 2
922. 1
16
34
www.ck12.org Chapter 4. Applying Proportions, Answer Key
23. 148
24. 6 14 inches,9 3
4 inches,16 14 inches
25. 15 f oot
26. 110 meter
27. 300 feet
35
4.4. Scale in Two Dimensions, Answer Key www.ck12.org
4.4 Scale in Two Dimensions, Answer Key
1. 3 inches2. 2 inches3. 5 inches4. 1.5 inches5. 6 inches6. 11 inches7. 2.5 inches8. 200 miles9. 400 miles
10. 600 miles11. 50 miles12. 150 miles13. 300 miles14. 500 miles15. 900 miles16. 1400 miles17. 9 feet18. 18 feet19. 108 square feet20. 2 miles21. 2.75 miles22. 2 square miles23. 16 cm24. 2.25 the size25. 1
9 the size26. 40 square feet
36
www.ck12.org Chapter 4. Applying Proportions, Answer Key
4.5 Scale in Three Dimensions, Answer Key
1. 15 feet2. 25 feet3. 1,875 cubic feet4. 600 m5. 1.125 km6. Sample explanation: Each contour line represents an elevation. The lines are closer together where the
mountain is steeper and farther apart where it is less steep.7. 384 cubic feet8. 27 times the size9. 1
64 the size10. 1,000 cubic inches11. True12. False13. True14. True15. True16. False17. False18. True19. True20. False
37
4.6. Customary Units of Measure, Answer Key www.ck12.org
4.6 Customary Units of Measure, Answer Key
1. 8.5 feet2. 400 ounces3. 10 gallons4. 0.075 tons5. 72 inches6. 30 feet7. 66 inches8. 75 feet9. 2 pounds
10. 20 pounds11. 96 ounces12. 240 ounces13. 3 pints14. 12 quarts15. 16 pints16. 12 quarts17. 2 cups18. 2 pounds19. 35,200 yards20. 300 inches21. 6,600 feet22. 83,635,200 square feet
38
www.ck12.org Chapter 4. Applying Proportions, Answer Key
4.7 Metric Units of Measure, Answer Key
1. 3000 m2. 2 km3. 5500 m4. 2.5 km5. 12 km6. 5 m7. 60 m8. 400 cm9. 1100 cm
10. 3 cm11. 30 mm12. 150 mm13. 2 kg14. 35 kg15. 7000 g16. 5600 centimeters17. 0.041 liter18. 0.857 kilograms19. 4,700,000 millimeters20. 0.1 kilogram21. 36,000 meters22. 1250 meters23. 150,000 square centimeters24. 75 centimeters25. 31,680 feet
39
4.8. Formulas and Unit Analysis, Answer Key www.ck12.org
4.8 Formulas and Unit Analysis, Answer Key
1. 278 cm/sec2. 88 ft/sec3. d = rt4. 32.5 miles5. 384 minute6. 780 miles7. 6 hours8. 30 minutes9. Velocity is speed.
10. V = dt
11. 200 miles/hour12. 35 hours13. 840 kilometers14. 691.2 kilometers15. 0.25 pounds per cubic inch16. 225 grams per cubic centimeter
17 –22 Answers will vary
40
www.ck12.org Chapter 5. Applying Percents, Answer Key
CHAPTER 5 Applying Percents, AnswerKey
Chapter Outline5.1 FRACTIONS, DECIMALS AND PERCENTS, ANSWER KEY
5.2 PERCENTS AND PROPORTIONS, ANSWERS KEY
5.3 USING THE PERCENT EQUATION, ANSWER KEY
5.4 PERCENT INCREASE AND DECREASE, ANSWER KEY
5.5 CONSUMER PERCENT, ANSWER KEY
5.6 PERCENT AND STATISTICS, ANSWER KEY
5.7 SIMPLE INTEREST, ANSWER KEY
5.8 COMPOUND INTEREST, ANSWER KEY
41
5.1. Fractions, Decimals and Percents, Answer Key www.ck12.org
5.1 Fractions, Decimals and Percents, AnswerKey
1. 64100
2. 3100
3. 119100
4. 4.7100
5. .186. .3577. .06098. .000089. 52%
10. 2%11. 117%12. 500%13. 4
2514. 2
515. 1
5016. 4 1
217. 66.7%18. 76.7%19. 5.3%20. 1050%21. 2722. 1623. 31.524. 9
2825. 6
10026. 178%27. 80%28. About 22,500 people
42
www.ck12.org Chapter 5. Applying Percents, Answer Key
5.2 Percents and Proportions, Answers Key
1. 46.7%2. 1.4%3. 94.1%4. 75%5. 60%6. 20%7. 26.7%8. 19.559. 105
10. 3.0511. 312. 213. 61,75014. 40015. 810.816. 1.217. About 3.0318. About $222919. 26.25 watts20. 12308lbs.21. About 2.8%
43
5.3. Using the Percent Equation, Answer Key www.ck12.org
5.3 Using the Percent Equation, Answer Key
1. 112. 3.53. 120,0004. 5.45. 12.36. 577. 9.58. 859. 222.8
10. 136.511. 13.7%12. 94.4%13. 85.7%14. 44.4%15. 48.6%16. 13.6%17. 16.7%18. 38.3%19. 33.4%20. 32%21. 255.622. 28.623. 707.324. 18.8%25. 762.2 miles
44
www.ck12.org Chapter 5. Applying Percents, Answer Key
5.4 Percent Increase and Decrease, AnswerKey
1. 71.4%2. 61.3%3. 34.7%4. 87.5%5. 15%6. 11.1%7. 23.3%8. 43.9%9. 25%
10. 33.3%11. 52.7%12. 75%13. 17.4%14. 12.5%15. 33.3%16. 10.8%17. 60%18. 94.7%19. 54.5%20. 41.2%21. 155.822. 57.623. 13.9524. 5858.1
45
5.5. Consumer Percent, Answer Key www.ck12.org
5.5 Consumer Percent, Answer Key
1. $8.872. $1040.403. $.344. $82.625. $417.956. $9.437. $46.788. $382.959. $8.80
10. $163.0611. $86.2712. $1.6513. $85.8414. $32.2715. $94.3516. $98.6417. $102.9218. $1379.1419. $61.0520. $62.1021. $44.91
46
www.ck12.org Chapter 5. Applying Percents, Answer Key
5.6 Percent and Statistics, Answer Key
1. 409.1%2. 312.5%3. 400%4. 455%5. 180%6. 200%7. 133%8. .64%9. .29%
10. 16.7%11. 40%12. 20%13. 2.17×109
14. 4.55×1012
15. 1.13×10−16
16. .000018%17. .00001122418. .000819. 1913.9%20. .77%21. 3.12×1019
22. .2%23. About 482,160,000,000 miles
47
5.7. Simple Interest, Answer Key www.ck12.org
5.7 Simple Interest, Answer Key
1. $45,7902. $2,469.603. $240.004. $1656.005. $30806. $1007. $189.008. $360.009. $504.00
10. $22811. $60,264.5012. $921213. $944014. $21,60015. $28,75016. $405017. $14,40018. $14,40019. $930020. $34,10021. 11.8%22. The interest on the credit card will be the same in just over 3 years as the savings account in 6 years.23. She won’t reach her goal in that time at that rate because her balance in 17 years will only be $73,675.
48
www.ck12.org Chapter 5. Applying Percents, Answer Key
5.8 Compound Interest, Answer Key
1. $3002. $9603. $25004. $75005. $30006. $13,8007. $2,4008. $24,0009. $3,120
10. $5,15011. $12,24012. $35,70013. $18,54014. $8,11215. $8,75516. $337.6517. $584.9318. $7878.5619. $2164.8620. $4502.0421. $2536.4822. $427.7323. $5072.9724. $2281.2225. $8000.00
49
www.ck12.org
CHAPTER 6 Geometry andTransformations, Answer Key
Chapter Outline6.1 ANGLE PAIRS, ANSWER KEY
6.2 TRIANGLES AND ANGLES, ANSWER KEY
6.3 QUADRILATERALS AND ANGLES, ANSWER KEY
6.4 POLYGONS AND ANGLES, ANSWER KEY
6.5 CONGRUENT POLYGONS, ANSWER KEY
6.6 REFLECTIONS AND SYMMETRY, ANSWER KEY
6.7 TRANSLATIONS, ROTATIONS AND TESSELLATIONS, ANSWER KEY
6.8 SIMILARITY AND DILATIONS, ANSWER KEY
50
www.ck12.org Chapter 6. Geometry and Transformations, Answer Key
6.1 Angle Pairs, Answer Key
1. Parallel lines –lines that are equidistant apart and will never intersect2. Intersecting lines –lines that cross at one point3. Perpendicular lines –lines that intersect at a 90◦ angle.4. ‖5. ⊥6. Intersecting7. Perpendicular lines8. Yes, because the lines can intersect at a 90◦ angle.9. 35◦
10. 57◦
11. 7◦
12. 17◦
13. 170◦
14. 100◦
15. 150◦
16. 165◦
17. 68◦
18. 178◦
19. Vertical angles are opposite angles that have the same measure.20. Adjacent angles are angles that are next to each other.21. Corresponding angles are angles that are matching angles and have the same measure.22. Interior angles are angles that are found inside intersecting lines.23. Exterior angles are angles that are found outside the intersection of lines.
51
6.2. Triangles and Angles, Answer Key www.ck12.org
6.2 Triangles and Angles, Answer Key
1. Acute2. Obtuse3. Right4. Obtuse5. Acute6. Acute7. Right8. Obtuse9. Isosceles
10. Scalene11. Equilateral12. Isosceles13. Scalene14. Equilateral15. 90◦
16. 60◦
17. 40◦
18. 40◦
19. 40◦
20. 120◦
21. Answers will vary22. Answers will vary23. Answers will vary
52
www.ck12.org Chapter 6. Geometry and Transformations, Answer Key
6.3 Quadrilaterals and Angles, Answer Key
1. Square2. Parallelogram3. Rectangle4. Quadrilateral5. Rhombus6. True7. True8. False9. True
10. True11. True12. False13. False14. 360◦
15. 90◦
16. 90◦
17. 60◦
18. 110◦
19. 128◦
20. 138◦
53
6.4. Polygons and Angles, Answer Key www.ck12.org
6.4 Polygons and Angles, Answer Key
1. True2. False3. False4. False5. True6. True7. Regular hexagon8. Irregular octagon9. Equilateral triangle
10. Irregular pentagon11. Regular Pentagon12. Irregular decagon13. 720◦
14. 1080◦
15. 180◦
16. 360◦
17. 1440◦
18. 1260◦
19. 900◦
20. 540◦
21. 128.57◦
22. 144◦
23. 135◦
24. 120◦
25. 108◦
54
www.ck12.org Chapter 6. Geometry and Transformations, Answer Key
6.5 Congruent Polygons, Answer Key
1. False2. True3. True4. True5. False6. True7. False8. False9. False
10. False11. Angle D12. Angle E13. Angle F14. DE15. EF16. DF17. DF18. Angle D19. Angle E20. Yes21. Yes
55
6.6. Reflections and Symmetry, Answer Key www.ck12.org
6.6 Reflections and Symmetry, Answer Key
1. When a figure is flipped and a figure can be flipped over the x or y−axis.2. The coordinate plane is represented by four quadrants and two axis’. Each point on the coordinate plane is
represented by an x value and a y value.3. The horizontal axis4. The vertical axis5. (-1, 3) (-2, 5) (-3, 2)6. (-2, 1) (-5, 1) (-2, 4)7. (1, 1) (1, 3) (4, 1)8. (-1, 2) (-1, 5) (-5, 2) (-5, 5)9. (-1, 2) (-6, 1) (-6, 3) (-2, 3)
10. (1, 3) (3, 1) (5, 1) (4, 6)11. (1, -3) (2, -5) (3, -2)12. (-1, -1) (-1, -3) (-4, -1)13. (2, -1) (5, -1) (2, -4)14. (1, -2) (1, -5) (5, -2) (5, -5)15. (-1, -3) (-3, -1) (-5, -1) (-4, -6)16. Triangle17. Triangle18. Triangle19. quadrilateral20. quadrilateral21. quadrilateral22. triangle23. triangle24. triangle25. triangle26. quadrilateral
56
www.ck12.org Chapter 6. Geometry and Transformations, Answer Key
6.7 Translations, Rotations and Tessellations,Answer Key
1. A translation is a slide on the coordinate plane. Figure can be translated up, down, to the left and to the right.2. A rotation is a turn. Figures can be turned clockwise or counterclockwise, 90 or 180 degrees.3. A tessellation is a pattern made when a figure is repeated. There aren’t any gaps or spaces in a tessellation.4. False5. False6. True7. True8. x coordinate9. 2nd coordinate or y coordinate
10. True11. (-4, -4) (-4, -2) (-1, -1)12. (-4, 4) (-2, -4) (-1, -1)13. (4, -4) (4, -2) (1, -1)14. (1, -3) (5, -1) (5, -3)15. (-3, 1) (-1, 5) (-3, 5)16. (-1, -3) (-5, -1) (-5, -3)17. (1, 1) (3, 4) (5, 1)18. (1, 1) (4, 3) (1, 5)19. (-1, 1) (-3, 4) (-5, 1)20. Yes21. Line segments are all the same - the figures are congruent.22. No. There aren’t any gaps or spaces in a tessellation.
57
6.8. Similarity and Dilations, Answer Key www.ck12.org
6.8 Similarity and Dilations, Answer Key
1. No2. Yes3. Yes4. No5. Yes6. No7. Yes8. No9. 18
10. 2011. 512. 313. 3014. 7.515. 416. 8, 10, 1817. 24, 30, 4218. 4, 8, 1219. 2, 3, 4, 520. 3, 4, 6, 8
58
www.ck12.org Chapter 7. Using Real Numbers and Right Triangles, Answer key
CHAPTER 7 Using Real Numbers andRight Triangles, Answer key
Chapter Outline7.1 RADICAL EXPRESSIONS, ANSWER KEY
7.2 RATIONAL AND IRRATIONAL NUMBERS, ANSWER KEY
7.3 THE PYTHAGOREAN THEOREM, ANSWER KEY
7.4 USING THE PYTHAGOREAN THEOREM, ANSWER KEY
7.5 THE DISTANCE FORMULA, ANSWER KEY
7.6 SPECIAL RIGHT TRIANGLES, ANSWER KEY
7.7 EXPLORING TRIGONOMETRIC RATIOS, ANSWER KEY
7.8 USING TRIGONOMETRIC RATIOS, ANSWER KEY
59
7.1. Radical Expressions, Answer Key www.ck12.org
7.1 Radical Expressions, Answer Key
1. 42. 53. 94. 115. 66. 137. 58. 49. 3
10. 1211. 3 and 412. 3 and 413. 4 and 514. 4 and 515. 5 and 616. 9 and 1017. 9 and 1018. 419. 420. 1221. 922. 323. 1124. 325. 1226. 527. 6
60
www.ck12.org Chapter 7. Using Real Numbers and Right Triangles, Answer key
7.2 Rational and Irrational Numbers, AnswerKey
1. real, rational2. real, integer, rational3. real, whole, rational4. real, rational5. real, rational6. real, integer, rational7. real, integer, rational8. real, rational9. real, rational, whole
10. irrational11. True12. False13. True14. True15. False16. False17. False18. True19. True20. True21. 6.4122. 6.5823. -2.1624. 2.8925. -0.68
61
7.3. The Pythagorean Theorem, Answer Key www.ck12.org
7.3 The Pythagorean Theorem, Answer Key
1. 52. 103. 154. 455. 256. 307. 128. 219. 40
10. 4411. 212. 4813. False14. True15. True16. True17. True18. False19. False20. True21. No22. Yes23. No24. Yes25. No26. Yes27. Yes
62
www.ck12.org Chapter 7. Using Real Numbers and Right Triangles, Answer key
7.4 Using the Pythagorean Theorem, AnswerKey
1. Yes2. No3. Yes4. Yes5. No6. Yes7. Yes8. No9. Yes
10. Yes11. c = 11.712. c = 8.613. c = 11.414. c = 1015. c = 1516. c = 17.217. b = 818. a = 919. b = 2020. a = 2421. 24 sq. yds.22. 17 in.23. Yes24. 72 in.
63
7.5. The Distance Formula, Answer Key www.ck12.org
7.5 The Distance Formula, Answer Key
1. 52. 133. 11.34. 55. 5.16. 67. 6.48. 169. 5.4
10. 3.211. 412. 5.113. 12.04 km14. 2 or 1415. 10 or -1416. -3 or 1317. 25 or -7
64
www.ck12.org Chapter 7. Using Real Numbers and Right Triangles, Answer key
7.6 Special Right Triangles, Answer Key
1. 5√
22. 4√
23. 6√
24. 3√
25. 7√
26. 7.077. 5.668. 8.499. 4.24
10. 9.911. 3
√3
12. 4√
313. 2
√3
14. 8√
315. 10
√3
16. 5.217. 6.918. 3.4619. 13.920. 17.321. 30◦−60◦−90◦
22. 45◦−45◦−90◦
23. 2 ft.24. 12.73 inches25. 3.46 cm
65
7.7. Exploring Trigonometric Ratios, Answer Key www.ck12.org
7.7 Exploring Trigonometric Ratios, AnswerKey
1. .82. .63. .754. .65. .86. 1.337. 10
108. .89. 1.66
10. .29211. 3.42912. .2813. .2814. tangent15. tangent16. sine17. 1.73218. .86619. .98520. .86621. .98522. opp
hyp
23. adjhyp
24. oppadj
66
www.ck12.org Chapter 7. Using Real Numbers and Right Triangles, Answer key
7.8 Using Trigonometric Ratios, Answer Key
1. True2. False3. True4. True5. True6. 8.17. 3.88. 33.59. 10.9
10. 6.611. 1.712. Tangent = opp
adj
13. Cosine = adjhyp
14. Sine = opphyp
15. 91.44 ft.16. 120.75 ft17. 57.5 yds
67
www.ck12.org
CHAPTER 8 Measurement, Area andVolume, Answer Key
Chapter Outline8.1 AREA OF POLYGONS, ANSWER KEY
8.2 AREA OF CIRCLES, ANSWER KEY
8.3 SOLID FIGURES, ANSWER KEY
8.4 SURFACE AREA OF PRISMS AND CYLINDERS, ANSWER KEY
8.5 SURFACE AREA OF PYRAMIDS AND CONES, ANSWER KEY
8.6 VOLUME OF PRISMS AND CYLINDERS, ANSWER KEY
8.7 VOLUME OF PYRAMIDS AND CONES, ANSWER KEY
8.8 SURFACE AREA AND VOLUME OF SPHERES, ANSWER KEY
68
www.ck12.org Chapter 8. Measurement, Area and Volume, Answer Key
8.1 Area of Polygons, Answer Key
1. 25 sq.in.2. 19.25 sq.in3. 24 sq. f t4. 33.75 sq. f t5. 54 sq.meters6. 90 sq. f eet7. h = 2 in8. h = 6 f t9. b = 12 in
10. b = 15 f t11. h = 17 f t12. h = 27 f t13. 75 sq.in14. 108 sq. f t15. 154 sq. f t16. 399 sq. f t.17. 99 sq. f t.18. 143 sq.in.19. 418 sq. f t20. 837 sq.meters21. 26 sq.in.22. 35 sq.in.23. 99 sq. f t.
69
8.2. Area of Circles, Answer Key www.ck12.org
8.2 Area of Circles, Answer Key
1. 31.4 in2. 15.7 in3. 21.98 ft4. 37.68 mm5. 43.96 cm6. 25.12 in7. 37.68 meters8. 50.24 ft9. 69.08 in
10. 94.2 cm11. 50.24 sq. in.12. 28.26 sq. ft.13. 19.63 sq. in.14. 78.5 sq. cm15. 38.47 sq. in.16. 254.34 sq. mm17. 379.94 sq. cm18. 314 sq. in.19. 153.86 sq. ft.20. 200.96 sq. in.21. 3.53 sq. in.22. 7.68 sq. mm23. 13.08 sq. cm.24. 13.5 sq. in.25. 2.44 sq. in.
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www.ck12.org Chapter 8. Measurement, Area and Volume, Answer Key
8.3 Solid Figures, Answer Key
1. Cylinder2. 23. 04. 05. Square pyramid6. 5 faces7. 8 edges8. 5 vertices9. Cone
10. 1 face, 0 edges, 0 vertices11. Triangular prism12. 5 faces13. 9 edges14. 6 vertices15. Cone16. Cylinder17. Picture of a cone18. Picture of a pentagonal prism19. 520. 121. 14
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8.4. Surface Area of Prisms and Cylinders, Answer Key www.ck12.org
8.4 Surface Area of Prisms and Cylinders, An-swer Key
1. Rectangular prism2. 538 cm2
3. Cylinder4. Circle5. 2 bases6. 428.61 f t2
7. Rectangular prism8. 564.9 m2
9. Triangular prism10. Triangle11. Two12. Rectangle13. 314. 240 in2
15. Cylinder16. Radius17. 560.49 yd2
18. 1256 f t2
19. Surface area20. 1506 in2
21. 100.25 f t2
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8.5 Surface Area of Pyramids and Cones, An-swer Key
1. Cone2. 8 cm3. 12 cm4. 200.96 cm2
5. Square Pyramid6. 20 in7. 2000 in2
8. Triangular Pyramid9. Triangle
10. Four faces11. 62.4 f t2
12. Cone13. Circle14. 34 m15. 2,332.71 m2
16. 20 ft17. 15 m18. 151.03 f t2
19. 1,380 in2
20. 969.48 cm2
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8.6. Volume of Prisms and Cylinders, Answer Key www.ck12.org
8.6 Volume of Prisms and Cylinders, AnswerKey
1. Rectangular prism2. 73. 34. 45. 84 unit cubes6. Cylinder7. 7 cm8. 3.5 cm9. 500.05 cm3
10. Triangular prism11. Triangles12. Rectangles13. 816 f t3
14. Rectangular prism15. 1,679.29 cm3
16. 12 ft.17. 9 m18. 20 times19. 320,000 f t3
20. 480,000 f t3
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8.7 Volume of Pyramids and Cones, AnswerKey
1. V = 13 πr2h
2. True3. False4. V = 1
3 Bh5. Area6. Cone7. 4 m8. 28.07 m3
9. Pyramid or square pyramid10. square11. 657.7 in3
12. Pyramid or Triangular pyramid13. one base is a square and one is a triangle14. 51.6 f t3
15. Triangle16. 6 cm17. 21 cm18. 197.82 cm3
19. 14 m20. 21 yd21. 126.6 in3
22. 224 cm3
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8.8. Surface Area and Volume of Spheres, Answer Key www.ck12.org
8.8 Surface Area and Volume of Spheres, An-swer Key
1. 200.96 sq.in.2. 50.24 sq.in3. 153.86 sq. f t.4. 563.82 sq.in.5. 1,808.64 sq.cm6. 32.15 sq. f t.7. 1,017.36 sq.m8. 113.04 m3
9. 523.33 in3
10. 904.32 in3
11. 65.41 m3
12. 113.04 mm3
13. 267.94 in3
14. 523.33 in3
15. 1,519.76 cm3
16. 904.32 f t3
17. 56.52 in3
18. 10 bottles
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www.ck12.org Chapter 9. Linear Functions and Graphs, Answer Key
CHAPTER 9 Linear Functions andGraphs, Answer Key
Chapter Outline9.1 RELATIONS AND FUNCTIONS, ANSWER KEY
9.2 LINEAR EQUATIONS IN TWO VARIABLES, ANSWER KEY
9.3 USING INTERCEPTS, ANSWER KEY
9.4 THE SLOPE OF A LINE, ANSWER KEY
9.5 SLOPE-INTERCEPT FORM, ANSWER KEY
9.6 LINEAR FUNCTIONS, ANSWER KEY
9.7 SYSTEMS OF LINEAR FUNCTIONS, ANSWER KEY
9.8 GRAPHS OF LINEAR INEQUALITIES, ANSWER KEY
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9.1. Relations and Functions, Answer Key www.ck12.org
9.1 Relations and Functions, Answer Key
1. No, 4 and 8 have more than one value in the range.2. Function3. Function4. Not a function, 2 has more than one value connected to it.5. Function6. Function7. Function8. c = domain,d = range9. {1, 5, 9, 13}
10. {-10, -8, -6, -4, -2}11. {14, 17, 20, 23, 26}12. {-8, -7, -6, -5, -4}13. 44.6◦,52.2◦,77◦F14. f (x) = 3x15. f (x) = 4x+216. f (x) = 2x17. f (x) = 2x−218. f (x) = x
219. f (x) = x
320. c(s) = 3.45s21. $10.35, $20.70, $31.05
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www.ck12.org Chapter 9. Linear Functions and Graphs, Answer Key
9.2 Linear Equations in Two Variables, AnswerKey
There are many possible answers for 1 –8.
1. (6, 6)2. (8, 0)3. (5, 9)4. (7, 3)5. (10, 11)6. (9, 9)7. (8, 7)8. (7, 5)9. 2x− y =−3
10. 4x+ y = 611. 2x+ y =−412. −5x+ y = 413. 3x+ y =−214. 4x+ y = 6
15.
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9.3. Using Intercepts, Answer Key www.ck12.org
9.3 Using Intercepts, Answer Key
1. x = 4,y = 32. x = 2,y = 63. x = 5,y = 44. x = 2,y = 45. x = 5,y = 36. x = 3,y =−27. x =−3,y = 98. x =−3,y =−39. x = 3,y = 7
10. x = 18,y = 411. x = 2,y = 312. x = 7,y = 513. x =−4,y = 414. x = 1.5,y = 315. x =−1,y =−116. x =−3,y =−317. 5 to the front or 10 to the rear18. Minimum $50 to Maximum $70
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9.4 The Slope of a Line, Answer Key
1. False2. True3. False4. True5. True6. True7. False8. True9. False
10. True11. 112. -113. −2
314. 215. 1
216. 117. −3
418. −1
219. -120. -421. c = 5g,k = 5
TABLE 9.1:
g c0 05 2510 5015 7520 10025 12530 150
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www.ck12.org Chapter 9. Linear Functions and Graphs, Answer Key
9.5 Slope-Intercept Form, Answer Key
1. slope = 2,y int = 42. slope = 3,y int =−23. slope = 4,y int = 34. slope = 5,y int =−15. slope = 1
2 ,y int = 26. slope =−2,y int = 47. slope =−3,y int =−18. slope =−1
3 ,y int = 59. y =−1
2 x+310. slope =−1
211. y int = 312. y =−1x+413. slope =−114. y int = 415. y =−1
2 x+ 13
16. slope =−12
17. y int = 13
18. m = 4w+20
19.20. 7 weeks21. 25 lamps = 300 watts22. e =−12b+600
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9.6. Linear Functions, Answer Key www.ck12.org
9.6 Linear Functions, Answer Key
1. y = 2x+42. y =−3x+23. y =−4x+44. y = 3x−55. y = 1
2 x−26. y =− 1
3x +27. y = x+88. y =−2x+49. y =−x−1
10. y = 5x−211. y = 712. y =−413. x = 214. x =−515. y =− 2
3x −116. y = 3x−317. y = x+118. y =− 1
2x +12
19. d =−30t +110020. e = 1.5b+300021. 4, 667 books
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www.ck12.org Chapter 9. Linear Functions and Graphs, Answer Key
9.7 Systems of Linear Functions, Answer Key
1. d2. b3. (6,−3)4. Infinite5. Infinite6. Infinite7. No solutions8. No solutions9. True
10. False11. True12. True13. (2,1)14. Infinite15. (−1,4)16. No Solutions17. (−2,3)18.
(−1
2 ,0)
19. (2,4)20. Infinite21. At that rate, Angelica’s father will catch up to her after 400 miles. She will have driven for 8 hours and he will
have driven for 5. She can reach her before she gets to the grandmother’s house.The system of equations is
d = 50h
d = 80(h−3)
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9.8. Graphs of Linear Inequalities, Answer Key www.ck12.org
9.8 Graphs of Linear Inequalities, Answer Key
1. x− y > 82. 1
2 x≥ 3y3. x+y
4 < 154. 7x+(y−3)≤−165. 6x >−306. 5x+6≤ 397. 12
y < 78. 6x+(y−2)≤ 129. no
10. no11. yes12. no13. yes14. no15. yes16. no
17.
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www.ck12.org Chapter 9. Linear Functions and Graphs, Answer Key
18.
19.20. .60b+ .90m≤ 7.50 You could purchase any combination in the shaded region or on the line.21. 1.5E +d ≥ 500 Using the ordered pair (d,E), he could have (550, 0), (400, 50), (100, 300).
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CHAPTER 10Analyzing Data, Answer KeyChapter Outline
10.1 MEASURES OF CENTRAL TENDENCY AND DISPERSION, ANSWER KEY
10.2 STEM-AND-LEAF PLOTS AND HISTOGRAMS, ANSWER KEY
10.3 BOX-AND-WHISKER PLOTS AND OUTLIERS, ANSWER KEY
10.4 SCATTERPLOTS, ANSWER KEY
10.5 MISLEADING STATISTICS, ANSWER KEY
10.6 USING DATA DISPLAYS, ANSWER KEY
10.7 COLLECTING DATA, ANSWER KEY
10.8 INTERPRETING DATA, ANSWER KEY
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10.1 Measures of Central Tendency and Disper-sion, Answer Key
1. mean: 19, median: 18, mode: 24, range: 11, deviations from the mean (see table)
TABLE 10.1:
Difference from mean Deviation from the mean19 –13 619 –14 519 –16 319 –17 219 –18 121 –19 224 –19 524 –19 524 –19 5
2. mean: 114.2, median: 118, mode: none, range: 64, deviations from the mean (see table)
TABLE 10.2:
Difference from mean Deviation from the mean114.2 –75 39.2114.2 –98 16.2116 –114.2 1.8120 –114.2 5.8137 –114.2 22.8139 –114.2 24.8
3. mean: 27.2, median 32, mode –none, range –18, deviations from the mean (see table)
TABLE 10.3:
Difference from mean Deviation from the mean27.2 –22 5.227.2 –24 3.227.2 –25 2.230 –27.2 2.832 –27.2 4.834 –27.2 6.837 –27.2 9.838 –27.2 10.840 –27.2 12.8
4. The average of a set of data
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10.1. Measures of Central Tendency and Dispersion, Answer Key www.ck12.org
5. The middle value of a set of data6. The value that occurs the most times in a set of data7. How far a value is from the mean8. The breadth of data from the smallest to the largest value9. Answers will vary. Example: 7, 10, 10, 16, 18, 19, 20, 28
10. Answers will vary. Example: In this case, mean is most useful because it gives you an idea of the group as awhole. The mean of the Pacific Ocean group is 137.8kg and the mean of the Atlantic Ocean group is 131.6kg.This might indicate that the health and accessibility to food is worse in the Atlantic Ocean but there may beother factors that account for the difference in weight.
11. In this case, the best measure of central tendency is the deviation from the mean for each store for July. Store1 has mean sales of $78,714 for the 7 months. The deviation from the mean for July for Store 1 was $1,286more than the mean. Store 2 has mean sales of $109,714 for the 7 months. Its deviation from the mean for Julywas $6,714 less than the mean. The mean for Store 3 was $62,286. Its deviation from the mean was $5,714greater than the mean. For that reason, Store 3 showed greater sales even though the actual amount sold wasthe least.
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10.2 Stem-and-Leaf Plots and Histograms, An-swer Key
1. Answers will vary. Example:
19 7720 17, 30, 51, 8721 05, 13, 662223 44, 45, 9024 06, 32, 7525 01, 80
2. The graph shows the paychecks of 16 employees. It shows a range from $1977 to $2580. The amounts of thepaychecks are spread out over the range fairly evenly except that nobody earns in the $2200 interval.
3. The best interval goes by 100’s starting at $1900 to $2500. If you use thousands place, the plot will be veryshort and wide and will not show the range of the paychecks. If you use tens place, the graph will be very talland you will not be able to see the trend well because it would be too spread out.
4. If you do not include the $2200 interval, it would make it look like the data is closer together than it really is.5. Answers will vary. Example:
6. Intervals of 100 make sense because intervals of 50 would be too many; it would spread the data out too far.Intervals greater than 100 may not allow the company to understand the data clearly enough; the informationwould be too general to plan future expenses, for example.
7. You can see from the histogram that most trips cost between $300 and $399. The company should be preparedfor a few more expensive trips, though, or supervise more carefully some individuals’ expenditures.
8. By looking at the histogram, you can see that many 4 gifts were in the $60-69 interval and 6 were in the $70-79interval while only 4 were less than $60. If you look carefully at the stem-and-leaf plot, you can see that all ofthe gifts in the $60-69 category were actually far closer to $70.
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10.2. Stem-and-Leaf Plots and Histograms, Answer Key www.ck12.org
9. The stem-and-leaf plot reveals each data item and suggest that Melanie has been dishonest with her husband.10. Answers will vary.11. Hybrid is less than a regular car.12. Answers will vary.13. It seems clear that employees in Germany like to take more days off, even if they are unpaid. Perhaps their
living expenses are lower or their priorities are different.14. The company would have to make adjustments for the absence of so many employees throughout the year.
They would need more employees to cover those that are on vacation. Another option is to place limits on thenumber of unpaid vacation days that each employee can take.
15. They probably chose 5-day intervals because that is a work week.16. Answers will vary.17. Answers will vary.18. Answers will vary.19. Answers will vary.20. Answers will vary.
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10.3 Box-and-Whisker Plots and Outliers, An-swer Key
1.2. Extremes: 81 and 1563. median: 130.54. first quartile: 101; third quartile: 144.5.5. A visual display of data values on a number line.6. Data divided into four equal parts7. the middle value in a set of data8. the first and last points or the lowest and highest data value9. the range between the first and third quartile
10. data values that are far away from the general trend11. Median: 30012. Quartiles: 275 and 34513. Interquartile Range: 7014. Extremes: 125 and 40515. Outlier: 12516. All data:
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10.3. Box-and-Whisker Plots and Outliers, Answer Key www.ck12.org
17. Extremes: 310 and 64018. Median: 35919. Quartiles: 330 and 39820. Outlier: 64021. Outlier Removed:
22. Extremes: 310 and 417 Median: 357 Quartiles: 330 and 387.523. In the first plot, it appears that the biggest quarter of data is spread out over a wide range. In reality, the
data is not. If you look at the second graph, you can see that if you take out the single outlier of 640, thebox-and-whisker plot is practically symmetrical and the ranges of each quarter fairly similar.
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10.4 Scatterplots, Answer Key
1.2. negative3. positive4. no relationship5. positive6. no relationship
7.
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10.4. Scatterplots, Answer Key www.ck12.org
8.9. negative relationship
10. (10, 45) and (40, 10)
11.
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12.13. y =−5
4 x+1014. 8.125 or about 8 felines per 100 km2
15. check individual work on graphing calculators16. Input value is the independent value or the x value in a data table.17. Output value is the dependent value or the y value in a data table.18. Positive correlation is a correlation where the output value increases with the input value.19. Negative correlation is when the output value decreases with the input value.20. No correlation –there is not a connection between the independent and dependent variables.
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10.5. Misleading Statistics, Answer Key www.ck12.org
10.5 Misleading Statistics, Answer Key
1. True2. True3. False4. False5. False6. True7. True8. True9. True
10. The scale on the y-axis begins at 44,500. Also, the graph is relatively narrow which makes the slope lookgreater. The population only increased by 2,500 over 7 years.
11. The enormous bar on George’s Café makes it appear much larger than Rita’s Restaurant. However, thedifference is only 10 customers per day.
12. Answers will vary. Example:
13. Answers will vary. Example: It appears that the numbers of semesters needed to study increased five-fold.14. Answers will vary. Example:
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15. Answers will vary. Example: It appears that the difference in customers was small16. Answer will vary. Example:
17. Answers will vary. Example:
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10.6 Using Data Displays, Answer Key
1. Any data measured with numbers2. Any data assigned a name-counted by tallies3. Scatterplot4. Positive correlation5. Scatterplot6. Box-and-whisker plot7. A division of data on a box-and-whisker plot8. box-and-whisker plot9. line graph
10. histogram11. The average of a set of data12. The middle score in a set of data13. The score that is seen the most14. Conclusion 1: Yes, the data supports it. Conclusion 2: No, this graph does not discuss dangerousness.
Conclusion 3: No, since bats are not included, we cannot be certain.15. Conclusion 1: Yes, the data supports it. Conclusion 2: Yes, the data supports it because the slope gets steeper
after 2000. Conclusion 3: No, we cannot be sure the increase will continue based on the graph.16. Answer will vary. Example:
A bar graph is good because it is categorical data.17. Answers will vary. Example:
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10.6. Using Data Displays, Answer Key www.ck12.org
Because the whole class is shown, a circle graph makes it easy to show the results.18. Answers will vary.19. Answers will vary.20. Answers will vary.21. Answers will vary.22. Answers will vary.
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10.7 Collecting Data, Answer Key
1. A method of gathering information about a population2. Everyone has a chance to be chosen because the sampling is random3. equal numbers are selected from different levels4. a system is developed for collecting samples of information5. a number is selected because of convenience6. People who really want to complete the survey7. d8. c9. b
10. e11. a12. For number 1, this is a biased method because the people in her office building probably do not represent
entire population. Everyone in the population does not have an equal chance of being chosen. For number 2,this is unbiased because each car has the same likelihood of being chosen. Although, the traffic stop should beplaced on a road that all cars must travel. For number 3, this is unbiased because all of their customers have anequal chance of being chosen. For number 4, this is biased because the people who choose to participate maynot represent the entire population. All customers do not have an equal chance of being chosen since somepeople will not want to call. Also, the same people can call more than once. For number 5, this is unbiasedbecause all of the cows have an equal chance of being chosen.
13. This question assumes that the individual is married.14. This question does not allow a person to answer “never.”15. This question assumes that people know what the 1st and 2nd Amendments are.16. This question tends to lead the answerer to a “correct” response.
17. - 19. Answers will vary. Example: It could be displayed in two circle graphs since it is done in percentages butsince there are two groups, men and women, a bar graph makes it easier to see.
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10.7. Collecting Data, Answer Key www.ck12.org
17. Men clearly prefer Chicago while women clearly prefer Paris. Neither men nor women prefer Beijing andBuenos Aires.
18. The men and women differ greatly in their preferences.19. What would the data look like for different age groups? What would it look like for people who definitely
would go to the Olympics vs. those that would definitely not go? What would it look like for people who livein other parts of the world?
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10.8 Interpreting Data, Answer Key
TABLE 10.4:
Very Dissatisfied Dissatisfied Satisfied Very Satisfied12-20% 17-25% 37-45% 18-26%
TABLE 10.5:
Very Dissatisfied Dissatisfied Satisfied Very Satisfied40,800-68000 57,800-85,000 125,800-153,000 61,200-88,400
3. Answers will vary. Example: there are more satisfied employees than dissatisfied ones.
TABLE 10.6:
Hilton Marriott Holiday Inn Four Seasons15-25% 3-13% 27-37% 35-45%63-105 14-55 113-155 147-97
5. Few students prefer the Marriott or the Hilton.6. Most students prefer either the Holiday Inn or the Four Seasons.7. The cost, the distance, the security, the accommodations.
Answers will vary. Example:
7. The writer states that more people are interested in the team because of the new stadium. The writer also statesthat the increased interest caused the team to win more. Finally, the writer implies that they are much betterthis year but the difference is minimal (14-3 instead of 13-4).
8. I do not agree with them because there is no evidence that the stadium created more interest nor that theinterest caused the team to win more. Perhaps the better team caused more interest, not the stadium.
9. It seems that the writer wants to have a football stadium built and is using the argument that interest increasesbased on a new stadium.
Answers will vary. Examples:
10. Housing is generally cheaper in Utah.11. Housing prices increased in all 3 states from 1999 to 2000.12. Arizona is a better place to live because the houses are more expensive. This graph does not show any data
about quality of living.13. Costs in Arizona are greater than in the other states. This graph only shows data regarding housing, not about
other costs.
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CHAPTER 11 Using Probability, AnswerKey
Chapter Outline11.1 COUNTING METHODS, ANSWER KEY
11.2 PERMUTATIONS, ANSWER KEY
11.3 COMBINATIONS, ANSWER KEY
11.4 THEORETICAL AND EXPERIMENTAL PROBABILITY, ANSWER KEY
11.5 PROBABILITY AND ODDS, ANSWER KEY
11.6 CONDITIONAL PROBABILITY, ANSWER KEY
11.7 GEOMETRIC PROBABILITY, ANSWER KEY
11.8 PROBABILITY AND SIMULATIONS, ANSWER KEY
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11.1 Counting Methods, Answer Key
1. 6 outcomes: Single-Half, Single-Hour, Double-Half, Double-Hour, Racer-Half, Racer-Hour2. 9 outcomes: basic-home, basic-small, basic-large, premium-home, premium-small, premium-large, super-
home, super-small, super-large3. 12 outcomes; home-weekdays-weekly, home-weekdays-monthly, home-weekends-weekly, home-weekends-
monthly, home-seven-weekly, home-seven-monthly, office-weekdays-weekly, office-weekdays-monthly, office-weekends-weekly, office-weekends-monthly, office-seven-weekly, office-seven-monthly
4. 16 outcomes: green-green-green-green, green-green-green-red, green-green-red-green, green-green-red-red,green-red-green-green, green-red-green-red, green-red-red-green, green-red-red-red, red-green-green-green,red-green-green-red, red-green-red-green, red-green-red-red, red-red-green-green, red-red-green-red, red-red-red-green, red-red-red-red
5. 18 outcomes; sugar-teeny-blueberry, sugar-teeny-mango, sugar-teeny-choc, sugar-mega-blueberry, sugar-mega-mango, sugar-mega-choc, sugar-huge-blueberry, sugar-huge-mango, sugar-huge-choc, waffle-teeny-blueberry,waffle-teeny-mango, waffle-teeny-choc, waffle-mega-blueberry, waffle-mega-mango, waffle-mega-choc, waffle-huge-blueberry, waffle-huge-mango, waffle-huge-choc
6. 8 outcomes7. 18 outcomes8. 8 outcomes: right-right-right, right-right-wrong, right-wrong-right, right-wrong-wrong, wrong-right-right,
wrong-right-wrong, wrong-wrong-right, wrong-wrong-wrong9. 16 outcomes: right-right-right-right, right-right-right-wrong, right-right-wrong-right, right-right-wrong-wrong,
right-wrong-right-right, right-wrong-right-wrong, right-wrong-wrong-right, right-wrong-wrong-wrong, wrong-right-right-right, wrong-right-right-wrong, wrong-right-wrong-right, wrong-right-wrong-wrong, wrong-wrong-right-right, wrong-wrong-right-wrong, wrong-wrong-wrong-right, wrong-wrong-wrong-wrong
10. 16 more11. 18012. 2013. 36014. 120 more15. 270416. 2717. 1818. 3619. 21620. 1
921. 1
322. 2
323. 8
924. 19
2725. 7
27
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11.2. Permutations, Answer Key www.ck12.org
11.2 Permutations, Answer Key
1. yes, order matters. Spots, Dots, Slimey, Croaky is different from Dots, Slimey, Croaky, Spots2. yes, order matters. RAIL is different from LIAR3. no, order does not matter. Tim, Jim, Pam, Sam is no different than Pam, Jim, Sam, Tim.4. yes, order matters. 1, 2, 3, 4, 5, 6, 7, 8 is different from 2, 4, 7, 3, 1, 5, 8, 65. no, order does not matter. won-ton, shrimp, and noodles is no different than noodles, won-ton, and shrimp6. yes, order matters. 1024 is a different password than 2041.7. yes, order matters. JASMINE is different from SAJIMEN.8. yes, order matters. JASMINE is different from SAJIMEN.9. yes, order matters. METS is different from STEM.
10. yes, order matters. 456 is different from 564.11. 6
789 879 978
798 897 987
12. 24
ABCD BACD CABD DABC
ABDC BADC CADB DACB
ACBD BCAD CBAD DBAC
ACDB BCDA CBDA DBCA
ADBC BDAC CDAB DCAB
ADCB BDCA CDBA DCBA
13. 12014. 72015. 12016. 504017. 432018. $72019. 1220. 2021. 6022. 36023. 5624. 336
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11.3 Combinations, Answer Key
1. no, order does not matter; combinations2. yes, order matters. permutations3. no, order does not matter. Combinations4. no, order doesn’t matter. combinations5. no, order doesn’t matter. combinations6. no, order doesn’t matter. Combinations7. yes, order matters. Permutations8. no, order does not matter. combinations9. no, order does not matter; combinations
10. 3 rose-tulip, rose-daffodil, tulip-daffodil11. 6 rose-tulip, rose-daffodil, rose-lily, tulip-daffodil, tulip-lily, daffodil-lily12. 4 rose-tulip-daffodil, rose-tulip-lily, rose-daffodil-lily, tulip-daffodil-lily13. 1014. 1015. 1516. 1017. 1018. 1519. 2020. 3521. 45
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11.4. Theoretical and Experimental Probability, Answer Key www.ck12.org
11.4 Theoretical and Experimental Probability,Answer Key
1. 1. blue2. 13. 54. 1:5
1. red, green2. 23. 54. 2:5
1. red, blue, green, purple2. 43. 54. 4:5
1. 62. 13. 64. 1:6
1. 3, 4, 5, 62. 43. 64. 2:3
1. 3, 2, 12. 33. 64. 1:2
1. 1, 62. 23. 64. 1:3
1. 3, 2, 12. 33. 124. 1:4
2. 313. 604. 31:605. 96. 507. 9:508. 6
259. .28
10. 48%
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11. red, green, white12. yellow and blue13. red, blue, green
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11.5. Probability and Odds, Answer Key www.ck12.org
11.5 Probability and Odds, Answer Key
1. disjoint; Venn diagram should be non-overlapping2. complementary3. disjoint4. overlapping, 6 is a common outcome5. overlapping, 5 is a common outcome6. complementary7. disjoint; Venn diagram should be non-overlapping8. overlapping, green-left is common; Venn diagram should be overlapping9. non –complementary
10. complementary11. disjoint12. complementary13. disjoint14. 1 to 515. 5 to 116. 1 to 117. 2 to 118. 1 to 219. 1 to 120. 1 to 121. 1 to 922. 9 to 123. 4 to 124. 1 to 425. 7 to 3
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11.6 Conditional Probability, Answer Key
1. Independent2. Dependent3. Independent4. Independent5. Dependent6. Independent7. Dependent8. Independent9. Dependent
10. Dependent11. 1
1112. 4
3313. 1
5514. 3
1415. 2
716. 7
3017. 1
1018. 1
4019. 1
320. 1
221. 2
322. 1
623. 1
224. 1
325. Prediction: 1
6 of the time match26. Prediction: 5
6 of the time not match
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11.7. Geometric Probability, Answer Key www.ck12.org
11.7 Geometric Probability, Answer Key
1. 18
2. 38
3. 516
4. 1116
5. 4 miles6. 1
67. 1
38. 1
129. 29.4%
10. 62.8%11. 4%12. 1
25 or 4%13. 3
25 or 12%14. 5
25 or 20%15. 7
25 or 28%16. 9
25 or 36%17. It increases by 8% for each circle18. 60%19. 40%20. 80
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11.8 Probability and Simulations, Answer Key
1. 12, answers vary2. answers vary3. 24, answers vary4. Answers will vary5. Answers will vary.6. 16 for each value7. Answers will vary8. Answers will vary9. Answers will vary
10. 10 appearances each11. Answers will vary12. Answers will vary13. Answers will vary14. Answers will vary15. Answers will vary16. Answers will vary17. Answers will vary
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CHAPTER 12 Polynomials, Answer keyChapter Outline
12.1 POLYNOMIALS, ANSWER KEY
12.2 ADDING AND SUBTRACTING POLYNOMIALS, ANSWER KEY
12.3 MONOMIALS AND POWERS, ANSWER KEY
12.4 MULTIPLYING BINOMIALS, ANSWER KEY
12.5 EXPLORING PARABOLAS, ANSWER KEY
12.6 QUADRATIC FUNCTIONS, ANSWER KEY
12.7 EXPONENTIAL FUNCTIONS, ANSWER KEY
12.8 SEQUENCES, ANSWER KEY
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12.1 Polynomials, Answer Key
1. Monomial2. Binomial3. Binomial4. Trinomial5. Monomial6. Polynomial7. Trinomial8. Trinomial9. 2nd
10. 5th
11. Degree of 012. 3rd
13. 7th
14. Degree of 015. −2y3 +3y2 + y−8; third degree16. −12m7 +6m5 +m4−6m−8; seventh degree17. −x3y2 +5x3y+8xy; fifth degree18. −2x+1119. −4y3 +7y2−820. q2−6q21. 5n2m2−2n2m+11n22. 5623. 19624. 6425. 345
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12.2. Adding and Subtracting Polynomials, Answer Key www.ck12.org
12.2 Adding and Subtracting Polynomials, An-swer Key
1. 4x2 +10x−192. −4x4−3x3 +143. 10x3−5x2 +7x4. 10x2 +8x+155. 15x2−12x+66. −2y2−2x+17. 12x−38. x4− x3 +9x2−2x+39. 6x2y2 +4x2y+3x2 +2xy
10. 9xy−12x−311. x2 +2x+1412. 6y3−2y2−3y+313. −2m2 +9m−2314. −2z2−8z−315. 33x2 +16x+15716. 642x+9917. 126x−6318. 2 ·10(40x+8)+2 ·10(40x−12) = 1600x−80 (long walkway)19. 1
4(1600x−80) = 400x−20 (short walkway)20. sum of the large walkway and small walkway = 2000x−100
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12.3 Monomials and Powers, Answer Key
1. 54x7
2. 65d20
3. 42p5q7u3
4. 10000x4
5. −1024t15
6. 2592r37s15t6
7. 1681
8. 343k3
−8m3
9. x55
y45
10. 1296a16
11. w69y63z96
12. −3125x15
243h10 j40
13. 28x11
14. 48y12
15. 35x11
16. (16x2)(28x4)17. 448x6
18. 3375g12
19. 54 ·(1
2
)5
20. 1.6875 kg
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12.4. Multiplying Binomials, Answer Key www.ck12.org
12.4 Multiplying Binomials, Answer Key
1. x2 +8x+152. x2−8x+153. x2−94. x2−6x−165. 18x3 +12x2−6x6. 10x2−27xy−28y2
7. 4x2−36x+818. 4d2 +7d−29. 25x2−49
10. 8b3−20b2c2 +6bc−15c3
11. 5p2 +32p+1212. −42y3−38y2−8y13. x6 +6x4 +9x2
14. 2x2−7x−415. 15x2 +8x−2716. x2 +10x+2517. 25n2−20n+418. π(x2 +10x+25)19. 2z3−2z2−12z20. 10z2−2z−24
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12.5 Exploring Parabolas, Answer Key
1. True2. True3. False4. False5. True6. True7. Upward8. Downward9. Top or bottom
10. True11. Graph A is equation c. Opens downward, y-intercept 2, wide, symmetrical on y-axis. a =−1
2 ,b = 0,c =−2.12. Graph B is equation b. Opens upward, y-intercept -3, neither narrow nor wide. a = 1,b = 1,c =−3.13. Graph C is equation a. Opens upward, y-intercept 2, narrow, symmetrical on y-axis. a = 3,b = 0,c =−2.
14.
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12.5. Exploring Parabolas, Answer Key www.ck12.org
15.
16.17. y =−x2 +318. y = x2−5
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12.6 Quadratic Functions, Answer Key
1. It is quadratic. Standard form is y = 3x2− x+4; a = 3,b =−1,c = 4.2. It is quadratic. Standard form is y = x2 +4x−18; a = 1,b = 4,c =−18.3. It is not quadratic. When you subtract x2 from both sides, it is a 1st degree equation.4. It is quadratic. Standard form is y = 7
3 x2− 53 x−1; a = 7
3 ,b =−53 ,c =−1.
5. It is not quadratic because it is a 5th degree equation.6. It is quadratic. Standard form is y = 2x2−3; a = 2,b = 0,c =−3.
TABLE 12.1:
x y−3 1-2 -4-1 -70 -81 -72 -43 1
TABLE 12.2:
x y−3 -33-2 -18-1 -70 01 32 23 -3
TABLE 12.3:
x y−3 -25-2 -17-1 -110 -71 -52 -53 -7
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12.6. Quadratic Functions, Answer Key www.ck12.org
TABLE 12.4:
x y−3 -1-2 −2 1
3-1 −2 1
30 -11 1 2
32 5 2
33 11
11. The a value is 1. Its graph is neither wide nor narrow. It opens upward.
12. The a value is -2. Its graph is somewhat narrow. It opens downward.
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13. The a value is -1. Its graph is neither wide nor narrow. It opens downward.
14. The a value is 23 . Its graph is somewhat wide. It opens upward.
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12.6. Quadratic Functions, Answer Key www.ck12.org
radius 0 1 2 3 4 5 6 7 8 9 10
area 0 3.14 12.56 28.26 50.24 78.5 113.04 153.86 200.96 254.34 314
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t (seconds) 0 1 2 3 4 5 6 7
d distance ( f t) 0 96 160 192 192 160 96 0
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12.7. Exponential Functions, Answer Key www.ck12.org
12.7 Exponential Functions, Answer Key
1. Yes.2. Yes.3. No because b = 1 .4. No because a = 0 .5. Yes.6. No because b < 0 .
TABLE 12.5:
x y−3 1
27-2 1
9-1 1
30 11 32 93 274 815 2436 729
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TABLE 12.6:
x y−4 81-3 27-2 9-1 30 11 1
32 1
93 1
274 1
81
9. Exponential Growth10. Exponential Decay
TABLE 12.7:
t b0 10001 10602 11243 11914 12625 13386 14197 1504
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12.7. Exponential Functions, Answer Key www.ck12.org
TABLE 12.7: (continued)
t b8 15949 168910 1791
12.
TABLE 12.8:
Q b0 501 1002 2003 4004 8005 16006 32007 64008 128009 2560010 51200
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12.8. Sequences, Answer Key www.ck12.org
12.8 Sequences, Answer Key
1. The difference is 2 between each term.2. The difference is .05 between each term.3. No common difference4. Difference is -35. The difference is 1
46. 1, 1 1
4 , 1 12 on the 4th, 5th and 6th days
7. -5 is the common ratio8. 1
4 Common ratio9. 2 between each term
10. Not a geometric sequence-no common ratio11. Arithmetic sequence, common difference is 3.12. Geometric sequence, common ratio is 1
3 .13. Arithmetic sequence, common difference is -8.14. Neither.15. Geometric sequence, common ratio is -10.16. Arithmetic sequence, common difference is 3
62 .
TABLE 12.9: Option A
Days Pay1 1202 1603 2004 2405 2806 3207 3608 4009 44010 480
TABLE 12.10: Option B
Days Pay1 32 63 124 245 486 967 1928 3849 76810 1536
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Option A is better if you work 8 days or less. If you work more than 8 days, option B is better.
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