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Chapter 1
Practice 1-11. -4.2 2. 4 3. 4. 1 5. 6. 1.8 7. 6 8. 0.01 9.
10. = 11. 12. = 13. 14. 15. 16. 17. integer, rational, real 18. whole, integer, rational, real19. irrational, real 20. rational, real 21. natural, whole,integer, rational, real 22. rational, real 23. irrational, real24. integer, rational, real 25. Comm. Prop. of Add.26. Identity Prop. of Add. 27. Assoc. Prop. of Add.28. Inv. Prop. of Mult. 29. Dist. Prop.30. Comm. Prop. of Mult. 31. Identity Prop. of Mult.32. Inv. Prop. of Mult. 33. Inv. Prop. of Add.34. Assoc. Prop. of Mult.3538.
39. 40. -3; 41. ; 42. 4;
43. N: natural 44. H: rational; L: rational; n: natural45. t: rational; n: natural
Guided Problem Solving 1-11. An example that makes the statement false. 2. There maybe many valid counterexamples for each statement.3. Answers may vary. Sample: 4 is a whole number, but its reciprocal is not a whole number. 4. Answers may vary.Sample: 7 is a natural number, but its opposite -7 is not anatural number. 5. Answers may vary. Sample: 0 is a wholenumber, and since -0 = 0, the opposite of 0 is a wholenumber. 6. Answers may vary. Sample: The integer -1 has-1 as its reciprocal, so -1 is an integer whose reciprocal is aninteger. 7. Answers may vary. Sample: and - areirrational numbers, but their product -2 is a rational number.8. Answers may vary. They should be similar to counter-examples in (3) - (7). 9a. Answers may vary. Sample: 2 and5 are whole numbers but 2 - 5 =-3, which is not a wholenumber. 9b. Answers may vary. Sample: 5 is an integer, butits opposite -5 is not a whole number. 9c. Answers mayvary. Sample: 3 is a whole number but 32 = 9, which is not aneven number. 9d. Answers may vary. Sample:-1 is aninteger, but not a whole number. 9e. Answers may vary.Sample: 4 is a whole number and is 2, which is not anirrational number.
Practice 1-21. 7x 2. 14t - 5 3. -11a + b - 1 4. 2i + 7j 5. 12xy
6. 13x2 + 5x 7. 4m - 6 8. 9.
10. -a - 5 11. -8n2 - 16m 12. x2 - 2xy + y2
13a. 54 in.2 13b. 13.5 m2 14. $10.06 15. 85 16. 2617. -42 18. -1421 19. 10 20. 1 21. 32 22. 13
23. 186 24. 25 25. 0 26. -25 27. a + (a - b) + c + b +(a - 2c)+ b + c + (a - b); 4a
Guided Problem Solving 1-2 1. The number of eligible voters in millions in the UnitedStates from 1960 to 2000 2. The number of years since 19603. 28; about 180 million voters 4. 52, 60 5. about 242 millionvoters; about 263 million voters 6. -0.003y + 0.61 7. -0.0078y2 + 1.265y + 65.27 8. 20; about 87 million voters9. Answers may vary. Sample: Answers are reasonable.
10a. about 198 million eligible voters 10b. about 100 millionvoters
Practice 1-3
1.
2.
3.
4. ; no restrictions
5. ; a 2 b
6. x = t3 - 3; t 2 0 7. $20 and $35 8. 2.5 in., 6 in., 6.5 in.9. 41, 42, 43 10. 0 11. 1 12. 6 13. -1 14. 15. 1
16. 19 17. 18. Mikes bus: 35 mi/h; Adams bus: 55 mi/h
19. slower train: 50 mi/h; faster train: 100 mi/h 20. 81, 83, 85, and 87 21. length: 17 cm; width: 12 cm
Guided Problem Solving 1-31. $5000 2. $2000; $3000 3. 6%; 8% 4. P = 2000, r = 0.06,t = 1 5. $2120 6. P = 3000, r = 0.08, t = 1 7. $3240 8. $360 9. $746.40 10. Answers may vary. Sample:I = P(1 + r)t - P; Answers verify. 11. $26; $52.86
Practice 1-41. t -5
2. m 8
3. x -2
56 4321 0 4321
0 5 6 7 8 9 104321
56 4321 0 4321
152
274
x 5c(a 1 b)
b 2 a
x 5 94g 2 3
w 5 S 2 h 1 h
r 5 L 2 SL
h 5 3Vpr2
Year Eligible Voters1988 180 million2012 242 million2020 263 million
32t
2 1 2t13a 119b
!4
!2!2
14
214952
59
132
12; 2
25
3 2 1
1
0 321
0.532 2
23
76
Algebra 2: All-In-One Answers (continued)
75All-In-One Answers Algebra 2
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4. a
5. x -8
6. x
7. x 12
8. x
9. x -16
10. -3 x 2
11. x 2 or x 8
12. x -3 and x 6, or -3 x 6
13. x 1 or x 2
14. -3 x 5
15. -2 x -1
16. x -1 or x 3
17. x -1 and x 2, or -1 x 2
18. at least $450019. less than 35 ft20. more than 15 years old21. at least 1072 questionnaires22. between 10.3 lb and 12.8 lb23. at least 7.75 in. and at most 8.25 in.24. between 4 h and 4.8 h, or between 4 h and 4 h 48 min
Guided Problem Solving 1-4 1. between $700,000 and $750,000 2. $496,0003. 700,000 x + 496,000 750,000 4. 204,000 x 254,000 5. between $204,000 and $254,0006. $204,000 + $496,000 = $700,000; $254,000 + $496,000 =$750,000 7. between 18 hr and 25 hr
Practice 1-51. h - 8.3 2 2. a 2.5 3. x - 27.5 5.54. x -17 or x 7
5. k -16 and k 22, or -16 k 22
6. all real numbers
7. t -2 and t 12, or -2 t 12
8. x or x 2
54321 0 54321
23
223
42 0 2 4 6 161412108
54321 0 54321
20 10
16
0 20
22
3010
20 10
17
0 20
7
3010
54321 0 54321
54321 0 54321
54321 0 54321
4321 0 5 64321
54321 0 54321
4321 0 5 64321
0 5 6 7 8 9 104321
54321 0 54321
18 16 14 12 10 8 6
54321 0 54321
38
38
642 0 10 12 148642
54321 0 54321
12
212
56789 4321 0 1
56 4321 0 4321
72
272
Algebra 2: All-In-One Answers (continued)
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Algebra 2 All-In-One Answers76
9. b and b , or b
10. w or w 2
11. all real numbers
12. u -3 or u 3
13. -7, 7 14. no solution 15. 2 16. -27, 3 17. -21, 21
18. , 1 19. no solution 20. , 4 21. -3, 3
22. -4, 2 23. 24. no solution
25. x - 4.2 0.01; 4.19 x 4.2126. x - 3.5 0.002; 3.498 x 3.502
27. x - 10 ; x
28. T - 76 11; 65 T 8729. w - 40 0.25; 39.75 w 40.2530. d - 13.75 11.25; 2.5 d 25
Guided Problem Solving 1-5 1. Find a value for b that makes the equation true.2. distance 3. |4 - 8b| =-12 4. no 5. no solution6. For any value of b, the left side of the equality is negative.7. no solution
Practice 1-6
1a. , or 20% 1b. , or 40% 1c. , or 60%
1d. , or 80% 2a. < 0.42, or 42% 2b. < 0.21,
or 21% 2c. < 0.11, or 11% 2d. < 0.37, or 37%
3a. , or 50% 3b. < 0.33, or 33% 3c. < 0.17, or 17%
3d. < 0.83, or 83%4a. {$6, $11, $15, $21, $25, $30}; 6 outcomes
4b. < 0.17, or 17% 4c. 0 4d. < 0.33, or 33%
5. < 0.54, or 54% 6. < 0.67, or 67%
7. Answers may vary.; The experimental probability is expect-ed to be close to the theoretical probability
< 0.31, or 31%
8. Answers may vary.; The experimental probability is expected to be close to the theoretical probability
< 0.02, or 2%
9. , or 9% 10. < 0.03, or 3%
Guided Problem Solving 1-6 1. 1, 2, 3, 4, 5, 6 2. Answers may vary. Sample: (3,2)3. (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4),(2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3),(4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2),
(6,3), (6,4), (6,5), (6,6) 4. 36 5. 1 6. 7. 6 8.
9. Answers may vary. Experimental probabilities should beclose to theoretical probabilities. 10a. (H,H,H), (H,H,T),(H,T,H), (T,H,H), (T,T,H), (T,H,T), (H,T,T), (T,T,T) 10b. 8
10c. 10d.
1A: Graphic Organizer1. Tools of Algebra 2. Answers may vary. Sample: propertiesof real numbers, solving equations, solving inequalities,probability 3. Check students work.
1B: Reading Comprehension1. temperature scales 2. degrees of temperature 3. 18 years4. degree 5. 32 (the freezing point of pure water) 6. Fahrenheit used a mixture of salt and ice; Celsius used thefreezing point of pure water. 7. Answers may vary. Sample:No. There were 96 degrees between 0 F and normal bodytemperature. There are almost the same number of degreesbetween the freezing and boiling points of water. Since thedifference between the high and low temperatures on theCelsius scale is greater, Celsius degrees must be significantlygreater than Fahrenheit degrees. 8. b
1C: Reading/Writing Math Symbols1. 5 multiplied by 9 or 5 times 9 2. 1, 2, 3 and the patterncontinues in the same way. 3. 12 divided by 0.4 4. the square root of 7 5. |3| 6. x 8 or 7. w = 29 8. x5 9. 10. 2, 4, 6, . . .
1D: Visual Vocabulary Practice1. variable 2. term 3. coefficient 4. opposite 5. absolutevalue 6. compound inequality 7. multiplicative inverse 8. algebraic expression 9. experimental probability
"5 x8
38
18
16
136
132 5 0.03125
144p5000 < 0.09
164 5 0.015625
516 5 0.3125
4770
1324
13
16
56
16
13
12
719
219
419
819
45
35
25
15
10 11291112
112
12
22072115
54321 0 54321
54321 0 54321
54321 0 54321
23
223
54321 0 54321
32
12
122
32
122
32
Algebra 2: All-In-One Answers (continued)
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77All-In-One Answers Algebra 2
1E: Vocabulary CheckOpposite: The additive inverse of any number, a, is -a.Reciprocal: The multiplicative inverse of any nonzero number,a, is .Absolute value of a real number: The distance from a realnumber to zero on the number line.Variable expression: An expression that contains one or morevariables.Solution of an equation: A number that makes the equationtrue.
1F: Vocabulary Review1. multiplicative inverse 2. solution 3. algebraic expression4. additive inverse 5. theoretical probability 68. Answersmay vary. Samples given. 6. The of a number is thedistance between that number and zero on a number line.7. The additive inverse of a number is its .8. The is the multiplicative inverse of a number.
Chapter 2
Practice 2-1
1. -8; ; 17; 37 2. 3. 7.8; 3.3;-7.2;-19.2
4. not a function 5. not a function 6. function
7. ; domain: {1, 2, 3, 5};
range:
8. ; domain: {-3, 0, 1};range: {-2, 4, 5}
9. ; domain: {-1, 2, 3};range: {2}
10. ; domain: {0.5};range: {-1, 0, 1, 3}
11. not a function 12. function 13. not a function14. ; not a function
15. ; function
16. 1 17. 3 18. 19.
Guided Problem Solving 2-1 1. The radius. 2. 10.5 cm 3. v(r) = 4/3pr3 4. 10.5 or 10.5 cm5. cm3 6. about 4849 cm3 7. 4849 = pr3; r 10.58. v(s) = s3; 1520.875 cm3
Practice 2-2
1. 2. 5 3. 4. 5. 6. 2 7. 8.
9. 10.
11.
12. 13.
14.
O
2
2
2
2x
y
O
2
4
6
42xy
O
2
4
2 4x
y
y 1 2 5 2(x 1 3)
y 2 23 5 212 ax 2 12by 2 1 5 213(x 2 0)
27213
322
12
32
25
43
103
27
10 0
1
4
9
123
1
2
3
2
3
4
5
O
2
2
2
2x
y
O
2
2
2
2x
y
O
2
6
22x
y
e22, 34, 312, 9 fO
2
6
10
2 4x
y
123; 116; 0; 21
132
12
1a
Algebra 2: All-In-One Answers (continued)
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Algebra 2 All-In-One Answers78
15. 4x + y = 10 16. 2x - 5y = -17 17. y = -4
18. (0,-3); (4, 0) 19. 0; (0,-2); none
20. (0, 7); 21. undefined; none; (5, 0)
22. y = 2x + 5; 23.
24. x = -3; 25. y = 1;
Guided Problem Solving 2-2
1. , 2. The slope of the line through the
points 3. slope = 4.
5. slope = 6. 7. 8. 3
Practice 2-3
1. 2. 6; 18 3. 4. yes; 5. yes;-1.2
6. yes;-4 7. no 8. yes; 3 9. no 10. yes; 11. no
12. no 13. yes; 3; y = 3x 14. yes; 15. no
16. 17. y = -6x 18. y = -18x 19.
20. 21. 22. 23. y = 55x
24. 25. 26. 11 27. 28. y = 0.06x; 22 min
29. 46.08 in.
Guided Problem Solving 2-31. 392 mi 2. 14 gallons 3. k = 28 4. y = 28x 5. 103.6 mi6. 417.9 gallons 7. 8a. y = 28x; 392 = 28 3 148b. 103.6 = 28x; x = 3.7 8c. y = 28 3 417.9; y 11,700 9a. y = 58x 9b. 145 mi 9c. 75 gallons
Practice 2-41. y = 0.6x - 2.1 2. y = -2.04x + 7.548 3. y = 1.2x + 200; $214.40 4. y = 58x; 464 words 5. y = 146x + 5000; 6460 subscribers6. ;
yes; using (3, 3.1) and (7, 5.2): y = 0.525x + 1.5257. ; no
8. ;
yes; using (-1,-1.8) and (1, 1.9): y = 1.85x + 0.059. ; no
O
1
1 2 3
23456
x
y
O
2
4
2
2
4
2x
y
O
1
1 2 3 4 5 6 7 8 9 10
23456789
10
x
y
O
1
1 2 3 4 5 6 7 8 9 10
23456789
10
x
y
$0.056mi
5342
163
103
y 5 52xy 5 2356 xy 5
23x
y 5 37xy 513x
12; y 5
12x
35
49
916;
2716
232; 292
2 5132 513
13 2 (2
12)
223 232
a223, 13b(y2 2 y1)(x2 2 x1)a223, 13ba32, 212b
O
2
2
2
2x
y
O
2
2
2
2x
y
O
2
2
2
2x
y
O
2
2
2
2x
y
y 5 53x 243;
a2354 , 0b45;34;
Algebra 2: All-In-One Answers (continued)
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79All-In-One Answers Algebra 2
10a.
10b. using (9.4, 11.2) and (15.1, 19.1): y = 1.39x - 1.8310c. about 15.5% 10d. yes
Guided Problem Solving 2-4 1. Equation 2. Yes 3.
4. slope = 0.076 5. y = 0.076x - 10.04 6. about 15 g 7. Yes, it is a good fit. 8. about 606 Calories
Practice 2-51. E 2. C 3. A 4. F 5. B 6. D7. 8.
9. 10.
11. 12.
13. 14.
15. 16.
17. 18.
19. 20.
21.
O
2
4
2 4x
y
O
2
2 2
2
x
y
O
2
2 2
2
4
x
y
O
2
2 2
2
x
y
O
2
4
x
y
2 4 6
O
2
4
2 24x
y
O
2
4
2 2x
y
O
2
2
2
4
2 x
y
O
2
4
2 4x
y
O
2
4
6
62 4x
y
O
2
4
2 24x
y
O
2
4
24
2
x
y
O
2
4
24x
y
O
2
4
2 4x
y
O
2
4
2 4x
y
y
x
40
30
20
10
200Calories
Fat (
g)
300 400 500 600 700O
O
8
8 10 12 14 16 18 20
101214161820
x
y
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers80
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Guided Problem Solving 2-51. Graph the two equations. 2. Compare the graphs. Look forsimilarities and differences. 3a.
3b. 4.
5.6.
7. The graphs have the same size and shape. They havedifferent vertices, and one points up while the other pointsdown. 8. Test points should result in true statements.9.
The graphs have the same size and shape. They have differentvertices, and one points up while the other points down.
Practice 2-61. horizontal; 2. horizontal;
3. vertical; 4. combined;
5. combined; 6. horizontal;
7. y = x + 2 + 1 8. y = x - 4
9. y = -x - 1 + 3 10.
11. y = x + 3 - 2 12.
13. y = x - 3 14. y = x - 115. y = x + 2 + 1 16. y = -x + 217. y = -x + 2 18. y = -x - 1 - 219. y = 3x - 4 20. y = x - 221. y = 2x + 3 - 1
22.
23.
x
y
O
2
2
2
2
x
y
O
2
2
2
2
12
y 5 2 u x u 1 35
y 5 2 ` x 2 12 ` 2 32O
2
4
2 4x
y
O
2
4
2 4x
y
O
2
2
2
2x
y
O2 2
2
4
xy
O
2
4
24x
y
O
2
4
24 x
y
45
54321 1 2 3 54
321
12345
x
y
12x 1 6 5 y 1 3
12x 1 6 5 y 3,
4 4 8 12812O x
y
6
2
2
6
12x 2 6 5 2(y 2 3)
12x 2 6 5 y 2 3,2y 2 3 5 P 12x 1 6 P y 2 3 5 P
12x 2 6 P
Algebra 2: All-In-One Answers (continued)
81All-In-One Answers Algebra 2
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24.
Guided Problem Solving 2-6 1. A translation shifts a graph horizontally, vertically, or both.2. years 3. x-axis 4. horizontal 5. left 6. horizontal 7. The graphs and answers agree. 8. Vertical; the graph isshifted up
Practice 2-71. y x - 2 2. x - 2y 4 3. y - 2x 44. y -2 5. x 2 6. -2x - 3y 6 7. 3x - y 3 8. y - 3x 39. 10.
11. 12.
13. 14.
15. 16.
17. 18.
19. 20.
21. 22.
23. 24.
25. 26.
27. 28.
29a. x + y 150, where x represents the number of tunasandwiches and y represents the number of ham sandwiches
O
2
2 2
2
x
y
O
2
2
2
x
y
O
2
2 2
2
x
y
O
4
2
2 2x
y
O
2
2 2
2
x
y
O
2
2 2
2
x
y
O
2
2 2
2
x
y
O
2
2 2
2
x
y
O2 2
2
2
x
y
O2 2
2
2
x
y
O2 2
2
2
x
y
O2 2
2
2
x
y
O2 2
2
x
y
O
2
2 2
2
x
y
O
2
2
2
x
y
O
2
2
2
x
y
O
2
2
2
2x
y
O
2
2
2
2x
y
O
2
2
2
2x
y
O
2
2
2
2x
y
x
y
O
2
2
2
2
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers82
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29b.
29c. Yes; the sum of 90 and 80 is more than 150.30a. 150x + 200y 1800, where x represents the number of$150 models and y represents the number of $200 models30b.
30c. at least four $150 models
Guided Problem Solving 2-7 1. dashed 2. to the right or above 3. x =-34. not part 5. > 6. x -3 7. 0 -3; Yes 8. x 2
2A: Graphic Organizer1. Functions, Equations, and Graphs 2. Answers may vary.Sample: linear equations, direct variation, absolute valuefunctions and graphs, two-variable inequalities 3. Check students work.
2B: Reading Comprehension1. graph paper, pencil, a ruler, and colored pencils or pens2. plot; make; classify 3. points plotted on the same graph asthe line 4. three lists of points; one for above, one for on,and one for below the line 5. a phrase that is one of the 3 choices: on the line, above the line, and below the line.6. Step IV asks about the equation while Step III asks aboutan inequality.
2C: Reading/Writing Math Symbols1. The theoretical probability of 3 occurring is 1 in 6.2. the theoretical probability of not taking Spanish3. a function f of x 4. f of 5, or the value of function fwhen 5 is the value of the variable 5. The function A (orArea) of s (or the side of a square) is equal to s2 (or the
length of the side squared). 6. x2 2 0 7. z : 7 or
8. P(red) 9. or 4 : 10 = x : 18 10. g(7)
2D: Visual Vocabulary Practice1. Constant of variation 2. Slope 3. Scatter plot 4. Translation 5. Standard form of a linear equation 6. Absolute value function 7. Trend line 8. Slope-interceptform 9. Point-slope form
2E: Vocabulary CheckRelation: A set of pairs of input and output values.Domain: The set of all inputs, or x-coordinates, of the orderedpairs of a relation.Range: The set of all outputs, or y-coordinates, of the orderedpairs of a relation.Function: A relation in which each element of the domain ispaired with exactly one element of the range.x-intercept: The point at which a line crosses the x-axis (or thex-coordinate of that point).
2F: Vocabulary Review Puzzle
Chapter 3
Practice 3-11. Independent 2. Inconsistent 3. Dependent 4. Independent 5. Dependent 6. Independent 7. Independent 8. Inconsistent 9. Independent 10. Inconsistent 11. Independent 12. Dependent13a. Income: y = 2000x - 500, where x = 1 represents May;Expenses: y = -2600x + 24000, where x = 1 represents May 13b. October (the sixth month) 14. (6, 4) 15. (5, 2) 16. (12, 1) 17. (2, 1) 18. (1,-2) 19. (2, 3) 20. (-4, 0)
21. (-1, 3) 22. 23. (-8,-1) 24. (2, 2)
25. (5, 1)
Guided Problem Solving 3-1 1. 6; 80 2. 4; 100 3. The number of flyers addressed after x minutes 4. y = 6x + 80 5. y = 4x + 100
a32, 24b
1 2
54
6
7
3
D
O
M
A
I
N
T R N S L A T I O N
L
O
P
E
R
E
L
T
I
O
N
F
U
C
T
I
O
NR A G E
L N E A R
410 5
x18
z7
O 4 8 12 16
4
8
12
16
x
y
O 50 100 150 200
50
100
150
200
x
y
Algebra 2: All-In-One Answers (continued)
83All-In-One Answers Algebra 2
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6.
7. (10, 140) 8. 10 minutes 9. Yes; y = 6(10) + 80 = 140and y = 4(10) + 100 = 140 10. y = 3x + 5; y = 2x + 20;
After 15 minutes, thenumbers of newspapers isthe same at 50.
Practice 3-2
1. (6, 4) 2. (4, 1) 3. (5, 2) 4. (1, 2) 5. (4, 3) 6.
7. (1, 1) 8. (2,-2) 9. (5,-2) 10. C = 525 + 150p;I = 325p; three performances 11. (2, 3) 12. (4, 6) 13. (0, 3) 14. (-3, 5) 15. (4, 1) 16. (6, 3) 17. (2,-2) 18. (3, 0) 19. (-4,-4) 20. 8r + 1g = 4.60,6r + 3g = 4.80, where r represents number of oranges and g represents number of grapefruits; oranges = $.50,grapefruits = $.60 21. (1, 4) 22. (-2, 3) 23. (0, 3)
24. (1,-2) 25. 26. (-4, 5)
27. (-3, 2) 28. No solution 29. (2.25, 0)
Guided Problem Solving 3-2 1. $40,000 plus $2800 per performance 2. $36753. y = 40,000 + 2800x 4. y = 3675x5. 40,000 + 2800x = 3675x 6. x 45.7 7. 46 performances 8. Yes; y = 40,000 + 2800(46) = 168,800,y = 3675(46) = 169,050 9. 612 trips
Practice 3-31. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12.
O2 2
2
4
xy
6
O
2
2
2
2x
y
O
2
2 4 6x
y
O
2
2
2
2x
y
x
y
O4 6224
42
28
6
6
x
y
O4224
4
28
6
6
x
y
O424
4
42
8
6
6
O
2
2
2
2x
y
x
y
O4 62246
42
4
86
x
y
O42246
4
2
8
x
y
O42 626
46
46
2
x
y
O4 6426
46
46
2
e (x, y): y 5 2 15x 1 15 f
a5, 215b
10
5 10 15 20
20304050607080
x
y
O 2 4 6 8 1012x
y140
120
100
80
60
40
20
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers 84
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13a. ,
where x represents number of spiral notebooks and yrepresents number of three-ring notebooks13b.
Solutions correspond to points in shaded region with integercoordinates.
14a. ,
where x represents number of campers on the low trail and yrepresents number of campers on the high trail14b.
Solutions correspond to points in shaded region with integercoordinates.15. 16.
17. 18.
19. 20.
21. 22.
23.
Guided Problem Solving 3-31. 7, 8, 9, 10 2. more (or greater) 3. j 0; s 0; s j;j + s 7; j + s 104.
5. (1, 6), (1, 7), (1, 8), (1, 9), (2, 5), (2, 6), (2, 7), (2, 8), (3, 4),(3, 5), (3, 6), (3, 7), (4, 5), (4, 6) 6. Yes, substituting eachcombination listed in (8) into the inequalities of the systemresults in a true statement.7a. x 0; y 0; x + y 5; x + y 8; x y or y x7b. (3, 2), (4, 1), (4, 2), (4, 3),
(5, 0), (5, 1), (5, 2), (5, 3),(6, 0), (6, 1), (6, 2), (7, 0),(7, 1), (8, 0)
1
1 2 3 4 5 6 7 8
2345678
x
y
O 1 3 5 j
s
5
3
1
O
2
24x
y
2
O
2
2
2
2x
y
O
2
24x
y
2
6
x
y
O42 6426
42
6
64
x
y
O42 6426
46
46
x
y
O42 6426
46
6
x
y
O42 6426
2
4
O
4
4
4
4
x
y
x
y
O4 6426
2
6
6
O
20
40
20 40 x
y
x 1 y # 30x $ 10y $ 5
O
4
4
4x
y
x 1 y $ 62x 1 5y # 20x $ 0y $ 0
Algebra 2: All-In-One Answers (continued)
85All-In-One Answers Algebra 2
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Practice 3-41. ; (2, 1)
2. ; (0, 4)
3. ; (5, 0)
4. ; (2, 0)
5. ; (1, 0)
6. ; (0, 0)
7. (0, 10); 30 8. (4, 0); 4 9. (8, 8); 32 10a. Four loaves ofIrish soda bread and two Kugelhopf cakes 10b. $14 11a. 10 qt regular, 4 qt extra-rich 11b. $132
Guided Problem Solving 3-4 1. corn muffins: 4 c; bran muffins: 2 c; baker has 16 c2. corn muffins: 3 c; bran muffins: 3 c; baker has 15 c3. P = 3c + 2b4. c 0, b 0, 4c + 2b 16 (milk), 3c + 3b 15 (flour)5.
(0, 0), (0, 5), (4, 0), (3, 2) 6. At (0, 0), P = 0; At (0, 5),P = 10; At (4, 0), P = 12, At (3, 2), P = 13 maximized at (3, 2)7. 3 trays of cranberry muffins and 2 trays of bran muffins 8. Yes, other points in the feasible region result in P 13.9. 40 Q, 60 R
Practice 3-51. From the origin, move forward three units. 2. From theorigin, move right two units. 3. From the origin, move for-ward three units, left two units, and down 4 units. 4. From theorigin, move back six units, left four units, and down one unit.5. From the origin, move up four units. 6. From the origin,move forward one unit, right two units, and up three units.7. From the origin, move forward three units, left one unit,and up six units. 8. From the origin, move right four units,and down one unit.
(0,0) (4,0)
(3,2)
(0,5)
b
c
y
O4 6 71 3 5
21
4
6
3
5
7
x
y
(0, 5)
(1, 4)
(2, 0)
O1 2 3
2
3
x
y
(1, 0)
(0, 1)
( )3232 ,
O1 2 3 5 6 7
1
3
567
x
y
(2, 0)
(0, 2)
( )5656 ,
O1 2 3 4 6 7
1234567
x
y
(5, 0)
(0, 6)
(4, 2)
O1 2 3 4 5
123
567
x
y
(2, 3)(0, 4)
(5, 0)
O1 3 4 5 6
2
4567
x
y
(2, 2)
(2, 1)(4, 1)
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers86
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9.
10.
11.
12.
13.
14.
15.
16.
y
z
x
5
5
5
55
y
z
x
5
5
5
5
55
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
Algebra 2: All-In-One Answers (continued)
87All-In-One Answers Algebra 2
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17. (0, 0, 0) 18. (0, 0, 1) 19. (0, 2, 0) 20. (3, 0, 0)21. (0, 4,-2) 22. (0,-2, 3) 23. (-5, 0, 3) 24. (1,-1,-3)25.
26.
27.
28.
29.
30.
31.
10
10
10
10 y
x
z
10
10
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
y
z
x5
5
5
55
y
z
x
5
5
5
55
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers88
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.
32.
33.
34.
35. x + y = 3, x + z = 3, y + z = 3;
36. x + 2y = 6, x + 3z = 6, 2y + 3z = 6;
37. x + 3y = 6, x + 2z = 6, 3y + 2z = 6;
38. 2x + 3y = 6, 2x + z = 6, 3y + z = 6;
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
y
z
x5
5
5
5
55
6
4
6
3
y
x
z
y
z
x5
5
5
5
5
y
z
x5
5
5
5
55
Algebra 2: All-In-One Answers (continued)
89All-In-One Answers Algebra 2
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39. -4x + 2y = 8,-4x - 4z = 8, 2y - 4z = 8;
40. 4x - 2y = 12, 4x + 6z = 12,-2y + 6z = 12;
41. 6x - 3y = 6, 6x + z = 6,-3y + z = 6;
42. 7x - 3y = 21, 7x + 7z = 21,-3y + 7z = 21;
43. 4x - 3y = -12, 4x + 6z = -12,-3y + 6z = -12;
Guided Problem Solving 3-5 1. y and z 2. x and z 3. x and y 4. x-intercept: (6, 0, 0);y-intercept: (0, 6, 0); z-intercept: (0, 0,-3) 5. x + y = 66. x - 2z = 6 7. y - 2z = 68.
9. The results are the same.10. xy-trace: 4x + 9y =-36;
xz-trace: 4x - 9z =-36;yz-trace: 9y - 9z =-36
y
z
x
z
x6
6 y
3
y
z
x5
5
5
5
5
5
y
z
x5
5
5
5
5
5
y
z
x5
5
5
5
55
y
z
x5
5
5
5
5
y
z
x5
5
5
5
55
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers90
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Practice 3-61. No unique solution 2. (4, 0,-1) 3. (3, 3, 3) 4. No solution 5. (-1, 1,-1) 6. (4, 1, 3) 7. (5,-1,-2)8. (-3,-2,-1) 9. (2,-2, 2) 10. (2,-1,-3) 11. (-2, 0, 5) 12. (4,-1,-2) 13. (1, 1, 2) 14. (3, 1,-6)
15. 16. 17. (-2,-1,-2)
18. (-1,-3,-4) 19. (0, 5, 0) 20. (8,-1,-2) 21. (1, 2, 3)22. (2,-3,-2) 23. No unique solution 24. (1, 1, 1)
25. ,
where x represents the first number, y represents the secondnumber, and z represents the third number; 3, 5,-10
26. ,
where x represents the number of $1 bills, y represents thenumber of $5 bills, and z represents the number of $10 bills;Eleven $1 bills, seven $5 bills, five $10 bills
Guided Problem Solving 3-6 1. weight of tail, weight of head, and weight of body 2. 9 lb 3. t = 9 4. h = t + b 5. b = h + t6. (h, b, t) = (27, 36, 9) 7. 72 lb (27 + 36 + 9) 8. Yes, thethree weights satisfy each of the statements in the originalproblem. 9. 11 hours (mathematics 1 hr, history report 4 hr,speech 6 hr)
3A: Graphic Organizer1. Linear Systems 2. Answers may vary. Sample: graphingsystems of equations, solving systems algebraically, systems ofinequalities, graphs in three dimensions 3. Check students work.
3B: Reading Comprehension1. alphabetical order 2. where to find the word in the text3. It repeats the word being defined. 4. an example of what isbeing defined 5. See if it is defined in the glossary. If not,look it up in a dictionary. 6. a
3C: Reading/Writing Math Symbols1. The most commonly used letter is f, but accept allreasonable responses. 2. The most commonly used letters are x and y, but accept all reasonable responses. 3. m 4. w5. l 6. the measure of angle A, usually in degrees 7. P(7)
3D: Visual Vocabulary Practice/High-UseAcademic Words1. Define 2. Evaluate 3. Approximate 4. Interpret 5. Model 6. Set 7. Compare 8. Property 9. Test
3E: Vocabulary CheckLinear system: This is a set of two or more linear equationsthat use the same variables.Dependent system: This is a system that does not have aunique solution.Linear programming: A technique that identifies theminimum or maximum value of some quantity. This quantity ismodeled with an objective function. Limits on the variables inthe objective function are constraints, written as linearinequalities.Objective function: In linear programming, this is a modelof the quantity that you want to make as larger or as small aspossible.Trace: This is a set of ordered pairs that results fromsubstituting 0 for one of the variables in the equation of aplane.
3F: Vocabulary Review Puzzle1. consistent 2. dependent 3. equivalent 4. inconsistent5. independent 6. three
Chapter 4
Practice 4-11. 3 1;-3 2. 3 4; 5 3. 2 3; 12 4. 3 3; q5. 3 2; 4 6. 1 4;-4
7.
8. 2 7 9. 9.5; percent unemployment in construction inJune, 1996 10. 6.6; percent unemployment in services in June, 1992 11. Answers may vary.
Sample: 12. 3 2
13. 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 1994
M 5 3900 3300400 150100 50
c17.6 8.3 5.4 8.7 4.0 6.6 3.59.5 5.1 4.5 6.4 2.6 5.1 2.7
d
ETDEPENDENTT
EDNEPEPPENNS
ORDEREDTEECT
EERHTCEDTHQN
IRDNFSNSRTEI
HSEPIEIHARSA
IQDNPSOSEENR
PEIENADONDHT
ANDOPALNIOES
DNCNOQEDLRCN
INELBISAEFPO
IEQUIVALENTC
12
x 1 5y 1 10z 5 96x 1 1 5 y 1 zx 1 y 1 z 5 23
x 1 y 1 z 5 223x 1 2y 1 z 5 9y 2 12z 5 10
a23, 212, 112ba21, 4, 12b
Algebra 2: All-In-One Answers (continued)
91All-In-One Answers Algebra 2
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Guided Problem Solving 4-1 1. table 2. matrix 3. weeks 4. Estimates may vary. Sample:
5. Week 1 Week 2 Week 3 Week 4Rock 165 150 200 180
R & B 100 94 110 98
Rap 96 90 110 100
Classical 98 97 97 1026. Columns represent the weeks in August and rows are thetype of CDs sold.7. The new bar graph should be the same as the one given.8a.
8b.
Columns represent the days of Labor Day Weekend androws are the flavors of ice cream.
Practice 4-2
1. a = 5; ; c = 12; d = 7 2. ; y = -7;
x = 4; ; a = -3; b = 0 3. x = 3; z = -2
4. ;
5. 6.
7. 8. 9.
10. 11. 12.
13. 14. not equal; dimensions are different
15. equal; dimensions and corresponding elements are equal
Guided Problem Solving 4-2 1. 2, 3 2. 2
3. Plant 1: ;
Plant 2:
4. Plant 1: ;
Plant 2:
5.
6. Plant 1; 8007. Plant 2; 22008. The answers check.
9a. Carrier A: ;
Carrier B:
9b. ; B; A
Practice 4-31. product undefined 2. 3.
4. difference undefined 5. 6.
7. product undefined 8. 9. product undefined
10. 11.
12. product undefined 13. 14.
15. product undefined 16.
17. 18. c0.5 20.5 22.52.5 22.5 25.5
d 34 234 21412 2
12 1
0 0.420.4 0.2
20.2 0c2 00 2
dc7 30 2
dc3 23 212 22 4
dc1620
d 0 222 1
21 0
c1 213 22
dc4 213 1
dc 4 123 7
dc6 226 0
dc240 230
35 8d
EnvelopesBoxes
Big Small
160 300 B 25 100REnvelopesBoxes
Big Small
120 270 B 60 108R
c2200 22200800 21000
d1 color3 color
Plastic Rubber 1200 3600 B1800 4800
R1 color3 color
Plastic Rubber 1000 1400 B2600 3800
R1 color3 color
Plastic Rubber 400 1200 B600 1600
R1 color3 color
Plastic Rubber 500 700B1300 1900
R
c 0 24 324 22 5
dc21 24
0 4d227 101 22219 93 21
28 21 20 8 1113 14
4 11
272423
22 226 524 22
8 25 263 28 124 212 218
c22 3
2 0dM 2 F 5 14 22293 26
87 68212 22
F 5 23 5893 82
0 3418 29
M 5 37 560 7687 102
6 27
z 5 72
c 5 53b 5 272
VanillaChocolateStrawberry
Day 1 Day 2 Day 3 50 75 25C175 125 150S 25 50 25
Flavor Day 1 Day 2 Day 3Vanilla 50 75 25Chocolate 175 125 150Strawberry 25 50 25
Types of CD Wk 1 Wk2 Wk3 Wk4Rock 165 150 200 180R&B 100 94 110 98Rap 96 90 110 100Classical 98 97 97 102
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers92
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D T
19. product undefined 20. product undefined
21. 3 3 4; 22. 2 3 2;
23. 2 3 2; 24.
25. 26. 27.
28. 29. 30.
31.
Guided Problem Solving 4-31. no 2. yes 3. [7 6 5] 4. 1 3
5. 6. 3 3 7. 1 3
Thurs Fri Sat8. Revenue [2100 1950 2570] 9. The answers check.
10.
Practice 4-4
1. 2.
3. 4.
5. 6.
7. 8. 9.
10. 11.
12. 13.
14. 15.
16.
17.
18.
19.
Guided Problem Solving 4-4 1. 5 2. 1 3. subtract 5 from each x-coordinate4. add 1 to each y-coordinate
5. 6.
7. Yes, the graphs verify the answers.
8. c 7 2 826 28 0
d
c28 28 23 2321 23 21 23
dc25 25 25 251 1 1 1
d
c 0 2121 0
d c2 0 220 22 0
d 5 c 0 2 022 0 2
dc2 0 220 22 0
d 1 c 0 0 022 22 22
d 5 c 2 0 2222 24 22
d17 c 21 0 214 0214 27 0 7 d 5 c 3 0 22 022 21 0 1 d
O
4
4
4
4x
y
O
4
4
4
4x
y
O
4
4
4
4x
y
O
4
4
4
4
x
y
O
6
6
6
6x
y
c 4 4 2322 2 0
dc2 2 21.51 21 0
dc1 1 263 21 1
dc3 3 240 24 22
dc22 2 04 4 23
dc 2 22 024 24 3
dc2 22 04 4 23
dc 6 6 2124 28 26
dc6 6 24.53 23 0
dc5 5 226 2 4
dc44 44 23322 222 0
dSummer Winter
Cost 1,270,000 B1,010,000
R
150 130 160125 130 17560 52 80
C2 24 203
SD23 83
53 22
Tc 51 24117 55
d 8 14 14 1216 8 8 1018 18 20 14
11 1011 10
11 10c21 1 1
26 5 5d213 19 28224 42 214
25 8 23
72 2460 720 212
c4 55 4
dc71 3449 56
d 1 2 3 42 4 6 83 6 9 12
Algebra 2: All-In-One Answers (continued)
93All-In-One Answers Algebra 2
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Practice 4-5
1. 2. 3. 4.
5. 6. 7.
8. No inverse; the determinant of the matrix is zero.
9. 10.
11. no inverse, cannot be solved 12. 13.
14. -1 15. -21 16. 14 17. -29 18. 9 19. 3620. yes 21. yes 22. yes
Guided Problem Solving 4-5
1. subtract from both sides of the equation
2. A-1 3. 4. 1
5. 6.
7. Yes, the equation is true.
8.
Practice 4-6
1. 2.
3. 4. no inverse
5. 6. no inverse
7. 8.
9. 10. 11. no inverse, cannot be solved
12. 39 13. -47 14. -7 15. 9 16. 26 17. -42 18. no 19. yes
Guided Problem Solving 4-6 1. No, the determinant is a number. 2. Any square matrix hasa determinant.3. (a1b2c3 + a2b3c1 + a3b1c2) - (a1b3c2 + a2b1c3 + a3b2c1)4. -30 5. Yes, the determinant is the same. 6. 52
Practice 4-71. (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)
coefficient variable constant
13. =
14. =
15. =
16. ;
(331,975.0482, 216,327.9518); about 331,975 doctors
17. ; (20, 30);
20 one-bedroom and 30 two-bedroom apartments
18. 19. 20. no unique solution
21. (4, 32) 22. det A = 10, has a unique solution23. det A = 0, no unique solution 24. det A = -5, has aunique solution
Guided Problem Solving 4-7 1. l = 2w 2. 840 ft
3. 4. 6
5. 6.
7. width = 140 ft, length = 280 ft 8. The answers check.9. 6 yards; 14 yards
Practice 4-8
1. 2.
3. 4. (2,-3) 5. (6, 2)
6. (-3, 2) 7. (0.9, 0.08, 0.3) 8. (0.25, 0.75, 0.5) 9. (3, 1,-2)
10. 11. c1 34 1
`2301dc23 4
2 28`2816
d22x 1 9y 2 2z 5 203x 2 y 1 2z 5 29
6x 1 5y 1 5z 5 24
e12x 1 6y 5 242x 5 2
e 4x 2 2y 5 36x 1 11y 5 9
c140280
dC 13 162 13
13S
c2 212 2
dX 5 c 0840
d
a8, 43ba 317, 23317be x 1 y 5 50
425x 1 550y 5 25,000
e x 1 y 5 548,3030.2553415x 1 0.1167209y 5 110,017
9173xy
z 4 0 2112 2 0
1 21 12
c2924
dcxydc3 24
0 7d
c362dcx
ydc6 9
4 13d
23122
4253
20.4 20.4 20.10.2 0.5 0.220.1 0.2 20.1
20.6 0 20.20 20.5 020.4 0 0.2
0.65 21.45 20.220.8 1.4 0.4
0.4 20.2 20.2
29 11 191 21 225 26 210
3 21 2126 3 2
4 22 21 3 10 621 25 23
22 27 24
c5 12 22
dc1 230 1
dc 2 2721 4
dc4 71 2
dX 5 c4 251 21
dc 2 723 4
d
c34dc1
2d
2 310 225252 23
22 132 2
12
16 21618
18
c25 73 24
dc23 41 21
dc21 3
1 22dc 0 1
21 2d 12 12
21212
1 112 1
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers94
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12. 13. (-6,-8, 14) 14. (9,-3,-6)
15. (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)
Guided Problem Solving 4-81. 5 erasers and 2 pencils 2. 7 erasers and 5 pencils3. 5e + 2p = 0.23; 7e + 5p = 0.41
4. 5. 6.
7. e = 0.03, p = 0.04; one eraser is $0.03 and one pencil is$0.04 8. Yes, the prices match. 9. adult: $8; child: $5.50
4A: Graphic Organizer1. Matrices 2. Answers may vary. Sample: organizing datainto matrices, matrix multiplication, geometric transformationswith matrices, inverse matrices and systems 3. Check students work.
4B: Reading Comprehension1. They are to be taken together as a system. 2. 4 inequalities3. 6 elements 4. 2 rows 5. 3 columns 6. 2 by 3 or 2 3 37. -1 8. b
4C: Reading/Writing Math Symbols1. exponent 2. base 3. amn 4. a
3 5. 6.7. a2 + b2
4D: Visual Vocabulary Practice1. matrix 2. zero matrix 3. matrix addition 4. dilation5. matrix multiplication 6. scalar multiplication 7. matrix element 8. matrix equation 9. rotation
4E: Vocabulary CheckSquare matrix: A matrix with equal numbers of columns and rows.Determinant: A real number ad bc of a 2 2 matrix
.
Coefficient matrix: When representing a system ofequations with a matrix equation, this is the matrix containingthe coefficients of the system.Variable matrix: When representing a system of equationswith a matrix equation, this is the matrix containing thevariables of the system.Constant matrix: When representing a system of equationswith a matrix equation, this is the matrix containing theconstants of the system.
4F: Vocabulary Review
1. Answers may vary. Sample:
2. Answers may vary, but must have 3 rows and 2 columns.3. 9 4. Answers may vary.
Sample:
5. Answers may vary, but the two must be identical in everyway. 6. Answers may vary and can be of any dimensions, butevery element is zero.
Chapter 5
Practice 5-11. (x) = x2 2. (x) = x2 + 4x + 8 3. (x) = -2x2 + 12 4. (x) = 2x2 - 1 5. (x) = x2 + 6x + 9 6. (x) = x2 - 4x + 7 7. (0, 1); x = 0 8. (3, 0); x = 3 9. (-1,-2); x = -1 10. quadratic; quad: x2; lin: 2x; const:-8 11. quadratic;quad: 3x2; lin: 15x; const: none 12. linear; quad: none;lin:-25x; const: none 13. linear; quad: none; lin: 22x;const:-14 14. quadratic; quad: 3x2; lin:-4x; const: 8 15. quadratic; quad: 3x2; lin:-6x; const:-716. quadratic; quad: 3x2; lin: none; const:-12 17. quadratic;quad: 2x2; lin: x; const:-6 18. linear; quad: none; lin: 3x;const:-5 19. P9(0, 4), Q9(3, 1) 20. P9(-2,-2),Q9(-5,-5) 21. P9(2, 2), Q9(-1,-1) 22a. h = -16t2 + 272t 22b. 372 feet
Guided Problem Solving 5-11. 1974 2. (0, 10), (4, 15), (7, 18), (9, 20), (14, 25), (21, 32),(27, 34), (28, 37) 3. y =-0.0112x2 + 1.24x + 9.97 4. Answers may vary. Sample: Domain: whole numbers from 0 to 50, Range: whole numbers from 0 to 44. 5. x = 18; year1992 6. Answers may vary. Sample: The maximum value of thefunction is about (55, 44), so the first-class postage never reaches50. The quadratic model is useful over a limited number ofyears, but because it increases and then decreases, it does notmodel the data after 2021. 7. The quadratic model is usefulover a limited number of years, but because it increases and thendecreases, it does not model the data after 2021. 8. The answersare verified by the graph. 9a. y =-0.016x2 + 3.99x - 41.949b. Answers may vary. Sample: Domain: real numbers from 0 to100, Range: whole numbers from 0 to 200. 9c. 51 F 9d. 118 F; The sales may not follow this pattern when thetemperature gets so hot people do not leave their air-conditioned homes.
c 11 726 21
d 1 c21 02 5
d 5 c 10 724 4
d 3 2 57 22 8
4 21 12
ca bc d
d
"3 a 1 b"4 b
` 5 0.237 0.41
` 5 0.44` 0.23 20.41 5
` 5 0.33` 5 27 5
` 5 11
1 24 13 2 234 0 2
29924
Algebra 2: All-In-One Answers (continued)
95All-In-One Answers Algebra 2
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Practice 5-21. ; max. (1, 4)
2. ; min. (-1,-5)
3. ; max.
4. ; min. (2,-3)
5. ; max.
6. ; min. (0,-3)
7. ; min.
8. ; min. (1,-9)
9. ; min. (2,-16)
10. 11.
12. 13.4
1
O23 2 31 1
1
32
y
x
2
y
456
O23 2 31 1
x1
32
3 31 1
y
45
1 O x
3
12
y
45
O23 2 31 1
x12
6
O
8
16
2 4x
y
(2, 16)
O
4
2
8
2 4x
y
(1, 9)
a1, 292bO2
4
2
2
1
4x
y
,( )92
O
2
2
2
4
2 x
y
(0, 3)
a212, 54b
O
2
4
12
24
2
2
,
x
y
( )54
O
2
2
2 4x
y
(2, 3)
a23, 43bO
2 23
2
2
2
,
x
y
( )43
O
2
2 24
4
xy
(1,5)
O
4
6
22 4x
y
(1 ,4)
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers96
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14. 15.
16. 1.2 s; 24 ft 17. ; $6
18. $3.25 19. 81.125 ft; 156.25 ft 20. 20 fixtures per day21. 22.
23. 24.
25. 26.
27. 28.
29.
Guided Problem Solving 5-2
1. 10 ft 2. 10 ft 3. (0, 10), (10, 0) 4. a = , c = 10
5. 6. Yes, the graph verifies the model.
7.
Practice 5-31. y = x2 - 5 2. y = x2 + 2 3. y = (x - 2)2
4. y = -2x2 + 4 5. y = 2(x - 3)2 + 2 6. y = -2(x + 3)2 + 57. 8.
9. 10.
11. 12.
13. 14.x 6
(6, 2)
x
y
O42 28
24
2468x 1
(1, 1)x
y
O24
23
123
x 2
(2, 4)
x
y
O22
2468 4
246
x 1
(1, 3)
x
y
O11
12 3 4
123
x 1
(1, 2)
x
y
O1 21
1234
2
34x 1
(1, 1)
x
y
O3 41
1
12
2
234
x 6
(6, 6)
x
y
O2 4 6 82
2
210
468
10
x 2
(2, 3)
xy
O1 2 3 41
1
1234
5
5
y 5 2 1250x2 1 40
y 5 2 110x2 1 10
2 110
(0, 6)
x 0
x
y
O64 4 6
42
2468
(0, 3) x 0
x
y
O321 1 2 3
21
4
12
(1, 8)
x 1
x
y
O6428 2 4
642
10
2
(3, 13)
x 3x
y
O9 312 6
36
12963
(4, 16)
x 4x
yO
3 3 6 9 12 15
3
69
3
1215
(1, 7)
x 1x
y
O2648 2 4
42
42
8(3, 2)
x 3
x
y
O135 1
21
3
21
3
(4, 4)
x 4
x
y
O2 4 62 8 10
46
46
(1, 4)
x 1x
yO
2 21 41
1
345
c
p
O1 2 3 4 5 6 7 8
1000500
150020002500
y
xO8 242
46
46
4 521
y
112
x123
O
4
Algebra 2: All-In-One Answers (continued)
97All-In-One Answers Algebra 2
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15. 16.
17. 18.
19. y = (x + 2)2 - 4 20. y = 2(x + 2)2 - 5 21. y = -2(x + 2)2 + 8 22. y = -(x - 2)2 + 8
23. y = (x - 2)2 - 8 24.
25. y = 2(x - 0)2 - 6 26.
27. 28. y = (x + 4)2 - 13
29. 30. y = (x + 2)2 - 7
31. (2,-4); 8 32. (-6, 5);-7 33. (1,-1); 1
34. (-4,-3); 35. (1, 2); 3 36. (2, 4);-8 37. (5, 1); 101
38. (-5,-3);-53 39. (-2, 5);-15
Guided Problem Solving 5-31. price of a bagel in dollars 2. bakerys daily profit in dollars3. The domain is all nonnegative numbers. 4. x cannot benegative because that would mean the bakery pays people totake the bagels. 5. $277.50; $210.00 6. (0.55, 300) 7. $.558. $300 9. The graph verifies the answers. 10a. The domainis all nonnegative numbers. x cannot be negative becausethat would mean the theater pays people to see a movie.10b. 140, 74.375 or about 74 10c. $6.50 10d. 150
Practice 5-41. (x + 2)2 2. (x - 5)(x - 2) 3. (x + 8)(x - 1) 4. x(x - 6) 5. (2x - 1)(x - 4) 6. (x + 7)(x - 5) 7. (x + 5)(x + 1) 8. (x + 3)(x - 3) 9. (x - 16)(x + 3)10. (x + 2)(x - 2) 11. x(4x + 1) 12. (x - 25)(x - 4)13. (x - 3)(x + 2) 14. (3x + 1)(3x - 1) 15. x(3x - 2)16. (x + 8)(x - 8) 17. (x + 5)(x - 5) 18. (x + 9)(x - 9) 19. (x + 6)(x - 6) 20. (x + 10)(x - 10) 21. (x + 1)(x - 1) 22. (2x + 1)(2x - 1) 23. 4(x + 3)(x - 3) 24. (3x + 2)(3x - 2) 25. (x - 8)(x + 1) 26. (x + 9)(x + 4) 27. (x - 3)(x - 2)
28. (x + 4)(x + 1) 29. (x - 22)(x + 1) 30. (x + 5)(x + 8) 31. (2x + 1)(x - 3) 32. (x + 11)(x - 1) 33. (x - 12)(x - 2) 34. (x + 2)(5x - 6) 35. (x + 1)(2x - 7) 36. (x + 5)(2x + 3) 37. (x - 3)(3x + 2) 38. (x + 3)(3x + 7) 39. (x + 8)(x - 3) 40. (x + 36)(x - 2) 41. x(x - 11) 42. 3x(x + 7)43. (x + 2)(x + 6) 44. (x - 6)(x - 4) 45. (x + 10)(x - 3) 46. (x - 14)(x + 12)47. (x - 9)(x + 8) 48. (2x + 5)(2x - 5) 49. (x + 11)(x - 11) 50. (x + 16)(x + 1) 51. (5x - 1)(2x - 3) 52. (2x + 3)(2x + 3) 53. (2x - 5)(2x + 3) 54. (3x + 2)(3x - 2)55. (x + 10)(x - 4) 56. 2(x + 2)(x - 2)57. (x + 11)(x + 7) 58. 2(x + 7)(x - 7)59. (x + 14)(x + 7) 60. (x + 6)(x + 14)61. (3x + 2)(3x + 8) 62. (2x + 3)(4x - 9)63. (x - 9)(x + 6) 64. (x + 13)(x - 13)65. (5x + 3)(5x - 3) 66. 7(x2 + 7) 67. 2(x - 7)(x + 2)68. (x + 6)(x + 2) 69. (x + 5)(x - 7) 70. (x + 9)(x - 7) 71. (5x + 1)(4x - 3)72. (2x - 1)(6x + 5) 73. (4x + 3)(x - 2)74. (4x - 3)(2x + 7) 75. 3(x + 7)(x - 8)
Guided Problem Solving 5-41. x + y 2. y 3. (x + y)2 4. y2 5. (x + y)2 - y26. x(x + 2y) 7. The expressions are correct. For example,4(4 + 2 2) = 32 and 62- 22 = 32. 8. (x + y)2 - 4y2;(x - y)(x + 3y)
Practice 5-5
1. 20,-2 2. 0, 3. 0, 3 4. 7,-1 5. 7,-7 6. -1
7. 1,-1 8. 4,-1 9. -4,-5 10. -9, 11. 1,-11
12. 0, 13. 2, 14. 1, 15. 1, 16. -1,
17. 2, 18. 19. -1, 20. -2, 21. 4, 2
22. -6,-1 23. 0,-3 24. , 5 25. 2, 26. , 1
27. 2, 28. 12,-12 29. , 1 30. -1, 31. -1,
32. 1, 2 33. 1, 34. -1, 35. -9,-1
36. 6.24,-2.24 37. 7, 1 38. 4,-4 39. -2,-4 40. 3, 1
41. -2, 42. , 43. 44. 1,
45. 46. -2, 47. 2, 48. -1,
49. -1, 50. -4, 51. -2,-1 52. -1,
53. 54. 0, 2 55. 56. ,-6 57.
58. -11,-1 59. 2, 60. 11,-11 61. 3, 62.
63. -8,-1 64. -2,-6 65. 4,-10 66. 2,-2 67. 3,-2
212, 2142
14
16
12,
14
12
35, 2
35
12, 2
12
1112
122
19
254232
142
12, 2
15
2192214 , 2
354
23
122
32
2171
11
172
25
122
32
12
13
12
13
12
12,
132
12
213152
142
52
32
216
72
233
y 5 2ax 1 32b2 1 112y 5 ax 1 72b2 2 454
y 5 23ax 1 16b2 2 9512y 5 ax 1 52b2 2 254
x 1
(1, 2)
x
y
O12 1 2 3 4
123
23
x 1
(1, 5)
xy
O2468 2
2
810
2
x 2
(2, 0) x
y
O1 1 2 3 4 5
1
1234
x 3(3, 3)
x
y
O3 1 15
1234
12
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers98
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68. 1.65,-3.65 69. 3.46,-3.46 70. 0.9,-2.23
71. 3.87,-3.87 72. 73. -1,-4 74. -4,-9 75. 3, 2
Guided Problem Solving 5-51. 24 ft by 16 ft 2. 384 ft2 3. 276 ft2 4. length: (2x + 24),width: (2x + 16) 5. (2x + 24)(2x + 16) - 384 = 276 6. x =-23 or x = 3 7. 3 ft 8. Yes, the area of the borderis 276 ft2. 9. 5 ft
Practice 5-61. 2i,-4 + 2i, 12 - 14i 2. 1 + i, 1 + 3i,-7 + 7i3. -2 - 3i 4. 4 - i 5. -2i 6. 1 + i 7. 6i 8. -5 + 2i9. 2 - 3i 10. -4 11. 2 12. 13 13. 14. 15. 516. 17. 18. 19. 20. 3 21. 2 22. 23. 24. 25. 4 26.27. 28. -6i 29. 2 30. 0 31. 4 - 5i 32. -5 - 3i33. 26 34. 21 + 27i 35. 18 - 46i 36. -7 + 24i37. 13 38. 8 39. -9 + 7i 40. -1 + 6i 41.42. 43. 44. 2 + 4i 45. 15 - 8i46. 18 - 26i 47. 22 - 4i 48. 2 - 16i 49. 265 50. -2 + 8i 51. -5 + 16i 52. 169 53. 11 - 2i54. 10 - 10i 55. -144 - 130i 56. 57.58. 59. -7 + 22i 60. 6 + 6i 61. 3 - 4i
62. 7 + 6i 63. 7 64. 5 + 12i 65. 2 + 8i 66. -3 + 14i
67. 26 68. 69. 410i 70. 71.
72. 45i 73. 74. 420i 75. 76.
77. 45i 78. 43i 79.
Guided Problem Solving 5-61. Yes 2. a2 + b2 3. x2 + 3ix - 3ix - 9i2 or x2 - 9i24. x2 + 9 5. 25 6. 5 7. Yes,- 5 and 5 check and are bothsolutions. 8. x = 7
Practice 5-7
1. 9 2. 3. 36 4. 5. 16 6. 64 7. 8. 1
9. y = (x + 2)2 - 10; (-2,-10)10. y = (x - 3)2 - 3; (3,-3) 11. y = 4(x + 1)2 - 8; (-1,-8)
12. ;
13. y = 2(x + 1)2 - 7; (-1,-7)
14. ;
15. ;
16. y = (x + 1)2; (-1, 0)17. y = -5(x - 1)2 + 6; (1, 6)
18. y = -2(x - 1)2 + 5; (1, 5)
19. ;
20. ;
21. y = 6(x - 1)2 - 5; (1,-5) 22. y = -2(x - 2)2 - 1; (2,-1)
23. ;
24. 25. 26.
27. 28. 29. 30.
31. 0,-11 32. 7,-2 33. ,-1 34.
35. 36. 37.
38. 1,-3 39. 40. 41.
42. 43. 44.
45. 46. 47. 48. 0, 3
49. 0, 8 50. 51.
52. 53. 54. 2,-1
55. 56. 57.
58. 0, 59. 0,-14 60. 61. 1,
62. 63. 4,-1 64. 65. -1,
66. 2,-4 67. 68. 69.
70. 71. 72.
73. 74.
Guided Problem Solving 5-71. height in feet 2. horizontal distance from the base of theleft side of the arch in feet3.
Ox
y600
300
300 500
3 4 "7232 4 "292272 4
"5322
32 4
"4122
32 4
i"152
232 4"13
22 4 "53 1 5"15343
12 4
"1722
12 4
"216
25421 4"14
252
272 4"13
2232 4
"172
76 4
"1456
256 4"37
6254 4
i"154
212 4"11
2214 4
i"114
32 4
"192
54 4
"6541 4
i"62
238 4"41
8272 4
3"522
32 4
"172
1 4 i"232 4 "37272 4 "972214 4
"542
32 4
i"3222 4
"1062
232 4"23
212
1 4 "10245 4 i"1451 4 "3212 4 "5222 4 "312 4 "21226 4 4"2
a232, 234by 5 3ax 1 32b2 2 34a52, 32by 5 22ax 2 52b2 1 32
a252, 25by 5 ax 1 52b2 2 5
a12, 214by 5 23ax 2 12b2 2 14a223, 13by 5 23ax 1 23b2 1 13
a212, 0by 5 4ax 1 12b24414
94
494
4i"10 4i"5412i46i"242i"342i"544i"5
2i"2 23i"72i"115i"310i"3 4i"3
2i"22 2"10"103"5"173"2"5"13"29 "5"2
94, 2
94
Algebra 2: All-In-One Answers (continued)
99All-In-One Answers Algebra 2
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4. (315, 630) 5. The domain is real numbers from 0 to 630and the range is real numbers from 0 to 630. The distancesand heights must be nonnegative real numbers. 6. 630 ft7. 630 ft 8. vertex form: ; Yes,the answers verify.9a.
vertex (100, 50)9b. 50 ft 9c. 200 ft
Practice 5-81. 200; 2 real 2. 60; 2 real 3. 576; 2 real 4. 0; 1 real 5. 9; 2 real 6. -7; 2 imaginary 7. -7; 2 imaginary 8. 61; 2 real 9. -31; 2 imaginary 10. 9; 2 real 11. 0; 1 real 12. -8; 2 imaginary 13. 225; 2 real 14. -44; 2 imaginary
15. 0; 1 real 16. -3 17. 7, 8 18. , 1 19.
20. 21. , 1 22. -3,-5 23.
24. 25. 6,-2 26. 27. 2,
28. 29. 1 4 2i 30.
31. 32. -10,-8 33. 34. 4 4 3i
35. -4, 36. 37.
38. 39. 40.
41. 42. 43.
44. 45. 46. -5,-1 47. 4, 2
48. 49. No; When p = 4000, the discriminant is negative, so there are no real solutions. 50. 3,-1
51. -1,-4 52. 4,-2 53. ; 1.41, 0.30
54. ; 0.17,-1.17 55. -1, 56.
57. -3, 2 58. 16,-3 59. 0,
60. ; 0.79,-3.79 61. ; 3.73, 0.27
62. ; 1.28,-0.61 63. 7,-5 64. -5,-2
Guided Problem Solving 5-81. the year 1985 2. the amount of carbon monoxide releasedin a year in millions of tons 3.
4. Wherever y = 0.0721x2 - 2.8867x + 117.061 is below y = 100 is when less than 100 million tons were released.5. 0.0721x2 - 2.8867x + 117.061 < 100 6. Subtract 100 from each side. Then use the quadratic formula to solve.7. Answers may vary. 8. The results are the same.9a. Wherever is above y = 4500is when profit was greater than $4500. 9b. Solve -2x2 + 100x+ 4000 4500 by first subtracting 4500 from each side. Thenuse the quadratic formula to solve.
5A: Graphic Organizer1. Quadratic Equations and Functions 2. Answers may vary.Sample: properties of parabolas, transforming parabolas,quadratic equations, completing the square 3. Checkstudents work. Chapter: Quadratic Equations and Functions;Modeling Data with Quadratic Functions: using quadraticfunctions to model data; Properties of Parabolas: identifyingproperties of parabolas; Transforming Parabolas: translatingparabolas in the coordinate plane; Factoring QuadraticExpressions: factoring quadratic expressions; QuadraticEquations: working with quadratic equations; ComplexNumbers: defining and understanding complex numbers;Completing the Square: factoring quadratic expressions bycompleting the square; The Quadratic Formula: using thequadratic formula to solve quadratic equations
5B: Reading Comprehension1. factoring 2. ax2 + bx + c = 0 where a 2 0 3. because you need factors that have product ac and sum b4. (2x - 5) 5. Answers may vary. Sample: a(b + c) =ab + ac 6. Answers may vary. Sample: If two quantitieshave a product of zero, then one of them must be zero.7. Answers may vary. Sample: The Zero-Product Propertystates that one quantity must be zero. This means that onesolution or the other gives zero. And would mean bothsolutions satisfy the equation at the same time. 8. b.
y 5 22x2 1 100x 1 4000
100
200
x
y
5040302010
1 4 2"23
2 4 "323 4 "212252
12, 2
432
14
25 4 3"510
6 4 "157
3 4 "3 5 4 i"7183 4 i"18341 4 i"21 4 i"34521 4 "6110
21 4 i"5910
21 4 2i5
3 4 i"474
22 4 i"113
5 4 i"1196
34
29 4 "1332
23 4 "32
23 4 2i"3323 4 "13
12
3 4 "172
21 4 i"798
21 4 i"232
54
32,
45
23 4 i"314
23
10
100 200
20
30
40
50
60
x
y
y 5 2 2315(x 2 315)2 1 630
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers100
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5C: Reading/Writing Math Symbols1. Answers may vary. Sample: (2, 3) means 2 units to the right along the x-axis and then 3 units up along the y-axis.(3, 2) means 3 units to the right along the x-axis and then2 units up along the y-axis. The x distance is always listed first.
2. Answers may vary. Sample: is a 2 3 3 matrix
with 2 rows and 3 columns.
is a 3 3 2 matrix with 3 rows and 2 columns.
3. 12 4 3 means 12 divided by 3, which equals 4, while 3 4 12means 3 divided by 12, which equals one-fourth. 4. 15 - 5means to subtract 5 from 15 to get 10, while 5 - 15 means5 minus 15, which is -10. 5. No; by the Symmetric Property ofEquality, a = b means b = a.
5D: Visual Vocabulary Practice1. absolute value of a complex number 2. parabola 3. difference of two squares 4. imaginary number 5. Quadratic Formula 6. vertex form of a quadratic function 7. standard form of a quadratic equation 8. complex numberplane 9. perfect square trinomial
5E: Vocabulary CheckQuadratic function: A function that can be written in theform where a 0. Its graph is aparabola.Axis of symmetry: The line that divides a parabola into twoparts that are mirror images.Vertex of a parabola: The point at which the parabolaintersects the axis of symmetry.Factoring: Rewriting an expression as the product of itsfactors.Greatest common factor (GCF) of an expression: Thecommon factor of each term of the expression that has thegreatest coefficient and the greatest exponent.
5F: Vocabulary Review Puzzle
Chapter 6
Practice 6-11. y = -0.0439814815x3 + 0.6507936508x2 - 2.935185185x+ 24.84126984; 21.098 2. y = 0.0130787037x3 -0.1743055556x2 + 0.7951058201x + 3.125396825; 4.6362 3. 5x + 2; linear binomial 4. -3; constant monomial 5. 6x4 - 1; quartic binomial 6. 5s4 - 2s + 1; quartic trinomial 7. 2m2; quadratic monomial 8. -4x3 + x2 + 3x;cubic trinomial 9. 2x2 - 1; quadratic binomial 10. -3m3
+ 5m2; cubic binomial 11. -7x2 + 5x; quadratic binomial12. 3x3; cubic monomial 13. -x3 + 2; cubic binomial 14. -x; linear monomial 15. a5 + a4 + a3; quintic trinomial16. x2 - 25; quadratic binomial 17. p2 - 5p + 6;quadratic trinomial 18. 9c4; quartic monomial 19. b - 3; linear binomial 20. 12x - 6; linear binomial
21. ; quadratic binomial 22. ; quartic
trinomial 23. ; quintic binomial 24. 3x + 5 units
25. 0.0008797x3 + 0.2229900x2 - 3.1465532x + 29.0544437;about $1203.18 26. 0.0000006x3 - 0.0005101x2 + 0.1270416x + 2.0612682;about 12 yr
Guided Problem Solving 6-11. h = 10 cm 2. They are the same. 3.
4. 5. 6.
7. 8. Answers may vary.
9.
Practice 6-21. 5, multiplicity 3 2. 0; 8, multiplicity 2 3. 2;-7, multiplicity3 4. 0, multiplicity 2; 4, multiplicity 2 5. -3, 0, 3
6. ; 3, multiplicity 2 7. y = 2x3 - x2 - 50x + 25252
12pr
2 1 48r
V 5 23pr3 1 10pr2
V 5 23pr34
3pr3V 5 10pr2
pr2h
213z5 1 1
12x
4 1 x 2 54s2 1 23
1V E
2R T E X
R4
T
S
B N O M I A L5P
6F
N
A C T R D
R M A
A R
DB
O
L
I
N
O
I
A
L
A
3
f(x) 5 ax2 1 bx 1 c,
1 23 45 6
c1 2 34 5 6
dO
2
2
2
2x
y (2, 3)
(3, 2)
Algebra 2: All-In-One Answers (continued)
101All-In-One Answers Algebra 2
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Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers 102
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8. y = -2x3 + 15x2 - 22x - 15 9. V = x3 + 54x2 + 936x + 5184 10. y = x3 - 6x2 + 5x + 12 11. y = x3 - 4x2 + 5x - 2 12. y = x4 - 2x3 - 15x2
13. y = x3 + 6x2 + 12x + 8 14. x3 - 2x2 + x15. x3 + 7x2 + 15x + 9 16. 2x4 + 23x3 + 60x2 - 125x - 500 17. y = 2x(x + 2)(x + 3) 18. y = x2(x + 2)(x - 3) 19. y = -3x(x - 3)2
20. -1, 1, 3;
21. -2, 3;
22. -5, 0, 2;
23. rel. max.: 4.06; rel. min.:-8.21; zeros: 0, 2, 524. rel. max.: 16.9; rel. min.:-5.05; zeros:-3, 1, 325. x(x + 2)(x - 8) 26. x(x + 3)(x + 4) 27. x(x - 3)(x - 5) 28a. V = x2(20 - x) 28b. about 1185 in. 3
Guided Problem Solving 6-21. 4 ft 2. The volume will be twice as much. 3. x ft 4. 60 ft35. 120 ft3 6. 7. 1 8. 1 ft 9. Answers may vary. 10. 2 in.
Practice 6-31. yes 2. yes 3. no 4. yes 5. x2 - 3x + 2 6. x2 + 3x - 7, R 5 7. -2x2 + 9x + 5 8. x2 + 6x + 99. x2 - x + 8, R -12 10. x2 - 7, R -10 11. x3 + x, R 112. x3 + 2x2 + 6 13. x3 - x2 + x + 11, R 32 14. 2x3 + 15x2 - 125 15. -1 16. -13 17. 0 18. 39
19. x - 16 20. 2x + 11, R 48 21. x2 + 6x + 3, R 2 22. 3x2 - 7x + 7, R -8 23. (x + 1)(x - 3)(x + 5) 24. (x - 2)(x + 3)(x - 4) 25. 2x2 - 2x - 1, R 16 26. x3 + 3x2 + 3x + 4, R 1 27. x3 + 2x2 - x, R 1 28. x4 + x3 + x2 + x + 1 29. x3 + 2x2 + x + 2, R -630. 3x2 - 3x + 3 31. width: x - 3; height: x - 5
Guided Problem Solving 6-31. x + 3 2. 3. 0 4. -35. 6. 0 7. yes
8. (x + 3)(3x2 + x - 4) + 0 = 3x3 + 10x2 - x - 129. 3(-3)3 + 10(-3)2 - (-3) - 12 = 0 10. no
Practice 6-4
1. (2x - 3)(4x2 + 6x + 9); ,
2. (x + 4)(x2 - 4x + 16);-4,
3. 2(x + 3)(x2 - 3x + 9);-3,
4. 2(x - 5)(x2 + 5x + 25); 5,
5. 4(x - 2)(x2 + 2x + 4); 2,
6. (3x + 1)(9x2 - 3x + 1); ,
7. (4x - 1)(16x2 + 4x + 1); ,
8. (x - 3)(x2 + 3x + 9); 3,
9. (x + 1)(x - 1)(x + 2)(x - 2);-2,-1, 1, 210. (x + 1)(x - 1)(x2 - 11); -1, 1,11. (x2 - 2)(x2 - 8);12. (x + 2)2(x - 2)2;-2, 213. (x2 - 7)(x2 - 2);14. (x2 + 4)(x2 + 9);-2i, 2i,-3i, 3i15. (x + 1)(x - 1)(x + 3)(x - 3);-1, 1,-3, 316. (x + 1)(x - 1)(x2 + 4);-1, 1,-2i, 2i17. 5.52% 18. -2, 2,-0.71, 0.71 19. 0.06, 15.94 20. 0 21. -0.59, 0, 0.42 22. -0.67, 0, 1.4 23. -9, 0, 9 24. (n - 1)n(n + 1) = -336;-8,-7,-6 25. (x - 5)(x2 + 5x + 25) 26. (x2 - 3)(x2 - 5) 27. (x + 1)(x - 1)(x2 + 2) 28. (x + 1)(x2 - x + 1) 29. (x2 - 6)(x2 + 4) 30. (x2 + 1)(x2 + 9) 31. (x + 3)(x2 - 3x + 9) 32. (x2 - 2)(x2 + 9)
33. 0, 1, 34.
35. 36.37. -3, 3,-3i, 3i 38.39. 0,-2, 2, 40. 0, 2, 62i"3, i"32"5, "5, 2i"5, i"5
2i"2, i"2, 22i"2, 2i"22"14, "14, 2i, i 21, 1, 2"6, "621 4 i"32
2"7, "7, 2"2, "22"2, "2, 2"8, "82"11, "11
23 4 3i"32
21 4 i"38
14
1 4 i"362
13
21 4 i"325 4 5i"3
2
3 4 3i"32
2 4 2i"323 4 3i"3
432
3 10 21 21229 23 12
3 1 24 0
23 k3x3 1 10x2 2 x 2 12
V(x) 5 (x 1 5)(x 1 4)(x 1 3)
O
10
20
4 4 x
y
(5, 0) (2, 0)(0, 0)
O2 2
2
4
6
xy(2, 0) (3, 0)
O
2
2
2
2x
y
(1, 0) (1, 0)(3, 0)
Guided Problem Solving 6-41. 60 m3 2. the length of the box 3. width = x - 2 4. height = x - 1 5. V(x) = x(x - 1)(x - 2)6. x(x - 1)(x - 2) = 60 7. (5, 60). The length of the boxwhen the volume is 60 m3. 8. 5 meters 9. 5 4 3 = 60 10. 10 years old
Practice 6-51. 2. 3.4. 5. x4 - 8x3 + 21x2 - 32x + 686. x4 - 4x3 - x2 + 8x - 2 7. x4 + 3x2 - 54 8. x4 - 6x3 + 9x2 + 6x - 20 9. 4, 2,-1 10. 3, 1,-5
11. -4,-3, 12. 7,-2,-4 13. 3;
14. -2,-1, 1, 2 15. 2, 16. -1, 17. 1,18. -2, 19. 1,-1, 5 20. -4, 2 21. -2, 1, 3
22. 10, 23. 1,-3 24.
25. 2, 26. -3,
27. 41,43,45,415; none 28.41,42,44,4 ,4 ,4 ,
4 ,4 ,4 ,4 ,4 ,4 ,4 ,4 ,4 ;-4, ,
29. 41,4 ;-1, 30. 41,42,44,4 ,4 ,4 ,4 ,4 ,
4 ,4 ; none 31. 41,4 ; 32. 41,47,449; none
33. x3 - 7x2 + 17x - 15 = 0 34. x3 - 5x2 + 4x - 20 = 0 35. x3 - 5x2 + 4x + 10 = 0 36. x3 + 7x2 + x + 7 = 0 37. x3 + 4x2 + 16x + 64 = 0 38. x3 - 12x2 + 49x - 78 = 0
Guided Problem Solving 6-51. two 2. four 3. 3 - i 4. 2i5. (x - 2i)(x + 2i)(x - 3 + i)(x - 3 - i) 6. (x - 2i)(x + 2i)(x - 3 + 1)(x - 3 - i) =(x2 + 4)(x2 - 6x + 10) = x4 - 6x3 + 14x2 - 24x + 407. x4 - 6x3 + 14x2 - 24x + 40 = 08. Check students work. 9. Answers may vary.10.
Practice 6-6
1. -1, 0, 1 2. -4, 0, 4 3. 4.
5. -1, , 0 6. -5, 0, 5 7. 2; 2 or 0;41,43,4 ,4
8. 2; 2 or 0;41,42,45,410,4 ,4 ,4 ,4
9. 4; 4, 2, or 0;41,45,4 ,4 10. 3; 3 or 1;41,43,49,
4 ,4 ,4 ,4 ,4 ,4 11. 5; 5, 3, or 1;41,43,45,
415,4 ,4 ,4 ,4 ,4 ,4 ,4 ,4 12. 3; 3 or 1;
41,47 13. 3; 3 or 1;41,42,43,44,46,412
14. 4; 4, 2, or 0;41,42,43,46,4 ,4 15. 5; 5, 3, or 1;
41,42,43,46,4 ,4 ,4 ,4 16. 6; 6, 4, 2 or 0;41,42,
43,46,49,418,4 ,4 ,4 ,4 ,4 ,4 17. 5; 5, 3, or
1;41,45 18. 5; 5, 3, or 1;41,42,43,46,4 ,4 ,4 ,4 ,
4 ,4 19. 3 20. 4,-3i, 3i 21.
22. 2, 23. 1, 24. -3, 1, 4
25. -4, 26. -1, 27. -3, 3,-2i, 2i28. -2, 2, 29.
30.
Guided Problem Solving 6-61. three 2. three 3. 41,42,43,44,46,49,412,418,436 4. 4 5. 6. 3i,-3i 7. 4,43i8. Answers may vary. 9. Answers may vary.10. -1,42i
Practice 6-71. combination 2. permutation 3. permutation 4. combina-tion 5. 12 6. 66 7. 792 8. 12 9. 1 10. 15 11. 1 12. 8413. 1 14. 252 15. 2002 16. 2,118,760 17. 40,320 18. 11019. 17,280 20. 360 21. 479,001,600 22. 239,500,800 23. 95,040 24. 12 25. 3024 26. 455 27. 60 28. 360 29. true, comm. prop. of mult. 30. false; Let a = 2. (22)! =24 2 4 = (2!)2 31. false, Let a = 2 and b = 3. 2 ? 3! =12 2 720 = (2 ? 3)! 32. true; identity prop. of add.33. false; Let a = 2 and b = 3. (2 + 3)! = 120 2 8 =2! + 3! 34. false; Let a = 2. (2!)! = 2 2 4 = (2!)2
Guided Problem Solving 6-71. 2; 5; 3; 2 2. the number of different ratings possible 3. No; a particular television set will fall into one price rangeor the other. 4. 1 5. the Multiplication Counting Principle6. 2 5 3 2 7. 60 8. Answers may vary. 9. 240
Practice 6-81. x4 + 8x3 + 24x2 + 32x + 16 2. a7 + 14a6 + 84a5
+ 280a4 + 560a3 + 672a2 + 448a + 128 3. x7 + 7x6y+ 21x5y2 + 35x4y3 + 35x3y4 + 21x2y5 + 7xy6 + y7
4. d9 - 18d8 + 144d7 - 672d6 + 2016d5 - 4032d4
+ 5376d3 - 4608d2 + 2304d - 512 5. 256x8 - 3072x7
+ 16128x6 - 48384x5 + 90720x4 - 108864x3 + 81648x2
- 34992x + 6561 6. x9 - 9x8 + 36x7 - 84x6 + 126x5
- 126x4 + 84x3 - 36x2 + 9x - 1 7. 64x12 - 384x10y2
+ 960x8y4 - 1280x6y6 + 960x4y8 - 384x2y10 + 64y12
8. x35 + 14x30y + 84x25y2 + 280x20y3 + 560x15y4
+ 672x10y5 + 448x5y6 + 128y7 9. about 1% 10a. about 99% 10b. about 95% 10c. about 5% 11. about 3% 12. about 3% 13. about 8% 14. about 0.6% 15. n3 - 9n2 + 27n - 27 16. 16n4 + 64n3 + 96n2 + 64n + 16 17. n5 - 30n4
+ 360n3 - 2160n2 + 6480n - 7776 18. n6 - 6n5
+ 15n4 - 20n3 + 15n2 - 6n + 1
x2 1 9
2"3, "3, 212i, 12i 223,
23, 2i, i2"3, "3 21 4 i"32i"7, i"7
21 4 i"521 4 "5
22, 1 4 "7381834
14
32
12
187
97
67
37
27
17
34
14
32
12
32
12
56
16
53
13
152
52
32
12
94
34
14
92
32
12
52
12
103
53
23
13
32
122
15
212, 0, 132
13, 0,
12
x4 1 10x2 1 9 5 0
15; 1
15
112
16
14
43
23
13
122
12
12
162
16
136
118
112
49
29
19
16
14
43
23
13
12
23, 2
14
234"132
3, 12, 21221 4 i"191 4 2i
2 4 3i3 4 i2 4 i
2343"52
12
5 1 "6, 22 2 "10 4i, 6 1 i3 1 "2, 1 2 "32 2 3i, 2"7
Algebra 2: All-In-One Answers (continued)
103All-In-One Answers Algebra 2
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19. 8a3 + 24a2 + 24a + 8 20. x8 - 4x6y2 + 6x4y4 -4x2y6 + y8 21. 32x5 + 240x4y + 720x3y2 + 1080x2y3 +810xy4 + 243y5 22. 64x12 + 192x10y2 + 240x8y4 +160x6y6 + 60x4y8 + 12x2y10 + y12 23. x6 - 3x4y2 +3x2y4 - y6 24. 16b4 + 32b3c + 24b2c2 + 8bc3 + c4
25. 243m5 - 810m4n + 1080m3n2 - 720m2n3 + 240mn4
- 32n5 26. x18 - 6x15y4 + 15x12y8 - 20x9y12
+ 15x6y16 - 6x3y20 + y24 27. x7 + 7x6 + 21x5 + 35x4
+ 35x3 + 21x2 + 7x + 1 28. x8 + 32x7 + 448x6 +3584x5 + 17920x4 + 57344x3 + 114688x2 + 131072x+ 65536 29. x6 - 18x5y + 135x4y2 - 540x3y3
+ 1215x2y4 - 1458xy5 + 729y6
30. x5 + 10x4 + 40x3 + 80x2 + 80x + 32 31. x10 - 5x8y2 + 10x6y4 - 10x4y6 + 5x2y8 - y10
32. y5 + 15y4 + 90y3 + 270y2 + 405y + 243 33. x12 + 18x10 + 135x8 + 540x6 + 1215x4
+ 1458x2 + 729 34. x7 - 35x6 + 525x5 - 4375x4
+ 21875x3 - 65625x2 + 109375x - 78125 35. x4 - 16x3y + 96x2y2 - 256xy3 + 256y4
Guided Problem Solving 6-81. 0.5 2. 5 3. 0.5 4. 2 5. 6. 7. 8. about 31% 9. 1 10. 11. about 16% 12. 13. about 16% 14. Answers may vary. 15a. 37.5% 15b. 25% 15c. 25%
6A: Graphic Organizer1. Polynomials and Polynomial Functions 2. Answers mayvary. Sample: polynomials and linear factors, dividingpolynomials, solving polynomial equations, the FundamentalTheorem of Algebra 3. Check students work.
6B: Reading Comprehension1. x 2. y 3. 1 unit 4. parabola 5. y-axis 6. downwards7. (0, 0) 8. upper right 9. a
6C: Reading/Writing Math Symbols1. subtract 2. inverse 3. zero 4. inverse; 5. 16. inverse 7. identity
6D: Visual Vocabulary Practice/High-UseAcademic Words1. symbol 2. always 3. table 4. explain 5. graph 6. formula 7. common 8. never 9. simplify
6E: Vocabulary CheckPolynomial: A monomial or the sum of monomials.Degree of a polynomial: The largest degree of any term.Remainder Theorem: If a polynomial P(x) of degree n 1is divided by (x - a) where a is a constant, then the remainderis P(a).Multiplicity: The number of times the related linear factor isrepeated in the factored form of the polynomial.Relative maximum: The y-value of a point on the graph of afunction that is higher than other nearby points.
6F: Vocabulary Review Puzzle1. absolute 2. opposite 3. term 4. variable 5. evaluate6. complex
Chapter 7Practice 7-11. 12 2. -5 3. not a real number 4. 0.1 5. 0.3 6. 3
7.-3 8. 0.3 9. 6 10. -7 11. -0.4 12. 13. -20, 20
14. no real square roots 15. -100, 100 16. -0.25, 0.2517. no real fourth roots 18. -4, 4 19. -0.1, 0.1 20. -5, 521. 9x2 22. 11 y5 23. 2g2 24. 5x3 25. 3xy3
26. x - 9 27. 5(x + 2)2 28. 29. -2, 2 30. -3, 3
31. -0.4, 0.4 32. 33. 20 cm 34a. about 25.30 ft/sec
34b. about 10.48 ft/sec
Guided Problem Solving 7-11. K and L, respectively 2. length, L 3.4. ; L 35 ft 5. ; L 55 ft 6. 20 ft longer 7. The answers check. 8a. 72,000 cars 8b. 6,500 cars
Practice 7-21. 2 2. 9xy2 3. 5yz2 4. 48x 5. 2xy
6. 7. 8. 9. 10.
11. 12. 13. 10 14. 54 15. 9 16. -3
17. 18. 2xy3 19. 20.
21. 22. 23. 24.
25. 26. 27. 28. 29.
30. 31. 32. 33.
34a. 34b. 2.88 in.
Guided Problem Solving 7-21. distance in miles from the satellite to the center of Earth2. 3950 mi 3. r = 3950 + 100 = 4050 4. 17,498 mi/h 5. r = 3950 + 200 = 4150 6. 17,286 mi/h 7. 212 mi/hgreater 8. The answers are reasonable. 9. 0.22 gram
r 5 3 3V4p ; r 5 "3 6p2V2p3"3
a"3 12y
22x
25y23k
"3 4x"25uv2"4 u5r"3r6xy"3 x 4st3"4 s3xy5"z22a4"3 23k3"25z"3 y2z6x"x3x2"2
"3 6abc22bc
"2xy4y
"4 54x33x
"3 9x2y23y
"3y3
3"2x227"2y
"3 6x2"y"6
10 5 1.35"L8 5 1.35"L K 5 1.35"L247,
47
4x37
103
18
5b1g45b4g110b3g25C3 5 10b
3g2
Algebra 2: All-In-One Answers (continued)
Algebra 2 All-In-One Answers104
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Practice 7-31. -63 2. -6 3. 73 4. 11 5. 5 + 26. 3 - 7 7. 11 8. -2 - 9. 10 - 5
10. - 11. 12. 22 13. 4
14. 0 15. 13 16. -3 - 17. -38 + 718. 67 - 15 19. 28 - 16 20. 9 + 221. 30 + 12 22. 12 23. 1824. 41 - 3 25. 6 + 4 26. 10527. 26y 28. 6y + 13 - 25 29. x - 3
30. 31. 32.
33a. ft or about 2154 ft
33b. ft2 or about 212,942 ft2
Guided Problem Solving 7-3
1. 2. subtract 3. 4. 5.
6. 1 7. Yes, it equals the reciprocal of the golden ratio.8.
Practice 7-41. 3 2. 81 3. 32 4. 256 5. 1 6. 4 7. -1 8. 9 9. 2
10. 11. 2 12. 4 13. 1 14. 15. 16. 0
17. 12 18. 19. 20. 21. 22.
23. 24. 25. 26. 27.
28. 10.1% 29. 30. 31. 32.
33. 34. 35. 36. 37.
38. 39. 40. 41. 42. 43.
44. 36a2 45. 46.
Guided Problem Solving 7-4
1. 39% 2. number of years ago that the organism died
3. fraction of A left after T years 4.
5. 78% 6. 61% 7. 37% 8. Yes, the answers check.9. 81%; 65%; 12%
Practice 7-51. 127 2. -8, 8 3. 9 4. 3 5. no solution 6. 25 7. 9 8. -14 9. 1 10. 27 11. 4, 2 12. 9 13. 7 14. 2 15. 4 16. 29,-25 17. 10 18. 16 19. 4 20. 13 21. 4
22. -27, 27 23. 64 24. 0,-1 25. no solution 26. 64 27. 23 28. 0 29. no solution 30. -2 31. 1 32. -123 33. 8 34. 12 35. 1 36. 16 37. 8 38. -6, 2 39. 2
Guided Problem Solving 7-5
1. 2. ; ; 3. about 8.8 in.
4. about 15.2 in. 5. Yes, the answer checks. 6a. about 10.7in. 6b. about 11.5 in.
Practice 7-61a. (x) = 1.8x 1b. g(x) = 0.75x 1c. g(f(150)) = $202.501d. No; it doesnt matter whether you first multiply by 0.75 or by 1.8. 2. 2x2 + 4x + 2; all real numbers 3. -2x2 + 4x - 4; all real numbers 4. 8x3 - 2x2 + 12x - 3; all real numbers
5. ; all real numbers 6. 2x2 - 4x + 4; all real
numbers 7. ; all real numbers except 8. -4
9. -2 10. 7 11. 12. -4x + 7
13. 2x2 - 3x - 7 14. 15. 16. -8x + 6 17.
18. 19. 20. 3x2 - 13
21. 3x3 + 2x2 - 15x - 10 22. -2x2 + 3x + 1223a. (x) = 0.75x 23b. g(x) = x - 5 23c. g((50)) = $32.50 23d. Yes; multiplying by 0.75 andthen subtracting by 5 is different than subtracting by 5 andthen multiplying by 0.75.
Guided Problem Solving 7-61. cost in dollars to produce x violins; income in dollars fromselling x violins 2. profit earned when he makes and sells xviolins 3. I(x) = 5995x 4. C(x) = 1000 + 700x 5. P(x) =5295x - 1000 6. 157,850 7. He made a profit of $157,850when he makes and sells 30 violins. 8. The answers match.9a. P(x) = 56x -30 9b. $13,970
Practice 7-71. 2.
x
y
O2 646 2
2
246
46
x
y
O 2 4 64
246
75
23x 1 25
245165
175
23a 1 25
14
2x2 1 34x 2 1
4x 2 12x2 1 3
#2A"33
2A"39
2A3"3s"32
RA 5 (2.7)
T
8033
(5ab)34n
45
(26)12b
342
13y
23(5y)
12m
13x
32
1"5 a81"7 t2"5 m12"4 ab"3 z2"5 b"a3"3 2y"3 x4
3x2y12x
13201
98a341
x2
21
y3140
b3
a41y6
9ab23
3
y16
x76
94
12y
32x
56
2243 1 525
21 1 52
1 2 521 1 51 1 52
270,000 1 90,000"32
(900 1 300"3 1 300"6)x 1 2"3 x2
x"2"5 2 2"23"5y"5 "x"
3 9"3 3"6"3 "10"7"6"14"3"7 "10"5"
4 3
"2"222 1 14"3133 1 "52"3"3"3 xy"3 x"7 "3"2"3
Algebra 2: All-In-One Answers (continued)
105All-In-One Answers Algebra 2
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3. 4.
5. 6.
7. ; no 8. y = x - 2; yes
9. ; yes 10. ; no
11. ; yes 12. ; no
13. ; no 14. ; no
15. ; no 16. ; no
17. ; no 18. ; no
19. (x) = 6x; The domain and range of f and is theset of all real numbers; is a function.
20. ; The domain and range of f andis the set of all real numbers; is a function.
21. ; Domain of f = all real
numbers = range of ; Range of f = the set of real
numbers greater than or equal to -2 = domain of ;
is not a function.
22. ; Domain of f = all real numbers = range of ; Range of f = all real numbers
greater than or equal to 4 = domain of ; is not a
function.
23. ; Domain of f = all real numbersgreater than or equal to 1 = range of ; Range of f = allreal numbers greater than or equal to 0 = domain of ;
is a function.
24. ; The domain and range of f and is
the set of all real numbers greater than or equal to 0; is a function.
25.
26.
27. -1 28. 3 29. 30. ; in 2009
Guided Problem Solving 7-71. v is the velocity of the water in feet per second; g is theacceleration due to gravity (32 ft/s2); x is the height of the
water in feet. 2. v2; ; 3. 25 4. 25 ft 5. 6.25 6. 6.25 ft
7. Yes, the answers check. 8. ; r 8.4%
Practice 7-81. 2.
x
y
O2 4 62
246
246
8 10x
y
O2 4 6426
246
246
r 5 SP 2 1v264
v22g
f21(x) 5x 2 635,600
198,900212
O
2
2
2
2x
y
x 3 1 0 2
y 0 1