answer keys - amazon s3 · 11 4/5= p • 5/4; 64% 12 0.005 • w = 16; 3,200 problem solving 13 6...

Answer Keysfor Calvert Math

Lessons 61–80

08CMAKD0613-0615

CONTENTS

Math Textbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Math Workbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Math Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Lessons 61–80 Math textbook answer key

C A LV E R T E D U C AT I O N

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CHAPTER 5

5.1 Fractions, Decimals, and Percents

Try These1 20% 2 75% 3 45% 4 235%

Exercises1 57 1/7% 2 137 1/2% 3 122 2/9% 4 156 1/4% 5 242 6/7% 6 9/20 7 3/10 8 2/25 9 1/20 10 27/100 11 1 3/5 12 1 39/100 13 7/8 14 1/6 15 1/9 16 1 4/9 17 1 7/16 18 24% 19 0.6% 20 10.2% 21 124% 22 107% 23 90% 24 20.5% 25 70.9% 26 0.7 27 0.36 28 0.415 29 0.706 30 1.37 31 2.45 32 0.009 33 0.006 34 0.002 35 1.3 36 0.0116 37 0.0683 38 > 39 > 40 = 41 >

Problem Solving42 28 4/7% 43 66 2/3% 44 80% 45 0.875 and 87.5%

5.2 Finding Percents Mentally

Try These1 –4 Answers will vary due to estimation. Possible answers: 1 25% 2 10% 3 66 2/3% 4 120%

Exercises1 c 2 a 3 d 4 f 5 i 6 b 7 e 8 h 9 g 10 –35 Answers will vary. Possible answers: 10 1/4 11 2/3 12 1 13 1/3 14 0 15 1/20 16 1 1/2 17 1/10 18 1/200 19 1/3 20 1/4 21 1/2 22 2 7/10 23 0 24 1 1/5 25 16 26 21 27 3 28 51 29 $12 30 $5.50 31 2 32 100 33 2 34 50% 35 300

Problem Solving36 Answers will vary; about 13 free throws 37 about 341 people 38 about 210 people

Constructed Response39 Answers will vary. Possible answer: $5 is not a reasonable estimate for a 15% tip on a bill that is $58.50, because if you round $58.50 to $60, a 15% tip on $60 would be $9.

Mixed Review40 2 1/4 41 13/21 42 20 3/40 43 2 1/5 44 6 1/2 45 3 1/6 46 13 1/3 47 136 1/2

5.3 Percents and Proportions

Try These1 part = 20; whole = 80; 25% 2 part = 35; whole = 70; 50% 3 part = 10; whole = 15; 66 2/3%

Exercises1 24 2 63 3 10% 4 1,200 5 3,000 6 12,000 7 3 8 25% 9 58.5 10 50 11 450 12 800

Problem Solving13 $10,740 14 $900 15 12 days 16 76%

Mind Builder1 $389.40 2 $0.82 3 Answers will vary. See student’s work.

5.4 Percent Equations

Try These1 part: 96; whole: W; percent: 33 1/3% 2 part: P; whole: 750; percent: 15% 3 part: 584; whole: 1,250; percent: P 4 part: 89.25; whole: W; percent: 105%

Exercises1 820 = 0.20 • W; 4,100 2 P = 0.042 • 68; 2.9 3 17,000 = P • 8,500; 200% 4 25 = 0.625 • W; 40 5 68 = 0.02 • W; 3,400 6 P = 0.0005 • 48; 0.024 7 25 = P • 350; 7 1/7% 8 2.25 • W = 900; 400 9 P = 1.27 • 250; 317.5 10 P = 0.6667 • 324; 216 11 4/5= P • 5/4; 64% 12 0.005 • W = 16; 3,200

Problem Solving13 6 1/4 gallons 14 85%

Constructed Response15 Cassie must sell $937.50 to earn $200 per week. She makes $125 per week, which means she needs to make $75 in commissions in order to total $200 per week ($75 + $125 = $200). In order to make $75 in commissions, she needs to determine 8% of what number is $75: 75 = 0.08w; w = $937.50.

Mid-Chapter Review 1 9 2 128.25 3 75% 4 37.5% 5 120 6 600 7 0.2; 1/5 8 88%

Problem Solving100 miles

Extension125 miles

Cumulative Review1 55, 83, 97 2 100, 50, 12.5 3 7 1/2, 6 3/4, 6 4 15, 9, 2 5 21.5 6 19 7 3.2 8 25 9 m = 6 10 r = 7 1/2 11 x = 12 12 y = 10 1/2 13 m = 12 14 y = 13 15 x = 54 16 y = 441

Answer KeysLessons 61–80

Math Textbook



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17 m = 3/4 18 y = 8 19 c = 40 20 x = 1 21 1 1/4 22 3/5 23 3/7 24 2 2/15 25 8/45 26 1 1/24 27 1/12 28 13 3/4 29 12 1/4 30 2 17/24 31 5 5/16 32 2 4/11 33 n = 10 34 c = 13 1/2 35 x = 7 1/2 36 m = 66 2/3 37 $16,320 38 43 1/2 pounds 39 5 cups 40 3 inches by 4 1/2 inches

5.5 Percent of Change

Try These1 10% increase 2 12% decrease 3 12 1/2% increase 4 20% decrease

Exercises1 28% decrease 2 50% decrease 3 33 1/3% increase 4 6 2/3% decrease 5 20% increase 6 10% decrease

Problem Solving7 12% decrease 8 8% decrease 9 16 2/3% decrease 10 25% increase 11 12 1/2% increase

Constructed Response12 The final sales price is $39.38. The boots were originally $42, and the price was increased by 25% to $52.50. Next, the $52.50 was reduced by 1/4 or 25% to $39.38.

Test Prep13 a

5.6 Markup, Discount, and Sales Tax

Try These1 discount = $8; sale price = $32 2 discount = $90; sale price = $210 3 discount = $2.83; sale price = $5.66 4 discount = $79.90; sale price = $719.10

Exercises1 $72.98 2 $36 3 $25 4 $11.97

Problem Solving5 $22.50 6 book at sale price: $10.40; calendar at sale price: $6.40; total cost: $16.80; with sales tax: $17.81 7 20% 8 $140 9 $15.50 10 $11,557.53

Constructed Response11 Luisa can buy the shirt and sandals because 40% of $25 is $15, and 1/2 of $18 is $9. The total price for both items is $24, since $15 + $9 = $24. Luisa has $25.

Test Prep12 c

5.7 Simple and Compound Interest

Try These1 $650 2 $750

Exercises1 $763.75 2 $5,315 3 $130,180 4 $62.72 5 $463.88

Problem Solving6 $3,096 7 $7,500

Constructed Response8 The interest rate is 6.5%. When the formula I = prt is used, the interest is $975, the principal is $5,000, and the time is 3 years, so the unknown variable is the rate. When the values are substituted in the formula, the result is $975 = $5,000 • r • 3. When the equation is solved for r, r = 6.5%.

5.8 Problem-Solving Strategy: Guess and Check

Try These1 about $100 2 5 quarters and 1 nickel

Solve1 10% 2 son = 9 years old; Mr. Cox = 36 years old 3 $21.70 4 $134.51 5 A = 2; B = 1; C = 9; D = 7; E = 8 6 2 packages 7 $23.77 8 99%

Mixed Review9 4 10 5.4 11 165 12 43 13 s/4 = 5 14 n + 3 = 6 15 4n + 5 = 37

Chapter 5 Review

Language and Concepts1 percent 2 part 3 original 4 discount 5 markup 6 compound interest

Skills and Problem Solving7 87.5% 8 180% 9 40% 10 37.5% 11 106% 12 1/4 13 1/3 14 2/25 15 3/250 16 1 1/20 17 –20 Answers will vary due to estimation. Possible answers: 17 50% 18 33 1/3% 19 30% 20 10% 21 125 22 13 23 50% 24 33 1/3% 25 200 26 92 27 40 28 0.354 29 250% 30 0.5% 31 5 32 11 33 25% decrease 34 66 2/3% increase 35 tax = $3.50; cost = $73.50 36 tax = $5.81; cost = $134.81 37 tax = $0.30; cost = $5.25 38 $76.50 39 $29 40 $121.80 41 $156 42 $31.25 43 9% 44 7 dogs and 3 birds

Chapter 5 Test1 37% 2 6.1% 3 31% 4 230% 5 76% 6 –9 Answers will vary due to estimation. Possible answers: 6 1 7 45 8 50 9 125 10 42 11 19.6 12 12% 13 50% 14 4.5 15 89.5 16 2.5 17 184 18 1,000% 19 0.3% 20 36 21 12 22 120 23 103% 24 60% increase 25 10% decrease 26 $22.46 27 $9.78 28 $192 29 $36.75 30 $8.93 31 $129 32 $604.80 33 $4,188.60 34 3 adult tickets 35 $744



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Change of PaceNumerical Values: 7; 49; 343; 2,301; 17,007; Answers will vary. Possible answer: The pattern is to multiply each number by 7. The rope core does not fit the pattern for the last two numerical values. The fourth numerical value should have 1 more rope core so that the value is 2,401. The last numerical value should only have 8 rope cores instead of 10 so that the value is 16,807.

Cumulative Test1 b 2 c 3 b 4 b 5 d 6 b 7 a 8 c 9 b 10 c

CHAPTER 6

6.1 Angle Relationships

Exercises1 QTN 2 RTS 3 QTS 4 32° 5 PTQ 6 4 7 6 8 40° 9 40° 10 40° 11 45° 12 x° 13 180° – y°

Problem Solving14 50° 15 45° 16 47° 17 125° 18 x = 30° 19 Yes, two supplementary angles can have the same measure, because if both angles are 90°, the sum of their measures equals 180°. 20 60°

6.2 Parallel Lines and Angles

Try These1 corresponding angles 2 alternate exterior angles 3 alternate interior angles 4 other (or vertical angles) 5 alternate exterior angles 6 alternate interior angles 7 other 8 corresponding

Exercises1 150° 2 150° 3 150° 4 30° 5 30° 6 30° 7 m 1 = 62°; m 2 = 62°; m 3 = 62° 8 m 1 = 81°; m 2 = 81°; m 3 = 81° 9 m 1 = 105°; m 2 = 105°; m 3 = 105° 10 None, because alternate interior angles are not congruent. 11 a and b, because corresponding angles are congruent. 12 a and b, because corresponding angles are congruent.

Problem Solving13 No; in order for both lines to be parallel, the corresponding angles must be congruent when both lines are intersected by a transversal.

Constructed Response14 The interior angles on the same side of the transversal are related because the sum of the angles is 180°. The interior angles on the same side are supplementary.

Test Prep15 b

Mind Builder1 m 1 = 60°; m 2 = 120°; m 3 = 60°; m 4 = 85°; m 5 = 95°; m 6 = 95° 2 m 7 = 60°; m 8 = 120°; m 9 = 60°; m 10 = 120°; m 11 = 85°; m 12 = 95°; m 13 = 85°; m 14 = 95° 3 1, 3, 7, 9 4 1 could have the same measure as 4 if lines e and f are parallel.

Cumulative Review1 1.69 2 216 3 0.9 4 900 5 11 6 438 7 80,620 8 10 9 400 10 2,800 11 4 12 3 13 36; 1,296; 7,776 14 37, 49, 55 15 9, 36, 49 16 16, 64, 128 17 a = 2 18 c = 0.5 19 d = 22 20 e = 9 21 d = 9.7 22 h = 14.7 23 m = 2.4 24 m = 14 25 b = 5.62 26 x + 4.5 = 72.3; best time is 67.8 seconds 27 w = (0.6)(60); width is 36 meters 28 944.9 miles 29 318 strokes 30 0.003 of the truckload is left.

6.3 Constructions: Line Segments and Angles

Try These1–2 Check student work for accuracy.

Exercises1 –4 Check student work for accuracy.

Problem Solving5 Solution for constructing an equilateral triangle: First draw a line segment. Measure the segment by putting the point of the compass at one end of the segment and making a small arc at the other end of the segment. Keeping this setting, keep the point of the compass at the end of the segment and draw an arc over the top of the segment. Keeping the same setting, put the point of the compass at the other end of the segment and draw a second arc over the top of the segment, intersecting the first arc. Connect each endpoint of the segment to the intersection of the arcs with a straightedge.

Mixed Review6 245 = (2 • 102) + (4 • 101) + (5 • 100) 7 1,587 = (1 • 103) + (5 • 102) + (8 • 101) + (7 • 100) 8 1,040 = (1 • 103) + (4 • 101) 9 12,074 = (1 • 104) + (2 • 103) + (7 • 101) + (4 • 100) 10 70,475 = (7 • 104) + (4 • 102) + (7 • 101) + (5 • 100) 11 153,000 = (1 • 105) + (5 • 104) + (3 • 103) 12 1,004,578 = (1 • 106) + (4 • 103) + (5 • 102) + (7 • 101) + (8 • 100) 13 2,506,000,000 = (2 • 109) + (5 • 108) + (6 • 106)

6.4 Constructions: Bisectors of Line Segments and Angles

Try These1–2 Check student work for accuracy.

30˚

150˚

150˚30˚



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Exercises1–7 Check student work for accuracy.

Problem Solving8 The method shown in the textbook to bisect a line segment makes a perpendicular bisector. If a perpendicular bisector is constructed, any other non-perpendicular line can be drawn through the midpoint located by the perpendicular bisector. 9 Right angles; check student work for accuracy. 10 Rhombuses, including squares

Mixed Review11 3/5 12 3/10 13 1/4 14 2/7 15 2/5 16 22/25

6.5 Constructions: Perpendiculars and Parallels

Try These1-3 Check student work for accuracy.

Exercises1-5 Check student work for accuracy. 6 The relationship between EF and CD in Exercise 5 is that the lines are parallel to each other.

Problem Solving7 Check student work for accuracy. 8 Answers will vary. One solution to construct a square: Extend the sides of segment EF. Construct two lines perpendicular to segment EF through its original endpoints. These lines will form two more sides of the square. To measure the length of segment EF, put the point of the compass at one intersection of a perpendicular with the segment and then make the pencil of the compass draw a small arc at the other intersection of a perpendicular with the segment. Now your compass is set to the distance of one side of the square. Mark this distance (so the two new sides will be congrunt to segment EF) by drawing small arcs on the perpendicular segments with the point of the compass at the intersections of the perpendiculars with segment EF. Three sides have now been drawn. Draw the fourth side. 9 Check student work for accuracy. 10 XS and YT are related to each other by being parallel to each other. They both are perpendicular to XY .

6.6 Problem-Solving Application: Constructing Golden Rectangles

Try These1 yes 2 yes 3 no 4 yes

Solve1 Check student work for accuracy. 2 Rectangle LDEN is a golden rectangle because the length is 40 mm and the width is 24 mm. The length divided by the width is 1.66. 3 Answers will vary. Sample: The Great Math Detective cut the pizza into 10 unequal pieces for himself and his

four friends. See illustration for the way he cut his pizza.

1 2

6

109

5

74

8

3

Mid-Chapter Review1 m 1 = 60° 2 m 9 = 60° 3 m 11 = 85° 4 m 8 = 120° 5 m 12 = 100° 6 There are no pairs of complementary angles because there are no right angles. 7 1 or 3 or 7 or 9 8 Possible answers include: 3 and 7, 2 and 10, 14 and 5. 9 Possible answers include: 1 and 9, 4 and 13, 6 and 12. 10 Possible answers include: 1 and 7, 2 and 8, 4 and 11, 5 and 12. 11 8 could have the same measure as 5 if EH and IL are parallel.

6.7 Triangles and Quadrilaterals

Try These1 equilateral, acute 2 scalene, right 3 isosceles, acute 4 scalene, obtuse

Exercises1 Answers will vary. Possible answer:

1 in .38

1 in .

1 in .

2 none 3 Answers will vary. None of the three angles should be congruent to any other angle, and each angle should be less than 90º.

60°

50° 70°

4 parallelogram, rectangle, rhombus, square 5 trapezoid 6 rhombus, square 7 rectangle, square 8 always 9 sometimes 10 sometimes 11 never 12 always 13 always 14 never 15 never

Problem Solving16 Answers will vary. Possible answers: Both parallelograms are made from two congruent trapezoids.

and



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17

a kite dividedinto two

non-congruentisosceles triangles

a kite dividedinto two

congruentscalene triangles

18

Constructed Response19 The triangles fit perfectly because all of their angles are 60º and six of them add up to 360º which makes a circle; a rhombus (two triangles).

20 Normally it does not, because it has no parallel sides except in two special cases: 1) If it is equilateral, then it is a rhombus. 2) If it is equiangular, then it is a square. 21 The sum of the angles is 360°. This sum is the same for all quadrilaterals because all quadrilaterals are made of 2 triangles. The measure of the angles of a triangle is 180° and 2 • 180° = 360°.

102º106º

62º90º

Mixed Review22 z = 28 23 s = 66 24 k = 208 25 t = 1.3 26 n = 22.1 27 c = 12 28 p = 273 29 r = 96

6.8 Polygons and Angles

Try These1 540° 2 900° 3 1,260° 4 1,440°

Exercises1 x = 100° 2 x = 139° 3 x = 142° 4 x = 150° 5 x = 90° 6 x = 72° 7 90° 8 108° 9 150°

Problem Solving 10 115° 11 120°

12 11 sides

Test Prep13 a 14 c

6.9 Congruent Figures

Exercises1 Sample answer: QRP and TVS 2 QR and VT, PR and VS 3 SAS 4 MN 5 MNP 6 NMP 7 DEF 8 DFE 9 DE 10 XYZ 11 XY 12 YZ 13 ASA 14 SAS 15 SSS 16 SSS 17 SAS 18 ASA

Chapter 6 Review

Language and Concepts1 acute 2 complementary 3 transversal 4 equilateral 5 isosceles 6 obtuse 7 vertical 8 scalene 9 rhombus 10 supplementary

Skills and Problem Solving11 8 or 6 12 2 or 4 13 6 or 8 14 8 15 180° 16 2 and 6, 4 and 8, 1 and 5, 3 and 7 17 JL and MP 18 KN 19 4 and 5, 3 and 6 20 105° 21–26 Check student work for accuracy. 27 parallelogram, rectangle, rhombus, square 28 acute, obtuse, right 29 27° 30 98° 31 138° 32 60° 33 ASA or SAS 34 SAS 35 SSS 36

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37

38 1/6 of his allowance; extra facts: 1/4 savings, spends the rest on miscellaneous

Chapter 6 Test1 c 2 g 3 a 4 f 5 e 6 h 7 d 8 b 9 i 10 AB , EF 11 3 and 6 12 3 and 6, 1 and 4, 2 and 5 13 1 and

2, 4 and 5 14 XY 15 AC 16 ZY 17 XYZ 18 ABC 19 BAC 20 Check student work for accuracy. 21 square, rhombus 22

1 2 3 4-3 -2 -1-1-2

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25 $19.80; extra fact: cost of the strawberries; Four pints of blueberries and 2 pints of raspberries cost $19.80. One pint of blueberries costs $2.50 ($17.50 • 7 = $2.50), so 4 pints cost $10 (4 • $2.50 = $10). One pint of raspberries costs $4.90 ($24.50 • 5 = $4.90), so 2 pints cost $9.80 (2 • $4.90 = $9.80). When the price of the blueberries is added to the price of the raspberries, the total is $19.80 ($10 + $9.80 = $19.80).

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Lessons 61–80 Math workbook answer key


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CHAPTER 5

Practice 58 – Fractions, Decimals, and Percents1 25% 2 7% 3 9% 4 54% 5 33 1/3% 6 64% 7 87 1/2% 8 44 4/9% 9 85 5/7% 10 258 1/3% 11 1/2 12 3/50 13 1/8 14 6/25 15 2/3 16 9/50 17 1/16 18 1 12/25 19 2 3/10 20 5/8 21 26% 22 93% 23 10% 24 139% 25 170% 26 10% 27 0.6% 28 12 1/2% 29 26 1/4% 30 0.75% 31 0.03 32 0.6 33 1.8 34 5 35 1.17 36 1.245 37 0.0675 38 1.2 39 0.009 40 0.00875 41 6 players 42 20 U.S. offices 43 75% of trip 44 14 dogs were pets; 21 dogs were strays 45a 33 1/3% volunteers under 18 b 66 2/3% volunteers over 18

Enrichment 59 – Percents, Decimals, Fractions Percent Decimal Fraction

92%

84%

0.92 23 25

1.4

0.625

0.28

62.5%

2.5%

28%

140%

0 .84

0 .025

58

725

21 25

2 5

1 40

1

1

2

3

4

5

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0 .4%

1.75

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30%

2%

175%

0 .3

0 .02

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211

3 10

1 50

1 250

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18 %

71 %

211

37

7

8

9

10

11

12

Percent Decimal Fraction

3 .25%

0 .725

0.825

0.152

0.014

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1.4%

72 %

82 .5%

7500

9200

15

33 40

2940

13 400

19 125 15 %

12

12

13

14

15

16

17

18

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Practice 60 – Finding Percents Mentally1 e 2 a 3 g 4 b 5 c 6 h 7 d 8 i 9 f 10 j 11 1 1/2 12 5 13 15 14 40 15 15 16 30% 17 15 questions 18 30% 19 60% 20 83 1/3%

Mixed Practice 1 0.7536 2 0.6561 3 0.9945 4 3° 5 40° 6 37°

Practice 61 – Percents and Proportions1 0.5 2 10% 3 44 4 0.2 5 200 6 4.5 7 20 8 120% 9 20% 10 65 11 6.3 12 0.3 13 9% 14 200 15 200 16 256 17 23 students 18 75% 19 4 girls 20 original 4 in. by 6 in. area = 24 in2; enlarged: 7 in. by 10.5 in. area = 73.5 in.2; reduced: 1 in. by 1.5 in. area = 1.5 in.2. The areas are different because as the dimensions change, both length and width, the areas change.

Practice 62 – Percent Equations1 4 = P • 5; 80% 2 0.25 • W = 6; 24 3 2 • 18 = P; 36 4 P • 36 = 27; 75% 5 9 = P • 20; 45% 6 0.15 • W = 18; 120 7 37 = P • 37; 100% 8 0.04 • W = 26; 650 9 0.85 • 20 = P; 17 10 2 = 0.001 • W; 2,000 11 0.31 • W = 279; 900 12 P • 12 = 3; 25% 13 0.625 • 320 = P; 200 14 54 = P • 24; 225% 15 P • 5 = 1; 20% 16 1.75 • 80 = P; 140; 17 P = 0.0005 • 125; 0.1 18 0.3333 • W = 78; 234.0 19 76% 20 200 houses 21 2% absent 22 600 students

Practice 63 – Percent of Change1 20% decrease in cost 2 100% increase in cost 3 9.8% decrease in population 4 9.1% increase in price 5 20% decrease in weight 6 20% increase in price 7 25% decrease in price 8 75% increase in population 9 12 1/2% decrease in cattle 10 100% increase in rainfall 11 25% increase in population 12 33 1/3% decrease in speed

Mixed Practice 1 200 2 400 3 24 4 80


Math Workbook



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Enrichment 64 – Applying Skills1 34,560 hours 2 19; 23; 29 3 Answers will vary; one possible answer is 148/296 + 35/70. 4 Check student’s work for accuracy. 5 Answers may vary depending on the size in square miles of Texas used. Check student's work for accuracy.

Practice 65 – Markup, Discount, and Sales Tax1 $121.10 2 $20 3 $337.50 4 $4.80 5 $182 6 $92.70 7 $32 8 $18.20 9 $1,051.70 10 $94.27 11 $10.60 12 $32.48 13 $118.80 14 $173.83 15 $37.41 16 $10.50; $199.50 17 $15.56 18 24%

Practice 66 – Simple and Compound Interest1 $19.25 2 $1,624 3 $49.50 4 $1,282.50 5 $144 6 $287 7 $1,093.96 8 $12,440.80 9 $1,298.92 10 $259 11 $20,000 12 $577.50 13 $5,040; $13,040 14 $2,210.29; $4,910.29 15 Answers will vary. Bank 2. Sample explanation: At Bank 1 Keith will earn $262.50 over 5 years and at Bank 2 he will earn $252.00 over 4 years. Even though it looks like more at Bank 1, the difference is only $10.50, which is not a high return for the fifth year. He would be better off moving his money to another account after 4 years with Bank B.

Practice 67 –Problem-Solving Strategy: Guess and Check1 $10.00 2 $5 3 $22,000 4 30% 5 5,520 employees 6 $150.72 7 $456.23 8 $6,000 more

Review 68 – Chapter 5 Review1 50% 2 40% 3 275% 4 9/10 5 1/8 6 1 1/5 7 17% 8 0.8% 9 243% 10 0.55 11 0.327 12 1.23 13 11.2 14 0.85 15 44.16 16 400 17 36 18 25% 19 20% 20 4,382 novels 21 20% increase in points 22 50% 23 $15.90 24 Check student’s work for accuracy. 25 $18.20 26 $57.57 27 15% 28 $80 29 $10.15 30 34% profit 31 $945 32 $10.56 33 $8.00

Test 69 – Chapter 5 Test Prep1 a 2 d 3 d 4 a 5 c 6 b 7 c 8 d

9 500 10 20%

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02

CHAPTER 6

Practice 70 – Angle Relationships1 CFD 2 AFC 3 DFB 4 AFC, DFE, DFB 5 46° 6 71° 7 1, 5 8 73° 9 180° 10 (90 – y)° 11 m A = 60° 12 m B = 35° 13 m C = 45° 14 m D = 24° 15 m E = 104°

Enrichment 71 – Angle Relationships1 54°45’ 2 62°44’ 3 74°6’ 4 60°41’38’’ 5 55°30’15’’ 6 2°57’57’’ 7 59°42’ 8 95°48’ 9 69°58’ 10 134°43’36’’ 11 140°38’6’’ 12 50°41’24’’

Practice 72 – Parallel Lines and Angles1 16 2 11 and 14; 12 and 13 3 9 and 16;

10 and 15 4 140° 5 40° 6 40° 7 180°, supplementary 8 They will be equal. 9 40° 10 140° 11 140° 12 180° 13 80° 14 not parallel; The two alternate interior angles are not equal. 15 parallel; The two 120° angles are corresponding angles and are equal.

Practice 73 – Constructions: Line Segments and Angles1 –6 See student’s work, since answers will vary.

Practice 74 – Constructions: Bisectors of Line Segments and Angles1–8 Check student work for accuracy.

Practice 75 – Constructions: Perpendiculars and Parallels1–3 Check student work for accuracy. 4a –b See student’s work. c perpendicular bisector 5 Check student work for accuracy.

Mixed Practice1 219 2 $49.19 3 $520.38



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Practice 76 – Problem-Solving Application: Constructing Golden Rectangles1 yes 2 no 3 yes 4 no 5 3.2 6 37.5 7 9.6 8 21.3

Enrichment 77 – Regular PentagonCheck student’s work. 1 five-pointed star 2 infinite

Practice 78 – Triangles and Quadrilaterals1 e 2 b 3 a 4 c 5 d 6 b 7 c 8 b 9 c 10 d

Practice 79 – Polygons and Angles1 pentagon 2 octagon 3 hexagon 4 720° 5 1,080° 6 1,800° 7 x = 85° 8 x = 120° 9 x = 42° 10 x = 80° 11 x = 120° 12 x = 72° 13 108° 14 156° 15 162° 16 No; when you add up the sum and divide by the number of angles, all the angle measurements will be equal due to finding the average angle measurement. An irregular polygon has different angle measurements. 17 71°

Practice 80 Congruent Figures1 SAS 2 ASA 3 SSS 4 ASA 5 SSS 6 ASA 7 90° 8 6 9 60° 10 4

Mixed Practice 1 8 blocks 2 21 classes 3 $636 4 1 5 1 6 49 7 36 8 27 9 16

Lessons 61–80 Math ManuaL answer key


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LESSON 65

Enrichment1 45 2 80 3 18 4 54 5 9 6 1 7 300 8 5 9 1.5 10 22.5 11 25 12 5.4 Puzzle answer: A skier who loved steep descents used to calculate slopes by percents, but computing the run wasn’t half as much fun as attending cast-signing events.

LESSON 66

Enrichment184 ft 10 1/4 in. = 2,218.25 in.; 212 ft 6 1/2 in. = 2,550.5 in.2,550.5 – 2,218.25/332.25; 332.25/2,218.25 ≈ 0.15 = 15%

LESSON 68

Enrichment

Summary

Clue 1: We know that Nick borrowed $1,500 at 10%. This means he paid $150 in interest. Clue 2: We know that Sue’s interest on her loan was $300 (twice Nick’s). 0.06n = 300, n = 5,000; Her loan was for $5,000 at 6%. Clue 3: We know that Penny must have borrowed $4,500 and Jack must have borrowed $2,000. Clue 4: We can calculate Jack’s interest rate. n • 2,000 = 160, n = 0.08 = 8%

LESSON 70

Warm-up1 8 2 6 3 3 4 4

LESSON 73

Enrichment1 12 2 8 3 4 4 3The number of rays equals the number of angles.

LESSON 76

Enrichment8 equilateral triangles; The 6 point triangles formed are congruent to each other. Likewise, the 2 larger triangles that make the star shape are congruent to each other. The 6 point triangles formed are similar to the 2 large, star-making triangles.

LESSON 79

Warm-up1 120° 2 135° 3 144°


Math Manual

answer keys - amazon s3 · 11 4/5= p • 5/4; 64% 12 0.005 • w = 16; 3,200 problem solving 13 6...

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