Chapter 4 Answers

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Chapter 4 AnswersPractice 4-11. 3 1; -3 2. 3 4; 5 3. 2 3; 12 4. 3 3; q5. 3 2; 4 6. 1 4; -417.6 8.3 5.4 8.7 4.0 6.6 3.5d9.5 5.1 4.5 6.4 2.6 5.1 2.78. 2 7 9. 9.5; percent unemployment in construction inJune, 1996 10. 6.6; percent unemployment in services inJune, 1992 11. Answers may vary.3900 3300Sample: M 5 400 150 § 12. 3 21005013. number of days lost to strikes per 1,000 employees inGreece in the given years 14. number of days lost to strikesper 1,000 employees in the United States from 1990 to 1994All rights reserved.7. cPractice 4-21. a 5; b 5 2 7 ; c 12; d 7 2. c 5 5 ; y -7;23x 4; z 5 7 ; a -3; b 0 3. x 3; z -2237 5623 580 7693 824. M 5 ;F 5 87 1020 346 2718 29 Pearson Education, Inc., publishing as Pearson Prentice Hall.14 22293 2622 3 6. cd5. M 2 F 5 87 682 0212 222725 262222812 § 8. 265 § 9. 24 §4 212 21824 222388 11227 101 2221 24d10. 13 14 § 11. 219 93 21 § 12. c044 1128 21 200 24 3d 14. not equal; dimensions are different24 22 515. equal; dimensions and corresponding elements are equalPractice 4-31d721d220 27. product undefined 8. 22 1 § 9. product undefined21 0163 23 2110. c d 11. cd202 224Algebra 2 Chapter 41 21221 18. c0.5 20.5 22.5d2.5 22.5 25.519. product undefined 20. product undefined1 2 3 471 3421. 3 3 4; 2 4 6 8 § 22. 2 3 2; cd49 563 6 9 12724 523. 2 3 2; cd 24. 605 40213 19 2825. 224 42 214 § 26.25 8 232472 §212c11 1021 1 1d 27. 11 10 §26 5 511 108238 14 14 12351 2428. 16 8 8 10 § 29. cd 30. DT117 555 2218 18 20 1432231. C 20 S431. c4444 2335 5 22d 2. cd22 22206 2466 24.566 21dd 4. c3. c24 28 263 2302 2202 22 0d 6. cd5. c44 2324 24 322 2033 2411 26d 8. cd 9. cd7. c4 4 230 24 223 21122 21.54 4 23d 11. cd10. c1 21022 2012.6 2241. product undefined 2. cd 3. c60234 2114. difference undefined 5. cd 6. c31312. product undefined 13. c17. 3 23 21444Practice 4-47. 313. c0 0.415. product undefined 16. 20.4 0.2 §20.2013.yy64xx 6O 66 4O4 47 32 0d 14. cd0 20 2Answers39

Chapter 4 Answers14.15.y(continued)0.65 21.45 20.25. 20.81.40.4 § 6. no inverse0.4 20.2 20.2y44xx 44O 44 4422 0d0 120 22cd22 24 220d2Practice 4-5221. (0.251, 0.3, 0.07) 2. (0.7, -0.3, -0.2) 3. (1, 5, -5)4. (2, 1) 5. (2, 1, -9) 6. (3, 2) 7. (-5, 15, 21) 8. (-1, 0)9. (0, 6, 2.8) 10. (-2, -1) 11. (-1, 7, -3) 12. (4, 2, -8)coefficientvariableconstant6 913. cd4 13xc dy c36d214. cxc dy c29d243 24d0741 112122121. 1§ 2. 1221 3. c0 1213d 4. cd21 21 221 2166234257 5. cd 6. cd 7. 1 213 2411888. No inverse; the determinant of the matrix is zero.2 3 221051§ 10. 9. 321222 5 232123414. -1 15. -21 16. 14 17. -29 18. 9 19. 3620. yes 21. yes 22. yesPractice 4-663 21 2132§4 22 211. 21 25 23 § 2. 2622 27 2429 11193. 1 21 22 § 4. no inverse5 26 210Answers0 21x920§ y§ 17 §1 21 12z3x1y 5 548,30316. e;0.2553415x 1 0.1167209y 5 110,017(331,975.0482, 216,327.9518); about 331,975 doctors15. 1217. ex1y550; (20, 30);425x 1 550y 5 25,00020 one-bedroom and 30 two-bedroom apartments3 , 233 b 19. a8, 4 b 20. no unique solution18. a 1731721. (4, –32) 22. det A 10, has a unique solution23. det A 0, no unique solution 24. det A -5, has aunique solution11. no inverse, cannot be solved 12. c d 13. c d403Practice 4-7210 214 03017. 17 cd 5 c214 270 722 2120 2200018. cd 1 cd 50 22022 22 220 21 20 220 219. cdcd 5 c210 0 22022 010234O 43412. 39 13. -47 14. -7 15. 9 16. 26 17. -4218. no 19. yesx2220.60 20.220.4 20.4 20.10 20.50 § 8. 0.20.50.2 §20.400.220.10.2 20.19. 25 § 10. 1 § 11. no inverse, cannot be solvedy 47. All rights reserved.16.OPractice 4-81. e4x 2 2y 5 312x 1 6y 5 242. e6x 1 11y 5 92x5 222x 1 9y 2 2z 5 203. 3x 2 y 1 2z 5 29 4. (2, -3) 5. (6, 2)6x 1 5y 1 5z 5 246. (-3, 2) 7. (0.9, 0.08, 0.3) 8. (0.25, 0.75, 0.5) 9. (3, 1, -2)10. c234 281 3 230 d 11. c d2 28 164 111 241 292 23 † 9 § 13. (-6, -8, 14) 14.(9, -3, -6)12. 3402 2415. (7, 1, 0) 16. (2, 6, -4) 17. (-1, 7, 0.5) 18. (-4, 3, 9)19. (5, 8, -2) 20. (1, 7, -9) 21. (-2, 3, 5)Algebra 2 Chapter 4 Pearson Education, Inc., publishing as Pearson Prentice Hall. 4

Chapter 4 Answers(continued)Reteaching 4-11. Answers may vary. Check students’ work.2. Trial12 3 4Left 36 24 26 55cdRight 15 43 22 463. Check students’ work.3. A9B9C9D9 c24 26 23 21d3675C yB 6D C4Reteaching 4-222325 121 211. cd 2. cd 3. cd14 221 21 224. cAll rights reserved.BA 1 1 21216 21 244.5 5.5d 5. cd 6. cd23 1 257 27 263 11.529729 26553.5 26.57. 01 § 8. 124 § 9. 1.5085217 2223.5525 23810. 3 22 24 §7 256x 6 4 2 A4. A9B9C9D9 c8B 64 Pearson Education, Inc., publishing as Pearson Prentice Hall.1 21 2 41. A9B9C9D9 cd221 2 0y CDD xB 2 A 22CA D 2 A241. c3 221 27 24d 2. cd 3. cd 4. no inverse7 525 9253283317331332331 227 § 7. 124 6. 322231 34 474 2§8. no inverse 9. 523224A 2. A9B9C9D9 cB D x5. C C Reteaching 4-5Reteaching 4-42y20 2628 31 3 3. f8 5 4g1. cd 2. 213 3326 1727 32422 0 3 5d4 7 8 6BReteaching 4-3BD223 25 22 0d2123 1B4C 2 4y CD AA 22Reteaching 4-61. -6 2. -21 3. 14 4. -50 5. 17 6. -3Reteaching 4-7D1. (2, 1) 2. (2, 1) 3. (-1, 0) 4. no unique solutionxReteaching 4-81. (-1, -1) 2. (-1, -2) 3. (-4, -14)Enrichment 4-1I think and think for months and years. Ninety-nine times,the conclusion is false. The hundredth time I am right.—Albert EinsteinAlgebra 2 Chapter 4Answers41

(continued)EUCLID OHIO301 5 1121 6 22 4 27 § ; 21 4 6 § ; cd;0 10 222 280 3 53 26 8524 2302 24 42§; 552 21 § ;0 23 11 2411 26 2621 2204 22 24 23 7 1 21 21 § ; 710 23 10 § ;10 22 2123 231 143 2742213 3 220 22 § ; 27 222§;49 23650 232150 24 2 25 215§5 2432Enrichment 4-31. The number of rows must be the same as the number ofcolumns.; so it can be multiplied by itself;0 0 0 0cd; cd ; A nonzero matrix may be nilpotent.0 0 0 0a 2 1 bc ab 1 bd2. cdac 1 cd bc 1 d 23. a2 bc 0; ab bd 0;ac cd 0; bc d2 04. b(a d) 0 5. b 0; a d 06. a2 0, so a 0; d2 0, so d 07. A 5 c0 00 00 bd ; A2 5 cd 8. cdc 00 00 0Enrichment 4-4y2 6 2Ox26 6Enrichment 4-51. ad - bc 2. eh - fg 3. adeh bcfg - bceh - adfg4. cae 1 bg af 1 bhdce 1 dg cf 1 dh5. (ae bg)(cf dh) - (af bh)(ce dg) adeh bcfg - bceh - adfg6. det(AB) det A ? det B42Answers7. The determinant of the product of two matrices is equal tothe product of the determinants.18. det I; 1; detA9. The determinant of the inverse of amatrix is equal to the reciprocal (inverse) of the determinantof the original matrix.Enrichment 4-61. det A a1(b2c3 - b3c2) - b1(a2c3 - a3c2) c1(a2b3 - a3b2) a1b2c3 - a1b3c2 - a2b1c3 a3b1c2 a2b3c1 - a3b2c1 a1b2c3 a2b3c1 a3b1c2- (a1b3c2 a2b1c3 a3b2c1)1 2 32. 25 3. 0 4. Answers may vary. Sample: 1 2 3 § ; 04 5 61 2d;05. Answers may vary. Sample: c1 26. Its determinant is zero.All rights reserved.Enrichment 4-2Enrichment 4-71. Let b equal the weight of the bread in the sandwich. Let mequal the weight of the meat in the sandwich. Let c equal theweight of the cheese in the sandwich. The three equations are:b m c 12e 0.6b 3m 1.5c 1.50(12)10b 50m 40c 30(12)5 lb bread; 3 lb meat; 4 lb cheese2. Let c, r, and s represent the number of pounds of chicken,rice and shellfish, respectively. The three equations are:c r s 181c 0.5r 3s 19e100c 20r 50s 85010 lb rice; 5 lb chicken; 3 lb shellfish3. Let y, t, and b represent the price per pound of frozenyogurt, topping, and bananas, respectively.The three equations are:2b 3t 4y 19-t y 1e1t y 0-4b 2frozen yogurt: 3.00/lb; topping: 2.00/lb;bananas: .50/lb4. Let b, y, and t represent the number of calories per poundin bananas, frozen yogurt, and topping, respectively. The threeequations are:e2b 3t 4y 54001t - y 0205b - 2t 2y frozen yogurt: 500 cal; topping: 1000 cal; bananas: 200 calAlgebra 2 Chapter 4 Pearson Education, Inc., publishing as Pearson Prentice Hall.Chapter 4 Answers

Chapter 4 Answers(continued)Enrichment 4-8 Checkpoint Quiz 21a. 2600, 24001. A9 (5, -5); B9 (6, -1); C9 (1, -4)2. A9 (4, -12); B9 (8, 4); C9 (-12, -8)3. A9 (1, 3); B9 (2, -1); C9 (-3, 2)4. A9 (-3, -1); B9 (1, -2); C9 (-2, 3)1.01x 1 y 5 50001b. e; 2589.64, 2384.463x 2 2y 5 3000x 1 0.99y 5 50001c. e; 2609.66, 2414.493x 2 2y 5 3000x 1 y 5 50001d. e; 2584.49, 2415.513.03x 2 2y 5 3000x 1 y 5 50001e. e; 2609.56, 2390.443x 2 2.02y 5 30001f. well-conditionedAll rights reserved.2a. 1, 50002b. e1.01x 1 y 5 5001; 1.00, 4999.993x 2 2y 5 29997x 1 0.99y 5 50012c. e; 21.12, 5030.183x 2 2y 5 29997x 1 y 5 50012d. e; 0.99, 5000.013.03x 2 2y 5 29997x 1 y 5 50012e. e; 20.92, 4980.083x 2 2.02y 5 299972f. ill-conditioned Pearson Education, Inc., publishing as Pearson Prentice Hall.Chapter ProjectActivity 1: OrganizingBTEX1 0.06 1 0.95 1 0.91 18.52 0.06 2 1.05 2 0.73 2 13.53 E0.35U , 3 E6 U , 3 E5.6 U , 3 E49 U ; Check students’ work.4 0.22 4 0.19 4 24 19.55 0.11 5 0.82 5 2.55 26Activity 2: Calculatingcombined amounts (mg/kg): 20.41, 15.34, 60.95, 21.91, 29.43BTEX1 0.01 1 0.90 1 0.85 1 18.452 0.01 2 1.00 2 0.68 2 13.453 E0.30U , 3 E5.95U , 3 E5.55U , 3 E48.95U4 0.17 4 0.14 4 1.95 4 19.455 0.06 5 0.77 5 2.45 5 25.95Activity 3: ResearchingCheck students’ work. Checkpoint Quiz 11. 2 3 2; 4 2. 1 3 3; 6 3. 3 3 3; 012 212205 § 5. c21525424 222167. 20 10 § 8. c321084. 10Algebra 2 Chapter 415 2310d 6. 21 18 §2526022 2112d 9. 47 § 10. C141 245. 27 21445212 6. 1 21365 2236 7. no inverse 8. c22d349. c15 4d 10. E 2 U0 1212Chapter Test, Form A85 234104 2272710771a. FV; 6 3 2 1b. 30 2. cd98302 24103 2181112923 20 22530 § 4. 621 2431886. product undefined 7. c03. 29 128a. c1429 230d12 § 5. c26312523d01 30d 8b. a 1 , 1 b , a 3 , 2b , a0, 2 5b2 2221 4 258c. (4, 3), (6, 6), (3, -3) 8d. (-1, -1), (-3, -4), (0, 5)8e. (1, 1), (4, 3), (-5, 0) 9. -13 10. -1 11. 5212. 1 213313. no inverse 121221 2142112 25 § 15. no inverse 16. cd14. 190 21222 17 22 262201d 18. cd 19. cd17. c22 1151 2226 211 114 2234 § 22. (0, -2)20. 21. 41 11 21223. (-2, -3, 4) 24. (-2, -2) 25. (0, 1, 3) 26. Answersmay vary. Check students’ work 27. Yes; Check students’work 28. 2 3 4 29. .75, 1.00Answers43

(continued)280245221a. F2512502582. c100134109V 1b. 6 3 2 1c. -451121161202 2525 27d 3. cd23 30522 34. product undefined 5. cd4 033 246a. cd 6b. a 3 , 1 b, a 3 , 22b, a21, 1 b4 4441 2816c. (-1, -1), (-1, -10), (-8, -1)6d. (-1, 3), (8, 3), (-1, -4)6e. (-1, -3), (8, -3), (-1, 4) 7. -2 8. 569. 3 25282112 10. no inverse11. c26 15 821 2592d 12. cd 13. cd2 21 316927 23223d 15. A 16. H 17. D14. c3128101 27d; cd ; no18. c10 2145 22319. the identity matrix with the same dimensions20. J 21. Child’s ticket: 8; Adult’s ticket: 12Alternative Assessment, Form CTASK 1 Scoring Guide:3 Matrix is constructed correctly. Student discussion isdetailed enough to indicate a clear understanding of theproperties of matrices. Addition, subtraction, andmultiplication operations are performed with nomistakes. Inverse matrix is correct or, if none exists,explanation is provided.TASK 2 Scoring Guide:a b c d1 2 2 1a. cd4 4 3 3b. c22 22 22 22d21 21 21 21c. matrix additiond. a9(-1, 3), b9(0, 3), c9(0, 2), d9(-1, 2)e. a9(2, 8), b9(4, 8), c9(4, 6), d9(2, 6)3 Student organizes vertices correctly into matrix. Matrixof the translation is written correctly. Correct answersare provided to all questions.2 Student organizes vertices correctly into matrix. Matrixof the translation is written correctly and correctanswers are provided to three of the last four questions.1 Student organizes vertices correctly into matrix.Translation matrix contains significant errors. Two orthree of the last three questions are answeredincorrectly.0 Student makes no attempt, or no response is given.TASK 3 Scoring Guide:1 2aa. C2 12a1 02121d2 S b. A A 5 AA 5 c0 1ac. No; matrix multiplication is not commutative.3 Inverse matrix is correct. Multiplication of AA21 andA21A gives I. Student indicates that multiplication ofmatrices is not commutative. Student discussion isdetailed and clear enough to indicate a clearunderstanding of the properties of matrices.2 Inverse matrix and multiplication are mostly correct butcontain minor errors. Student discussion is detailed.1 Inverse matrix and multiplication include errors. Two orthree questions are answered incorrectly.0 Student makes no attempt, or no response is given.2 Matrix is constructed correctly. Student discussion isdetailed. Addition, subtraction, and multiplication ofmatrices are mostly correct but contain minor errors.Inverse matrix contains minor errors or explanation isnot sufficiently detailed if no inverse exists.1 Matrix contains minor errors. Operations are attemptedbut include major errors. Inverse is not included, orexplanation as to why no inverse exists is not included.0 Student makes no attempt, or no response is given.44AnswersAll rights reserved.Chapter Test, Form BAlgebra 2 Chapter 4 Pearson Education, Inc., publishing as Pearson Prentice Hall.Chapter 4 Answers

Chapter 4 AnswersTASK 4 Scoring Guide:a. (1.25, -2) b. (-3, 1.5)(continued)c. (-9, 13, 6) d. (13, 8, 12)3 Student solves all systems correctly using inversematrices. Student shows the process for calculating theinverse and multiplying to solve X 5 A21B.2 Student solves two systems correctly and makes minorerrors in the solutions to the other systems. Studentshows the process and all calculations.1 Student solves one system correctly, while the otherscontain major errors.Cumulative Review1. C 2. H 3. A 4. F 5. C 6. G 7. D 8. G 9. D 10. J11. C 12. J 13. C 14. J 15a. ( 0, 0) 15b. a2 4 , 0b516a. -28 16b. 12 17. Answers may vary. Sample:preimage: (8, 4), (16, 8), (0, 0); image: (4, 2), (8, 4), (0, 0)18. Check students’ work. Pearson Education, Inc., publishing as Pearson Prentice Hall.All rights reserved.0 Student makes no attempt, or no response is given.Algebra 2 Chapter 4Answers45

3 S D 23 8 3 5 3 22 c T 51 24 117 55 d 8 141412 16 8 8 10 18 18 20 14 § 11 10 11 10 11 10 c § 2111 2655 d 213 19 28 224 42 14 25823 § 72 24 60 72 0 212 c § 45 54 d c 71 34 49 56 d 123 4 246 8 36912 § c 0.5 20.5 22.5 2.5 22.5 25.5 d 3 4 23 4 21 4 1 2 21 2 1 0

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