Chapter 1Practice 1-11. n � 5 2. ∆n∆ � 15 3. 60n 4. 5. 8y � 3 6. 4(∆n∆ � 3)7. j � 10; j � the amount of money Jon has 8. 25q or $.25q;q � the number of quarters 9. w � 30; w � the amount ofweight Kirk’s brother can lift 10. s � 5; s � the speed Danaeruns 11. a number divided by 4 12. 4 more than a number13. the product of a number and 3 14. 8 less than a number15. 81.6 16. 101 17. 2 18. 28 19. 291.2 20. 17.44 21. 70.422. 403.2 23. 14.6 24. 34.4
Guided Problem Solving 1-11. The cost for entering the amusement park and the cost perride. 2. Write an expression for the total cost and determinehow many rides you can go on for $16. 3. $5 4. $2 5. 5 � 2r6. 5 rides 7. Sample answer:Yes, the expression checks. $15 � $168. 35 � .25m; 60 miles
Practice 1-21. �160 ft 2. 3 yd 3. �$20 4. 58 5. No; the highesttemperature in Idaho was 118°F. 6. Yes; Minnesota has arecorded low temperature of �59°F. 7. Idaho 8. , 9. � 10. , 11. . 12. . 13. , 14. �25, �15, �5, 0, 5, 15, 2515. �18, �10, �8, �6, 3, 9, 27
Guided Problem Solving 1-21. the scores of the two golfers 2. The player with the lowestscore wins. 3. which golfer wins; by how much 4. Plot themon a number line.5.
6. –12 7. 3 8. 3 strokes 9. Sample answer: Yes; since the scoresare negative, find the answer with the larger absolute value.10. the diver; 115 feet
Guided Problem Solving 1-31. $151 2. $248 3. the amount to be deposited to preventyour account from going below zero 4. subtract 5. the opposite6. –$97 7. $97 8. negative 9. –5�F
Guided Problem Solving 1-41. 40,230 ft 2. miles 3. negative 4. –40,230 5. division 6. 5,000 ft 7. –8 miles 8. 40,230 ft � � 7.62 miles;yes, the answer 8 miles is reasonable. 9a. –52.3 9b. –17 yd
Guided Problem Solving 1-51. each item 2. the total cost of all the items 3. $2.97, $1.99,$.99 4. $11.88 5. $5.97 6. $4.95 7. $22.80 8. $2.97 � $2.97 � $2.97 � $2.97 � $1.99 � $1.99 � $1.99 �$.99 � $.99 � $.99 � $.99 � $.99 � $22.80; yes 9. $25.67
Practice 1-61. �12 2. �22 3. 15.53 4. 5. 18 6. �31 7. 28.59 8. 6 9. 45 10. 17 11. 13.3 12. 13. n � 7 �25; 18 boxes 14. t � 4 � 28; 32 books 15. m 2 13 � 17; 30 muffins 16. �22 � m � �71; m � �49; she would need to descend 49more meters. 17. 2; �2 18. 4; �4 19. �2; 4
Guided Problem Solving 1-61. $9.30 2. how much the collector paid for the card 3. less4. y + $3.75 = $9.30 5. subtract $3.75 from both sides of theequation 6. $5.55 7. yes 8. $48,000
9. �4.7 10. 963 11. �21 12. �6.3488 13. n � ; n � 7
14. n � 5($157.90); n � $789.50 15. n � ; n � $5.99 16. n � ; n � 4.5 17. 4; �4 18. 1; �1 19. 4; 0
Guided Problem Solving 1-71. 124 2. more 3. the number of students surveyed who arein the band 4. 4x � 124 5. Divide the total number ofstudents surveyed by 4. 6. x � 31 7. yes; 4(31) � 124 8. 12x � 288; x � 24; x � 24 students
Chapter 1B Reading Comprehension1. a solar eclipse 2. 15 min 3. � � of the sun 4. 97%5. 20% 6. The area of the sun is equal to 1.517 � 1012 km2.;Multiplying by 20% gives 3.03 � 1011 km2. 7. a
1120
14
45
94.57 ? 3
$83.8614
$90.65$12.95
78
1724
1 mile5,280 feet
�12 �11 �10 �9 �8 �7 �6 �5 �4 �3 � 2 �1 0 1 2
x 1 59
C2-ANS_C3 5/10/2006 4:38pm Page 45
Chapter 1C Reading/Writing Math Symbols1. the absolute value of five 2. the opposite of six 3. theopposite of the absolute value of eight 4. Negative two is lessthan negative one. 5. Three is not equal to five. 6. The absolutevalue of negative two is equal to the absolute value of two.7. 803 centimeters is approximately equal to 8 meters. 8. Ninehalves equals 4 and five tenths. 9. |–4| 10. 4x + 5 11. n ÷ 1212. –(–7) 13. –3 < 0 14. x – 4 = 6 15. 18C < 328F
Chapter 1D Visual Vocabulary Practice1. Distributive Property 2. Identity Property of Multiplication3. Associative Property of Multiplication 4. order of operations5. Commutative Property of Addition 6. integers 7. DivisionProperty of Equality 8. evaluate 9. Addition Property of Equality
Guided Problem Solving 2-11. Determine the number of classes that can receive suppliesand how many of each item each class gets. 2. 23 � 3 � 53. 2 � 3 � 13 4. 23 � 3 5. 2 � 33 6. 6; 2 � 3 7. 6 8. 20 paintbrushes, 13 boxes of markers, 4 pads of paper, and 9 sets ofwatercolors 9. Yes, since 6 is the greatest number that willdivide evenly into the number of each item 10. Each piece willbe 7 inches long; 42 inch piece: 6 pieces; 63 inch piece: 9 pieces;77 inch piece: 11 pieces; total: 26 pieces.
Guided Problem Solving 2-21. Write 0.219 as a fraction. 2. 3. 3 4. 5. Thefraction cannot be simplified, since 219 and 1,000 have nocommon factors. 6. Yes; 0.219 is read as two hundred nineteenthousandths, which is how it is written as a fraction. 7.
Guided Problem Solving 2-31. the hours worked by two people 2. Who worked longer?3. 60 4. 35 5. 6. 7. 8. Maria 9. Yes; ; compare . Maria worked 40minutes and Erika worked 35 minutes. 10. Anita; 3:25 � 4:05� 40 min; ; ; ;
Guided Problem Solving 2-41. in. thick; in. wide; two; in. surfaces touching 2. thethickness of two “2 by 4” pieces with their in. surfaces joinedtogether 3. addition 4. � 5. yes 6.(1 � 1) � ( + )� 2 � 7. 2 � � 3 8. Yes; you could multiply 2 � � 3in. 9. inches
.Course 3: All-In-One Answers Version A (continued)
Guided Problem Solving 2-51. pounds; of its waste 2. Find the number of pounds ofpaper that are recycled. 3. multiplication 4. 5. 6. 7. Yes; is more than half. One-half of 14 is 7 andthe answer is almost 11, which is more than 7. 8. Each personwill get inches.
Practice 2-61. P � 33.2 cm; A � 67.2 cm2 2. P � 90 m; A � 442 m2
Guided Problem Solving 2-61. V � pr2h 2. Find the height h of the cone. 3. Solve thevolume formula for h. h � 4. Plug in values and solve forh. h < 2.87 5. Substitute h into the given formula and solvefor V. 6. 2(P � 100) � a
Guided Problem Solving 2-71. h � 160t � 16t2 2. height; feet 3. time; seconds 4. thenumber of feet a model rocket rises in 2 seconds 5. time t6. height h 7. h � 160(2) � (16)22 8. evaluate the power 9. 256 ft 10. yes; 256 � 160(2) � (16)22 � 320 � 64 11. 1,350 inches2; S � 6e2 � 6(15)2 � 1,350
Guided Problem Solving 2-81. d � distance, r � rate and t � time. 2. how far the wavewill go in 30 minutes 3. d, distance 4. 6 places to the right;3,000,000 km/h 5. 30 min � h 6. d � 1,500,000 km 7. 6 placesto the left; 1.5 � 106 km 8. Sample answer: Half of 3 is 1.5; theexponent of 10 will not change. 9. 7 � 103 animals; 4.2 � 104
Chapter 2B Reading Comprehension1. Saffron Rice Salad 2. 10 3. teaspoon 4. 4 5. 7 6. 2cups cooked rice 7. 1 cup 8a. cup 8b. cup 9. a
Chapter 2C Reading/Writing Math Symbols1. The bar means subtraction. 2. The bar is a fraction bar,separating the numerator from the denominator. 3. The barmeans the 5 is negative. 4. The bar means the 6 repeatsindefinitely. 5. The 2 repeats indefinitely. 6. decimal point 7. multiplication 8. a period 9. The pattern continuesindefinitely. 10. 4 + (–3) 11. 2.5 – 3.
Chapter 2D Visual Vocabulary Practice1. formula 2. least common multiple 3. factors 4. greatestcommon factor 5. prime numbers 6. reciprocals 7. relativelyprime 8. composite numbers 9. least common denominator
Course 3: All-In-One Answers Version A (continued)
Guided Problem Solving 3-11. the distance in miles that one can see from 450 ft aboveground on the London Eye Ferris Wheel 2. d � 1.233. 450 ft 4. d � 1.23 5. 26.1 mi 6. d < 1.25 � 20 = 25;It checks. 7. 14.6 mi; d � 1.23 � 1.23 � 11.83
Practice 3-21. 17 in. 2. 15 m 3. 14.4 ft 4. 25 m 5. 22.8 cm 6. 24.0 7. 178. 29 feet 9. < 3.6 10. < 1.4 11. 5
Guided Problem Solving 3-21. east and north 2. the distance from the camp to the waterfall3.
4. a2 � b2 � c2 5. hypotenuse 6. 1.52 � 1.72 � c2
7. 2.25 � 2.89 � c2 8. 5.14 � c2 9. c = < 2.2671610. c < 2.3 11. about 2.3 km 12. If you round and estimate,the answer is reasonable. 13. about 14.4 blocks
Practice 3-31. 12.0 in. 2. 9 m 3. 20 m 4. 46.4 mi 5. 8.9 cm 6. 12 in.7. 24.5 m 8. 15 in. 9. 17.3 m 10. 7 mm 11. 40 yd 12. 24 cm13. 127.2 yd 14. 60 mi 15. No; Ritchie needs to calculate
, since the hypotenuse is the longest side.
Guided Problem Solving 3-31. the height of the deck and the length of the slide 2. thedistance from the bottom of the deck to the bottom of the slide3.
4. right triangle 5. leg 6. a2 + b2 = c2 7. 52 + b2 = 102
8. b2 � 75 9. b � < 8.7 10. about 8.7 ft 11. It is closebut not exactly correct, because of rounding errors. 12. 25.0 ft
Practice 3-41. (�5, 0) 2. (�5, �9) 3. (�6, �3) 4. (2, �2) 5. (0, 5) 6. (�2, 7) 7. (5, 2) 8. (2, 7) 9. III 10. x-axis 11. x-axis 12. III 13. IV 14. IV 15. I 16. II 17. 10 ways 18. (0, 5),(0, 4), (0, 3), (0, 2), (0, 1), (0, �1), (0, �2), (0, �3), (0, �4), (0, �5)
Guided Problem Solving 3-41. nine 2. first; second 3. Connect the points in order, anddescribe the figure that is formed. 4. the number of horizontalunits a point is from zero 5. the number of vertical units apoint is from zero 6. Check students’ work. 7. third
8.
9. the letter Y 10. Yes; the letter Y is made.11. a star;
Practice 3-51. 1 2. 11 3. �39 4. 137 5a. yes 5b. no 5c. no 5d. yes6a. no 6b. yes 6c. yes 6d. yes 7. 8.
9. 10.
11. 12.
13. x � 25 � 2m
Guided Problem Solving 3-5 1. find the maximum number of letters that can be engravedfor $20 2. 1.5l 3. $10 4. c � 10 � 1.5l5. Number Expression Total Cost
Guided Problem Solving 3-61. Match each rule with the correct translation. 2. left 1, down5; left 6, up 2; right 3, does not move up or down 3. right andup 4. left and down 5. A � II; B � III; C � I 6. Sampleanswer: Graph each point and its image. Check by counting.7. A � III, B � II, C � I
Course 3: All-In-One Answers Version A (continued)
Guided Problem Solving 3-81. Graph a right triangle and its images after three differentrotations. 2. the origin 3. Check students’ work. 4. a turn ofa figure around a center point 5. counterclockwise 6–8. 6. J9 (3, 1); K9 (2, 6); L9 (4, 6) 7. J9 (21, 3); K9 (26, 2); L9 (26, 4)8. J9 (23, 21); K9 (22, 26);L9 (24, 26)
9. Sample answer: Trace the original figure and rotate it thegiven number of degrees to see if the new images match.10.
Chapter 3A Graphic Organizer1. Real Numbers and the Coordinate Plane 2. 8 3. WritingExtended Responses 4. Check students’ diagrams.
Chapter 3B Reading Comprehension1. F2 2. I6 3. Shea Stadium 4. E4 5. 4 horizontal and 4vertical units 6. a
Chapter 3C Reading/Writing Math Symbols1. D 2. C 3. E 4. B 5. A 6. I 7. K 8. J 9. F 10. G 11. H 12. Two raised to the fifth power is thirty two. 13. Thesquare root of twenty five is five. 14. Six raised to the secondpower is greater then three raised to the third power.
Chapter 3D Visual Vocabulary Practice1. solve 2. table 3. equivalent 4. compare 5. sum 6. evaluate 7. estimate 8. define 9. order
Chapter 3E Vocabulary CheckCheck students’ work.
Chapter 3F Vocabulary ReviewI. 1. C 2. D 3. B 4. G 5. F 6. E 7. AII. 1. D 2. G 3. F 4. B 5. C 6. E 7. A
Guided Problem Solving 4-31. 1,500 U.S. dollars 2. 0.7975 U.S. dollar � 1 Canadian dollar;0.8352 U.S. dollar � 1 Canadian dollar 3. How many moreCanadian dollars will you get from the first bank than from thesecond bank? 4. ; C � 1,880.88 5. ;
C � 1,795.98 6. Subtract to find the difference between the twobanks, 84.90 Canadian dollars 7. 0.7975 � 1,880.88 < 1,500.008. 6.12 � 26.2 � 160.34; 6.39 � 26.2 � 167.42; 167.42 � 160.34� 7.08 minutes
.Course 3: All-In-One Answers Version A (continued)
Practice 4-41. yes; ABCD , EFGH 2. no; the corresponding sides arenot in proportion 3. yes; nDEF , nCAB 4. yes; GHIJ ,KLMN 5. x �100; y � 20 6. x � 4 ; y � 8 7. x � 18; y �
24 8. x � 21; y � 24 9. x � 20; y � 9 10. x � 21 ; y � 20 11. m � 24; n � 8 12. x � 4; y � 4 13. 65 inches 14. 63 inches
Guided Problem Solving 4-41. the length of the smaller t-shirt 2. proportional relationship3. 21.5 in. wide � 26.5 in. long 4. 5. � 6. Cross-multiply and solve for y. 7. y < 19 in. 8. yes 9. no;
Guided Problem Solving 4-51. 1 in., 1 in; 2 in., 1 in. 2. the scale factor 3. 4.
5. yes; � 6.
Practice 4-61. 120 mi 2. 60 mi 3. 310 mi 4. 5 in. 5. in. 6. 3 in. 7. 1 in.:25 mi 8. $31.44 9. 14 oz 10. 21.6 cm 11. $6.12 12. 1 in.: 444.4 ft13. 9 gal
Guided Problem Solving 4-61. 6 in. � 8 in. 2. 300 ft � 400 ft 3. the scale of the drawing4. c 5. Divide both parts of the ratio by 6. 6. The scale usedin the model can be expressed as 1 in. � 50 ft. 7. You couldhave used the ratio to compare the lengths of therectangles instead of their widths. 8. The scale is 1 in. � 4 ft.
Practice 4-71. 78 ft 2. 62 ft3. < 13.3 m 4. 68.75 km 5. 32 m 6. 8 ft 7. 5 ft 6 in. 8. 33 ft 4 in. 9. 75 ft 10. < 13.3 m
Guided Problem Solving 4-71. 221 ft. 2. 189 ft 3. 29 ft 4. the height of the tree 5. 6. 7. h � 34 ft 8. Since the triangles are similar, you can set up a proportion and solve for the variable. 9. 1.169; 1.169; yes; thequotients should be the same.
10. ; ;
6.5x � 4(35.75); x � 22 ft
Chapter 4A Graphic Organizer1. Applications of Proportions 2. 7 3. Using a Variable 4. Check student’s diagrams.
Chapter 4B Reading Comprehension1. strong 2. F4 and F5 3. 190 to 230 4. F0 and F1 5. 100% – (75% + 1%) = 24% 6. 66. % 7. 8. a
5. < 4 6. The ratio of H to J is equal to the ratio of Kto L. 7. The square root of nine is equal to three. 8. TriangleDEF is similar to triangle TUV. 9. Triangle EFG iscongruent to triangle MNP. 10. The perimeter of a rectangleis equal to twice the length plus twice the width. 11. The ratioof four to six is equal to the ratio of x to 3.
Guided Problem Solving 5-31. 27 2. 25 3. 44% 4. the percent of females in the originalclass 5. 44% � 25 � 11 6. 13 7. 14 8. 0.5185 9. 51.9%10. You could then find the original number of males, subtractfrom the total to get the number of females, and then find thepercentage. 11. 63.5%
Guided Problem Solving 5-41. 2% royalties; $53,000 in royalties 2. How much did heralbum earn in sales if she made $53,000 in royalties? 3. whole4. part � percent � whole 5. Move the decimal point twoplaces to the left. 6. 53,000 � .02w 7. $53,000 � 0.02w; w �$2,650,000 8. Yes, 53,000 � 0.02 � 2,650,000 9. 0.03 � whole� $225; whole � $7,500
Guided Problem Solving 5-61. $22.99 2. 40% 3. $45.00 4. the number of DVDs that canbe bought at the sale price 5. $13.79 6. 3.26 7. You cannotbuy part of a DVD. 8. 3 9. $13.79 � 3 � $41.37; yes; no 10. $4.99 � 0.35 � $1.75; $4.99 � $1.75 � $3.24; $3.24 � 3 �$9.72; yes, Ethan can afford all three books, because $9.72 isless than $10.00.
Practice 5-71. $18.00 2. $14.00 3. $37.28 4. $500.00 5. $442.00 6. $13.137. $125.00 8. Julie will earn more. 9. $220.00 10. $245.0011. $6,390.00 12. $1783.52 13. $115.00 14. $4808.96
Guided Problem Solving 5-71. $500 2. 36 months or 3 years and 5.36% 3. Find the finalbalance. 4. I � prt 5. years 6. I � $500 � 0.0536 � 3 � $80.407. $500 � $80.40 � $580.40 8. I � $580.40 � 0.0536 � 3 � $93.339. $580.40 � $93.33 � $673.73 10. No; the reinvested amountalready accrued interest. 11. Mrs. Smith; by $271�$262 � $9
Chapter 5A Graphic Organizer1. Applications of Percent 2. 8 3. Estimating the Answer 4. Check students’ diagrams.
Chapter 5B Reading Comprehension1. the characteristics of Earth 2. 3,963.1 miles 3. 4 4. It bulges at the equator. 5. 6. 1% 7. 158C 8. 598F
Chapter 5C Reading/Writing Math Symbols1. 6 % 2. nXYZ ~ nABC 3. 39% ≈ 4. >5. = 25% 6. > 45% 7. segment AC 8. the ray starting at C and passing through B 9. the point that corresponds to A�10. the angle with B� as its vertex 11. Segment AC is congruentto segment A�C�.
Chapter 5D Visual Vocabulary Practice1. balance 2. sale price 3. probability of an event 4. markup5. outcome 6. simple interest 7. sample space 8. interest rate9. percent
Chapter 5E Vocabulary CheckCheck students’ work.
Chapter 5F Vocabulary Review1. percent 2. original 3. solution 4. outlier 5. equation 6. principal 7. median 8. markup 9. absolute value 10. sample space 11. proportion 12. variable
Course 3: All-In-One Answers Version A (continued)
Practice 6-51. x # 1 2. x $ �3 3. x $ �2 4. x $ 1 5.
6.
7.
8.
9. m . �4
10. q # 5
11. w . �3
12. y , �1
13. x � 8 , 24; x , 16, less than 16 in.14. 235 � n . 462; n . 227, more than 227 points
Guided Problem Solving 6-51. more than $500 2. balance greater than $500; balance of$516.46; you write a check for $26.47 3. The amount of depositthat will allow you to avoid a fee. 4. 516.46 � 26.47 � d 500 5. 489.99 � d 500; d 10.01 6. more than $10.01 7. No, the balance has to be greater than, not equal to $500.8. c � 580 � 642 � 2,000; c � 778; no more than 778 calories
Practice 6-61. m . �4
2. j # 0
3. v . 4
4. b , 8
5. a . �2
6. c # �18
7. c , �6
8. i $ 4
9. d , �15
10. d , �12
11. n $ �5
12. p # 2
13. 5b # $20; $414. 5p # 50; 10 pages 15. 8t $ 125; at least 16tables
Guided Problem Solving 6-61. The lowest price; $182.89; $6.85 per hour 2. the number ofhours your brother needs to work to purchase the DVD player3. Multiply his wage rate, $6.85 per hour times the number ofhours, h. 4. 6.85 � h � $182.89 5. Divide $182.89 by $6.65; h� 26.7 hours 6. No, he would only have $178.10. Yes, he wouldhave $184.95. 7. 8p � 9(4); p � 4.5, so p � 5 pizzas
Chapter 6B Reading Comprehension1. 13 days 2. 1.7 � 104 mi 3. 52 miles per hour 4. 5.5 � 105
5. 2.9 � 104 ft, 1.7 � 104 mi 6. 5.5 � 105 ft3 7. = 8. a
Chapter 6C Reading/Writing Math Symbols1. D 2. F 3. B 4. A 5. E 6. C 7. 91% ≈ 8. 0.015 �103 < 20 9. (8 + x)3 10. 5% < 0.060 11. three thousandths times ten squared is equal to thirty percent 12. eighty-onepercent is approximately equal to four fifths 13. the quantityof a number plus five is greater than or equal to negative two
Guided Problem Solving 7-11. identify angle types and measures of angles 2. The measuresof two vertical angles are the same. 3. two angles with a commonvertex and a common side but no common interior points 4. Yes;they share side BL. 5. adjacent angles 6. /RBT and /KBL;/TBL and /RBK 7. 140� 8. /KBL or /LBK 9. /KBDor /LBT 10. 64 � x � 140; x � 76 11. Sample answer:m/LBD � m/DBK � m/TBR; 64 � 76 � 140; 140 � 14012a. vertical 12b. 20�
Practice 7-21. adjacent 2. vertical 3. corresponding 4. none of these 5. /1 and /3; /5 and /7; /2 and /4; /6 and /8 6. /2 and /7;/3 and /6 7. 858, 958, 858, 858 8. 608, 1208, 608, 1208
9. 908, 908, 908, 908 10. Sample answer: No; you could measure/1 and /7 (corresponding angles) to see if they are congruentor measure /2 and /7 (alternate interior angles) to see if theyare congruent.
Guided Problem Solving 7-21. Alternate interior angles lie within a pair of lines and onopposite sides of a transversal. 2. Find the measure of eachnumbered angle and sum of the angle measures of the triangle.3. angle 1 and the 80� angle; angle 3 and the 60� angle 4. The measures are the same. 5. 80� 6. 60� 7. straight 8. 180� 9. 180� � (80� � 60�) � 40� 10. 180�11. m�1 � m�2 � m�3 � 80� � 40� � 60� � 180�12. m�1 � 60�; m�2 � 50�; m�3 � 110�; m�4 � 110�
Practice 7-31. yes; nJKL > nVUT; SSS 2. no; not enough informationgiven. 3. yes; nABC > nEDC; ASA 4. yes; nWXY >nZYX; SAS 5. yes 6. yes 7. no 8. nCAB; SSS 9. m/X� 1138, m/Y� 378, m/Z � 308, � 27 cm, � 59 cm,
� 43 cm
Guided Problem Solving 7-31. SSS, SAS and ASA 2. Use the Pythagorean Theorem.3. 0.22 km 4. Yes; by SAS.5.
6. 0.13 km 7. 0.22 km 8. Subtract 0.13 km from 0.22 km; 0.09 km9. Sample answer: by SSS, using the Pythagorean Theorem.10. SAS; x � 67�, y � 43� and z � 8.2 m
Practice 7-41. parallelogram; opposite sides are parallel. 2. rectangle;there are 4 right angles. 3. square; there are 4 congruent sidesand 4 right angles. 4. rhombus; there are 4 congruent sides.5. rectangle; there are 4 right angles. 6. parallelogram; SincenABC < nCDA, /ACB < /CDA and /BAC < /DCA.So opposite sides are parallel using alternate interior angles.7. acute equilateral; all sides congruent 8. acute scalene; nosides congruent and all angles less than 908 9. right scalene;right angle and no congruent sides
Guided Problem Solving 7-41. parallelogram 2. Two pairs of opposite sides are parallel.3. The lengths of the opposite sides are equal. 4. the coordinatesof the fourth vertex 6. no 7. 5 units 8. (6, �1) or (-4, -1) 9. yes 10. (5, 5) or (9, 5)
Guided Problem Solving 7-61. the area of the floor, the number of cases needed, and the costof the tiles 2. square, rectangle, triangle and trapezoid 3a. square:144 ft2; rectangle: 8 ft2; triangle: 10 ft2; trapezoid: 27 ft2 3b. 189 ft2
4. < 4.30; 5 cases 5. $195.80 6. over 7. area largerectangle � 288 ft2; area small rectangle � 12 ft2 ; total area = 300 ft2; 1 gal of paint
Practice 7-71. C < 37.70 cm; A < 113.10 cm2 2. C < 25.13 in.; A < 50.27 in.2
3. C < 141.37 m; A < 1,590.43 m2 4. C < 56.55 m; A < 254.47m2
5. C < 135.09 ft; A < 1,452.20 ft2 6. C < 791.28 km; A <49,875.92 km2 7. 220 cm 8. 88 cm 9. 110 in. 10. r < 10.82 cm;d < 21.65 cm 11. r < 23.87 m; d < 47.75 m 12. r < 34.70 in.;d < 69.39 in. 13. A < 3.43 in.2
Guided Problem Solving 7-71. circle 2. the area of the bottom of the pool 3. thecircumference of the pool, 63 ft 4. A � pr2 5. C � pd or C� 2pr 6. 63 ft < 2(3.14)r; r < 10.03 ft 7. A < (3.14)(10.03)2;A < 315.9 ft2 8. 63 ft < 3.14d; 20.06 ft < d; A � pr2; A <(3.14)(10.03)2; A < 315.9 ft2 9. A � pr2; 452.2 ft2 < 3.14r2; r< 12 ft; C � 2pr; C < 2(3.14)(12); C < 75.4 ft
Practice 7-81–8. Check students’ constructions.
Guided Problem Solving 7-81. A trapezoid is a quadrilateral with exactly one pair ofparallel sides. 2. congruent angles, parallel lines; parallel lines3. One pair of sides; No, the sides can be any length. 4. No;no; there are no restrictions on the angles. 5. Sample answer:Construct a pair of parallel lines. 6. Sample answer: Choosetwo points A and B on the first line, then choose two points Cand D on the second line, such that and are notcongruent. Draw and to form the other two sides.7. Check students’ constructions. 8. Sample answer: Draw asegment . Draw another ray with endpoint P to form anacute angle, /P. Construct /Q congruent to /P, so that thesides of /P and /Q intersect to form a triangle with .Since the two angles are congruent, this is an isosceles triangle.
Chapter 7B Reading Comprehension1. 69 bones 2. 27 bones 3. 7 : 12 4. approximately 4% 5. 56 bones 6. approximately 25% 7. to help support thebody and protect its internal organs 8. b
Chapter 7C Reading/Writing Math Symbols1. The measure of angle 1 is equal to 50 degrees. 2. angle JKL3. Line a is parallel to line b. 4. Segment GH is congruent tosegment LK. 5. Angle R is congruent to angle T. 6. Line ABis parallel to line CD. 7. ray AB 1. t raised to the fifth power9. Line AB is perpendicular to line JK. 10. AB = SR11. /STU 12. || 13. m/JKL = 43º 14. /R > /Y15. x6 16. TY 17. m/ABC + m/XYZ = 90º
Guided Problem Solving 8-11. rectangular pyramid 2. lines that lie in the same plane andhave exactly one point in common 3. lines in the same plane thatnever intersect 4. lines that are neither parallel nor interesecting5. Check students’ work. 6. They would cross. 7. intersecting8. skew; parallel 9. They are intersecting lines. 10. skew
.Course 3: All-In-One Answers Version A (continued)
Practice 8-21. 2.
3.
4.
Guided Problem Solving 8-21. Draw a base plan for the set of stacked cubes. 2. A baseplan shows the shape of the base and indicates the height ofeach part of a solid. 3. c 4. b 5. 1, 2, and 3 6.
7. Make sure that the front and right are labeled and theheights are correct.8.
Practice 8-31. 6 rectangles 2. 1 pentagon and 5 triangles 3. 1 rectangleand 2 circles 4. 4 triangles 5. 1 circle and 1 part of a circle 6. 6 rectangles and 2 hexagons 7.
Guided Problem Solving 8-31. all the faces of the box 2. 7 feet 3. the number of boxes thatcan be stacked on top of one another to fit in the cargo space4. The label, “this side up” with the arrow, must be pointingupward. 5. 16 inches 6. 7 � 12 � 84 inches 7. 84 16 � 5.258. 5 boxes 9. Check students’ answers. 10. No; though thebox is tall enough, the vase diameter (10 in.) will not fit the boxopening (11 in. � 9 in.).
Guided Problem Solving 8-51. no 2. the student’s mistake and the correct solution 3. Thediameter is used instead of the radius. 4. 4 cm 5. L.A. � prl� p(4)(7) � 28p < 87.92 < 88 cm2 6. Multiply the radius bythe slant height by 3 (as an approximation for p). (3)(4)(7) �84; 88 cm2 is reasonable since it is close to the estimate of 84cm2. 7. L.A. � p(3)(8) � 24p < 75 cm2
Guided Problem Solving 8-61. 6 in., 2.5 in., 4 in. 2. 240 boxes 3. V � lwh or V � Bh4. 6 � 2.5 � 4 � 60 in.3 5. multiplication 6. 240 � 60 �14,400 in.3 7. 1,728 in.3 8. Divide the total number of cubicinches by 1,728. 9. ft3 10. Use compatible numbers. Infeet, the dimensions of each crayon box are about ft, ft, and
ft, which gives a volume of about . Multiply 240 boxes
times to get 8 ft3. 11a. 1 � 5.5 � 8.75 � 48.125 in.3 ;
7. h � 7.2 m 8. h � 18.6 in. 9. h � 7.5 yd 10. s � 4.3 cm11. 21.6 ft3 12. No; the tin holds about 904 in.3 of popcorn,the box holds 896 in.3 of popcorn.
Guided Problem Solving 8-71. 15 ft3, 27 ft2 2. the height of the pyramid 3. V � Bh4. the volume and the base area 5. 15 � (27)h 6. h 7. 15 � 9h;
ft 8. Sample answer: Substitute the base area and height intothe formula. 9. 113.04 � (28.26)h; 12 ft
Guided Problem Solving 8-81. 12.5 in. circumference 2. C � 2pr 3. surface area of theterrarium 4. Solve the circumference formula for the radius.Substitute the result into the surface area formula. 5. about 2inches 6. S.A. � 4pr2 � 4p(2)2 7. 50 in.2 8. yes; yes 9. 50 ft2
Practice 8-91–6.
7. Sample answer: If the three dimensions of a rectangularprism are doubled, the new surface area is four times the oldsurface area. 8. 1,200 cm3; 700 cm2 9. 150 cm3; 175 cm2
10. 15,360 m3; 4,608 m211. 122,880 m3; 18,432 m2 12. It ismultiplied by 6.
Guided Problem Solving 8-91. Determine how much plywood would be needed for a similar
storage bin. 2. 78 ft2 3. 4. one-half the dimensions of the
original storage bin 5. 6. � 7. x � 19.5 ft2 of plywood needed 8. Sample answer: The amount of plywood neededshould be of the amount needed for the original storage bin.
of 78 is 19.5 ft2. 9. (2 in.)3/ (4 in.)3 � � ; x � 600; 600 in.3
Chapter 8B Reading Comprehension1. the shapes and uses for traffic signs 2. 8 sides 3. none 4. 5 sides 5. equilateral triangle 6. exactly one pair 7. 3 more sides 8. a
Chapter 8C Reading/Writing Math Symbols1. side-angle-side 2. angle-side-angle 3. side-angle or surfacearea 4. leg-angle or lateral area 5. side-side-side 6. Areaequals base times height; the area of a parallelogram. 7. Areaequals one-half times the base times the height; the area of atriangle. 8. Circumference equals π times the diameter; thecircumference of a circle. 9. Circumference equals 2 times πtimes the radius; the circumference of a circle. 10. Surface areaequals 2 times π times the radius squared plus 2 times π timesthe radius times the height; the surface area of a cylinder.11. Surface area equals π times the radius squared plus 2 times πtimes the radius times the slant height; the surface area of a cone.
Chapter 8D Visual Vocabulary Practice1. lateral area 2. base plan 3. surface area 4. skew 5. cone6. pyramid 7. prism 8. volume 9. cylinder
Chapter 8E Vocabulary CheckCheck students’ work.
Chapter 8F Vocabulary Review Puzzle
Chapter 9
Practice 9-11. 1.5; 2; 2; 2 2. 3. ; 1; 0; 12 3. 29.1; 29.5; 25, 30, and 35; 11 4. 8.1 ; 9; 9; 7 5. mode; data are non-numerical. 6. mode; dataare non-numerical. 7. mean; there should be no outliers.8. mean or median; use median if there are outliers. 9. 92 10. at least an 87 11. 85 12. 86
33
75x
18
14
14
x78
14
14
a2
b2
Original Size Doubled Dimensions
Dimensions (m) S.A. (m2) Dimensions (m) S.A. (m2) New S.A. 4 Old S.A.
.Course 3: All-In-One Answers Version A (continued)
Guided Problem Solving 9-11. 5 tests 2. 1 test 3. mean and median 4. Add the scores anddivide by the total number of scores. 5. 425 points 6. 6 tests7. 522 points 8. 97 points 9. 78, 83, 83, 89, 92 10. Averagethe two middle scores. 11. 170 12. 87 13. Yes; mean [89, 92,78, 83, 83, 97] � 87; median [78, 83, 83, 87, 89, 92] � 85 14. 147
Practice 9-21.
2.
3.
4.
5.
Guided Problem Solving 9-21. gold 2. 2002 winter games 3. 8 4. line plot 5. number ofmedals from 4 to 12 7. with a mark above each number foreach country with that number of medals 8.
9. Sample answer: Distribution of Gold Medals at the 2002 Winter Olympic Games 10. No; it matches the numberof countries listed in the table.11.
Practice 9-31. 6 2. 9 3. 5 4. common factors: 1, 3, 9; GCF: 9 5. 6 6. 16
Guided Problem Solving 9-31. 15 2. the probability a student takes only math 3. The twocircles represent students who take English and Math. See whatnumber is in the circle for math but not in the overlap.4. Check students’ diagrams. 5. 5 6. 9 7. 4 8. 11;
9. 6; P (math only)� � 10. 15; yes 11. 5
Practice 9-41–5. Sample answers given: 1. Sault Ste. Marie Star orSarina Observer 2. Kingston Whig Standard 3. 1.5 4. The graph begins at 60,000. This makes the value appearfarther apart than they are.5.
Guided Problem Solving 9-41. line graph 2. that the recycling rate has stayed about thesame 3. b 4. 5. yes
6. Sample answer:
Practice 9-51. 10, 11, 12, 13 2. 4, 5, 9, 9 3. 115; 104 and 115 4. 23; 24 5. 8.1; 8.2 and 6.3 6. 586; no mode 7. 72.38 8. 638 9. 698
Course 3: All-In-One Answers Version A (continued)
Guided Problem Solving 9-51. make a stem-and-leaf plot of the data 2. the median andthe mode of the set of data 3. least: 6; greatest: 27 4. 0, 1, and 25.
.Course 3: All-In-One Answers Version A (continued)
6.
Guided Problem Solving 9-81. 81 2. circle graph 3. 100% 4. four 5. Divide the students thatchose each lunch by the total number of students surveyed and
3. line graph, shows change over time 4. bar graph, comparesquantities 5. scatter plot, shows a relationship between sets ofdata 6. circle graph, compares parts of a whole
Guided Problem Solving 9-91. why a circle graph is not a good choice to display the data2. an appropriate graph for the data 3. change over time 4.line graph; a line graph shows change over time, a histogramdisplays frequencies
5. 7. yes
8.
Chapter 9A Graphic Organizer1. Using Graphs to Analyze Data 2. 9 3. Measuring to Solve4. Check students’ diagrams.
Chapter 9B Reading Comprehension1. PVC pipe and fittings, and how they are joined 2. by theirdiameters 3. 135º 4. 4 5. 112 ° 6. a bend and a bend7. a
Chapter 9C Reading/Writing Math Symbols1. congruent to 2. greater than 3. absolute value of x4. greater than or equal to 5. equal 6. negative 4 7. multiply8. divided by 9. percent 10. angle 11. not equal to 12. square root 13. The ratio of R to L is equal to the ratioof S to T. 14. Triangle ABC is similar to triangle DEF.15. arc BC 16. Volume equals length times width timesheight. 17. Area equals base times height. 18. Circumferenceequals π times diameter.
Guided Problem Solving 10-11. Sample answer: There is one favorable event out of fourpossible outcomes. 2. the odds in favor of the event occurring3. four 4. the number of favorable outcomes 5. the number ofunfavorable outcomes 6. 1 : 3 7. Write the first number in theodds over the sum of both numbers or 8. � , sothe odds in favor are 3 : 5
Guided Problem Solving 10-21. Predict the number of favorable outcomes. 2. Sampleanswer: There are four favorable outcomes out of five possibleoutcomes. 3. all outcomes 4. � 5. 500 � 5x 6. 100 � x7. yes 8. 56
Practice 10-31. shoppers in a mall who are at least 16 years old 2. 909 never,606 occasionally, 505 regularly 3. 2,020 people 4. No, there isnot enough information to determine whether or not the surveywas random. 5. The question makes one type of package seembetter than another. 6. The question makes shortened schooldays seem inferior. 7. No; people who work full-time are morelikely to shop after work than midday. 8. Sample answer:Some things to consider are using good questions, getting alarge enough random sample, and avoiding biased questions.
Guided Problem Solving 10-31. the group of people that are surveyed 2. the experimentalprobability of a customer choosing the $20,000-$24,000 range3. randomly selected people who registered a car during the year4. people who registered a car during the year 5. P(event) �
6. P(event) � 7. yes 8. femalefitness club members aged 35–44
Practice 10-41. 2. 3. 4. 5. 6. 7. 8. 9. ;
independent 10a. 10b. 11.
Guided Problem Solving 10-41. Find the probability of winning the carnival game both times.2. independent 3. six 4. six 5. 6. 7. � � 8. no9. ? �
Guided Problem Solving 10-51. 25 2. three 3. the number of possible arrangements of thethree winners 4. 25 dogs 5. 24 dogs 6. 23 dogs 7. 25 ? 24 ? 23or 13,800 arrangements 8. 25P3 � 25 ? 24 ? 23 � 13,800arrangements 9. 10 ? 9 ? 8 ? 7 ? 6 � 30,240 numbers
Practice 10-61. 9 2. 70 3. 330 4. 1 5. 84 6. 924 7. 120 8. 6 9. 70 10. 210ways 11. 490,314 ways 12. 5,005 ways 13. 495 combinations14. 10,626 committees 15. B, J; B, E; B, M; B, X; J, E; J, M; J, X;E, M; E, X; M, X 16. 8C3
Guided Problem Solving 10-61. six 2. two 3. no 4. nCr � 5. 6C2 � � � 15
6. 6C4 � � � 15 7. Only two people can get on the plane, leaving four people who cannot get on the plane.While the combinations change there are still only six people,and the order of the selection of two people does not matter.
8. � 18,564
Chapter 10A Graphic Organizer1. Probability 2. 6 3. Answering the Question Asked 4. Check students’ diagrams.
Chapter 10B Reading Comprehension1. squid have two large tentacles in addition to their eightarms, while octopi do not 2. 2 : 8, or 1 : 4 3. 399.52 kg 4. 20.13 m 5. 5 in. 6. about 3 and three tenths feet 7. about5,280 ft 8. a
Chapter 10C Reading/Writing Math Symbols1. C 2. E 3. D 4. B 5. A 6. 5! � 3! 7. P(not X) 8. 6!, or6 � 5 � 4 � 3 � 2 � 1 = 720 9. P(5, then 2) 10. 36P411. 52C7
Chapter 10D Visual Vocabulary Practice1. dependent events 2. permutations 3. experimental probability4. combinations 5. random sample 6. counting principle 7. independent events 8. population 9. theoretical probability
Chapter 11Practice 11-11. 23, 28, 33; start with 3 and add 5 repeatedly 2. 112, 224, 448;start with 7 and multiply by 2 repeatedly 3. , , ; startwith 32 and multiply by repeatedly 4. 2, �1, �4; start with 14and add �3 repeatedly 5. �13, �25, �37; start with 35 andadd �12 repeatedly 6. 0.3, 0.03, 0.003; start with 3,000 andmultiply by 0.1 repeatedly 7. 8.7, 9.1, 9.5; arithmetic; 0.4 8. 26, 33, 41; neither 9. 500, 250, 125; geometric; 10. 80, 77, 74;arithmetic; �3 11. 243; 729; 2,187; geometric; 3 12. 4.5, 0.75,0.125; neither 13. arithmetic 14. geometric 15. geometric16. 0, �5, �10, �15 17. �2, 1,4, 7
Guided Problem Solving 11-11. A sequence is a set of numbers that follows a pattern.2. An expression for the sequence. 3. Multiply the side lengthtimes itself 3 times.4.
5. Cube the side length. 6. n3; where n is the side length 7. n3
8. Substitute numbers into the expression. 9. 4, 9, 16, 25; n2
Practice 11-21. a 2. f 3. d 4. c 5. b 6. e 7. Sample answer: 8. Sample answer:
9. Sample answer:
Guided Problem Solving 11-21. the lengths of the other sides increase as well 2. A � s2
Guided Problem Solving 11-31. cost and the number of fruits mixed in 2. the cost of asmoothie with 4 different fruits mixed in 3. addition andmultiplication 4. 1.50 + 0.50n 5. f(n) � 1.50 + 0.50n6. f(4) � 3.50; $3.50 7. Sample answer: Multiply $.50 timesfour then add the $1.50, you will get the same answer.8. f(x) � 4.5 + 0.75x; $9
Course 3: All-In-One Answers Version A (continued)
Guided Problem Solving 11-41. Determine which roof is steeper. 2. the slope 3. graph lineswith the given slopes on a coordinate plane 4. slope �5. y 6. x 7.
8. the one with a rise of 8 and a run of 4 9. The greater the slope,the steeper the line. 10. the ramp that has a run of 4 and a rise of 6
Practice 11-51. Sample answer: 2. Sample answer:
3. 4.
5. 6.
7. 8.
Guided Problem Solving 11-51. h � height (in centimeters), t � time (in hours) 2.
3. how long the candle has burned in hours 4. how tall thecandle is in centimeters 5. 8 centimeters; it is where the graphstarts on the y-axis. 6. The candle can burn for 16 hours. It iswhere the graph crosses the x-axis. 7. Substitute the answers inthe original formula. 8. 6 months
Practice 11-61. f(x) � 50 � 3.5x; x � number of tote bags; f(x) � expensesfor the day 2. f(x) � 150 � 45x; x � number of appliances sold;f(x) � total pay 3. f(x) � 3x � 2 4. no 5. f(x) � �x � 3 6. no7. f(x) � x 8. f(x) � x � 1 9. f(x) � x � 1 10. f(x) � x � 2
Guided Problem Solving 11-61. A caricature is a cartoon portrait of someone. 2. $30; $2 3. f(c) � 30 + 2c4.
5. 12 caricatures; f(12) � 54 6. Substitute $54 into theexpression, and solve for c. 7. f(b) � 25 + 0.50b
Chapter 11B Reading Comprehension1. approximately 1,150 mi 2. approximately 2 hours 3. approximately 80% 4. the southern route 5. March 6. 14,079 min 7. 10 days, 5 hour, 21 minutes longer 8. –99°F9. a
Chapter 11C Reading/Writing Math Symbols1. the probability of event B occurring 2. the probability ofevent A not occurring 3. Angle S is congruent to angle R.4. n factorial, or n � (n – 1) � (n – 2) � … 1 5. the numberof ways 8 items can be selected 3 at a time, where order doesnot matter 6. y is less than fifteen. 7. The sum of negativesixteen and the square of four is equal to zero. 8. x less thantwelve, or the difference of twelve and x 9. The square root ofsixty-four is eight. 10. The absolute value of negative forty-one is forty-one. 11. Three fourths is equal to seventy-fivepercent. 12. A function of has output values three greaterthan each input value. 13. Triangle ABC is congruent totriangle DEF. 14. Pi is approximately 3.14. 15. The ratio ofthree to four is equal to the ratio of nine to twelve.16. The square root of forty-eight is approximately seven.17. Area equals the product of base and height.
Chapter 11D Visual Vocabulary Practice1. y-intercept 2. parabola 3. slope of a line 4. quadraticfunction 5. geometric sequence 6. common ratio 7. arithmetic sequence 8. slope-intercept form 9. term
Guided Problem Solving 12-21. 12x2 + 4x; 6x2 � 12x 2. Subtract the polynomials to fit thearea of the deck around the pool. 3. 12x2 + 4x 4. 6x2 � 12x5. Add the opposite of each term in the second polynomial.6. 12x2 + 4x � (6x2 � 12x) 7. 12x2 + 4x � 6x2 + 12x8. 12x2 � 6x2 + 4x + 12x 9. 6x2 + 16x 10. Sample answer:Substitute numbers in each expression, simplify and subtract tosee if you get the same answer as the simplified form.11. 16x2 + 6x � (4x2 � 5x) � 12x2 + 11x
Practice 12-31. 37 2. 17 3. a3 4. (�y)5 5. (3x)2 or 9x2 6. 4.510 7. 38
Guided Problem Solving 12-41. Find the area of the figure. 2. Parallelogram 3. A � bh4. 2x + 1 5. 2x 6. A � 2x(2x + 1) 7. Use the distributiveproperty. 8. 4x2 + 2x 9. You could use the area model tomultiply a monomial by a binomial. 10. 3x(8x + 5) � 24x2 + 15x
Guided Problem Solving 12-51. the Sun’s 2. how many times larger the Sun’s diameter isthan Earth’s diameter 3. the exponents 4. subtract 5. 106 � 104 � 102; 102 � 100 6. about 100 7. Find the exactnumber of times the Sun’s diameter is greater than the Earth’s.1.09 � 102, or 108, is approximately 100. 8. about 1,000,000seconds; 1012 106 � 106; 106 � 1,000,000
Chapter 12A Graphic Organizer1. Polynomials and Properties of Exponents 2. 5 3. Working Backward 4. Check students’ diagrams.
Chapter 12B Reading Comprehension1. 23 years 2. more than 2.3 � 106 3. 2.5 tons 4. about 5,750,000, or 5.75 � 106, tons 5. 745 ft by 745 ft 6. square pyramid 7. 555,025 ft2 8. a
Chapter 12C Reading/Writing Math Symbols1. G 2. F 3. E 4. D 5. A 6. B 7. C 8. 5(n + 3)
