CHAPTER 11 Solutions Key Exponential and Radical Functions xzare YOU READY, PAGE 76 1. B; like terms: terms that contain the same variable raised to the same power. F; square root: one of two equal factors of a number. C; domain: the set of first elemtns of a relation 4. E; perfect square: a number whose positive square root is a whole number. D; exponent: a number that tells how many times a base is used as a factor 6. 16 7. 1 8. 6 9. 7 10. 4 11. -8 1. 0 1. 147 14. y 8 16. y x - 4 1. y x + 17. y x +. t(t - 1 t t - t 1 6 t - 6. 4r(4r - 4r 4r - 4r 16 r - 0r 11-1 GEOMETRIC SEQUENCES, PAGES 766 771 CHECK IT OUT! PAGE 767 1a. 80, -160, 0; (-10 -, 0 (-10 -, (-40 0 - So, the common ratio is -. (-40 (- 80, 80 (- -160, and (-160 (- 0 b. 16, 16, 11.; 84 1 4, 88 84 4, So, the common ratio is 4. 88 4 16, 16 4 16, and 16 4 11.. a n a 1 r n - 1 a 8 1000 ( 7 a 8 7.81. a n a 1 r n - 1 a 10 10,000 ( 4 9 a 10 14.18; $14.18 THINK AND DISCUSS, PAGE 768 1. Possible answer: Divide each term after the first by the preceding term. If the quotients are all the same, the sequence is geometric. 18. 0. 19. 0. 0. 0.1 1..0. 0.019. 0.00 4. 0.001. 0.0104 6. 6; 6 6 6 7. 9; 9 9 81 8. ; 9. 8; 8 8 64 0. h + 4 h h cm. h 6 + 8 h 100 h 10 ft. (m - m - 10m - 1 4. x(8x + 9 x 8x + x 9 4 x + 7x 1. h 1 + h 169 h 1 in.. Possible answer: EXERCISES, PAGES 769 771 GUIDED PRACTICE, PAGE 769 1. common ratio: the value that each term is multiplied by to get the next term. Copyright by Holt, Rinehart and Winston. 4 Holt Algebra 1
., 64, 18; 4, 8 4, 16 8 So, the common ratio is. Then, 16, 64, and 64 18., 1., 6.; 00 400, 100 00, 0 100 So, the common ratio is. Then, 0, 1., and 1, 6. 4. 4, -97, 916; (-1 4 -, 6 (-1 -, (-108 6 - So, the common ratio is -. Then, (-108 (- 4, 4 (- -97, and (-97 (- 916. a n a 1 r n - 1 a 10 1 10 10-1 a 10 1,000,000,000 7. 64 ; 16 a n a 1 r n - 1 a 64 ( 4 a 4 6. a n a 1 r n - 1 a 11 11-1 a 11 07 PRACTICE AND PROBLEM SOLVING, PAGES 769 770 8. -10, 60, -1,0; 10 - _ -; -0 -; 0 10-0 - So, the common ratio is -. Then, 0 (- -10, -10 (- 60, and 60, (- -1 0 9. 16, 4, 64.; 48 ; 7 48 ; _ 108 7 So, the common ratio is. Then, 108 ( and 4 ( 4, 64. 10. 6, 04.8, 16.84; _ 00 6 4 ; _ 400 00 4 ; _ 0 400 4 16, 16 ( So, the common ratio is 4. Then, 0 ( 4 and 04.8 ( 4 6, 6 ( 4 04.8, 16.84 11. 08, 14 406, 100 84; 4 7; _ 94 6 4 7 So, the common ratio is 7. Then, 94 7 08, 08 7 14, 406 and 14, 406 7 100, 84 _ -; _ -48 4-1. 96, -19, 84; - 1 -; 4 6-1 So, the common ratio is -. Then, -48 (- 96, 96 (- -19, and -19 (- 84 1., _ 18, _ 1 ; 10 40 10 So, the common ratio is 4. Then, ( 8 ( 4, ( ( 4 _ 18, and ( _ 18 ( 4 _ 1 14. a n a 1 r n - 1 a 18 (. - 1 a 701.1 4 ; 1. 100 1000 1 10 ; 10 100 1 10 ; 1 10 1 10 a a n 1 r n - 1 4 ; 8 4 a 14 1000 0.1 14-1 a 14 0.0000000001 or a 14 1 10-10 16. 8.9 m; _ 0 400 4 ; _ 6 0 4 a n a 1 r n - 1 a 8 400 ( 4 8-1 a 8 8.9 17. 0, 40, 80, 160; 40, so the common ratio is ; 0 40 80 and 80 160 18., 6, 18, 4; 18, so the common ratio is ; 6 and 18 4 6 19. 9,, 1, ; 9 ; So the common ratio is ; 1 0., 1, 48, 19, 768; 1 4, so the common ratio is 4; 1 4 48 and 19 4 768 1. 7, 1, 7, 1 49, _ 1 ; The common ratio is 4 7 ; 1 7 and 7 7 7 1 49. 400, 100,, 4 ; _ 100, so the common ratio 4 is 4. Then, 100 4 and 4 4 _. -, 6, -1, 4, -48; 4 -, so the common -1 ratio is -. Then, - (- 6 and 4 (- -48 4. 9, -, 1, -, 9; - 1 -; 9 - - So the common ratio is -. Then, 1 - - and - - 9 _. 1, 17, 89, 491; 17 17; 89 1 17 17 So the common ratio is 17. Then, 89 17 491 Copyright by Holt, Rinehart and Winston. 46 Holt Algebra 1
6. 10 ; 0 ; _ 0 10 0 The common ratio is ; yes. 7. 1 ; ; 9 The common ratio is ; yes. ; 4 6 18 4 ; 8 4 19 1 8. 18 There is no common ratio; no. ; -1 - ; - -1 There is no common ratio; no. 9. 9 _ 0. 1 ; 6 ; 189 7 1 6 The common ratio is ; yes. 4 ; - -; -4 1 - There is no common ratio; no. a. ; 4 ; 8 1 4 Plan is a geometric sequence with common ratio. 1. 4 b. Possible answer: Plan 1; Under Plan, the cost for the 10th week alone is $1, which is more than the cost for the entire summer under Plan 1. a. a n a 1 r n - 1 a 7 0.0 6 a 7 1.8 cm b. a n a 1 r n - 1 a 1 0.0 11 a 1 40.96 cm 4. a 1 a ( 1 6 a ( 1 a 4 ( 4. a 1 - a - (4 1-8 a - (4 - a 4 - (4-18 6. a 1 a (- 1-10 a (- 0 a 4 (- -40 7. a 1 a ( 1 4 a ( 8 a 4 ( 16 8. a 1 a ( 1 10 a ( 0 a 4 ( 0 9. a 1 1 a 1 ( 4 1 a 1 ( 4 4 a 4 1 ( 4 16 40. Each term is multiplied by n - 1, where n is the term number. For example, begin with the geometric sequence 4, 1, 6, 108...., where r. If r is doubled to 6, the sequence becomes 4, 4, 144, 864,... 41a. Stage 0 Stage 1: b. c. 4 Stage : Stage : Stage Squares 0 1 1 4 16 64 4; 16 4; 64 1 4 16 4 yes; r 4 d. r 4 and a 1 4 a n a 1 r n - 1 a n 4 (4 n - 1 a n 4 n 4. Divide each term by the preceeding term to find the value of r. Then use the formula a n a 1 r n - 1, where a 1 is the first term of the sequence. 4a. 00 1.1; 60 000 00 1.1 a 4 60 1.1 $99 a 99 1.1 $49.0 b. 00 1.1; 60 000 00 1.1 The common ratio is 1.1. c. $77.7; divide tuition years ago ($000 by 1.1, the common ratio. Copyright by Holt, Rinehart and Winston. 47 Holt Algebra 1
TEST PREP, PAGE 771 44. D: 10 ; 0 ; 40 ; there is a common 10 0 ratio. 4. J; since r -4 and a 1, ( -8-4; -4; -18-8 -4 a n (-4 n - 1 46. C; r and A 1 A n A a r n - 1 A 7 A 1 r 6 A 7 0 Hz CHALLENGE AND EXTEND, PAGE 771 47. x x x; x x x r x and a 1 x; a 4 x (x x 4 a x (x 4 x a 6 x (x x 6 _ 48. 6 x 4 x; 18 x x x 6 x r x and a 1 x ; a 4 x (x 4 x a x (x 4 16 x 6 a 6 x (x 486x 7 49. y; y y y y y r y and a 1 y a 4 y (y 1 a y (y 4 y a 6 y (y y _ 1 _ 0. x + 1 1 x + 1; 1 1 (x+1 x+1 x + 1 r x + 1 and a 1 1 (x+1 _ 1 a 4 (x + 1 x + 1 (x+1 a 1 (x + 1 4 (x + 1 (x+1 a 6 1 (x + 1 (x + 1 (x+1 1. a 10 a 1 r 9 a 1 a 10 r 9 _ a 1 0.781 (-0. 9 a 1-400. No; each term of the sequence is found by multiplying the previous term by the common ratio. of any positive number is always another positive (nonzero number.. a n a 1 r n - 1 r n - 1 a n a 1 (0.4 n - 1 0.0744 14 (0.4 n - 1 (0.4 6 Then, n - 1 6 n 7 4. Susanna assumed the sequence was geometric with r. She used the formula to find a 8 18. Paul did not assume the sequence was geometric. Instead, he noticed a pattern of add 1, add, and so on. He continued this pattern by adding, adding 4, etc., until he got the 8th term of 9. Both could be considered correct because it was not specified what type of sequence was given. SPIRAL REVIEW, PAGE 771. b - 4 > 6 b - 4 + 4 > 6 + 4 b > 10 6. -1 + x -8-1 + 1 + x -8 + 1 x 4 7. c + < c + - < - c < - 9. x + y > 6 y > -x + 6 8. y < x - 4 60. -y x + 1 y -x - 1 Copyright by Holt, Rinehart and Winston. 48 Holt Algebra 1
61. Vertical translation of +7; f(x x - + 7 f(x x + 4 6. Vertical translation of -; f(x x + 6 - f(x x + 4 Narrowing the graph. f(x a x + 4, where a >. Possible answer: f(x x + 4 THINK AND DISCUSS, PAGE 77 1. Possible answer: Make a table of values. Use x- values that change by the same amount each time as you move down the column. Then divide each y-value, starting with the second row, by the y-value before it. The quotient is the common ratio.. 11- EXPONENTIAL FUNCTIONS, PAGES 77 778 CHECK IT OUT! PAGES 77 77 1. f(x 8 (0.7 x f( 8 (0.7 f( 8(0.4187 f(.7 in. a. No; as the x-values change by a constant amount, the y-values are not multiplied by a constant amount. b. Yes; as the x-values change by a constant amount, the y-values are multiplied by a constant amount. a. y x b. y 0. ( x 4a. y - 6 x b. y - ( x EXERCISES, PAGES 776 778 GUIDED PRACTICE, PAGE 776 1. No; there is no variable in the exponent.. f(x 0,000 (0.97 x f(00 0,000 (0.97 00 f(00 16; 16 lumens/ m. No; as the x-values increase by a constant value, the y-values are not multiplied by a constant value. 4. Yes; as the x-values increase by a constant value, the y-values are multiplied by a constant value.. y x 6. y x 7. y 10 ( x 8. y ( x a. y 4 ( 4 x b. y -(0.1 x 6. f(x 1,0 (0.869 x 000 1,0 (0.869 x x log 0.869 ( 1,0 000 x 1; after about 1 yrs 9. y -( x 10. y -4 ( x Copyright by Holt, Rinehart and Winston. 49 Holt Algebra 1
11. y - ( x 1. y ( x 6 y. y 1. x 6. y 1_ ( x 1. y - ( 4 x 1. y ( 4 x 14. y ( x 16. y - (0. x 0 x 7. y 100 (0.7 x 9. y -1 ( x 8. y - (4 x 0. y - 1_ (4 x 17. f(x 7.8 (1.0 x 00,000,000 7.8 (1.0 x x 6; about 0 (6 years after 1960 PRACTICE AND PROBLEM SOLVING, PAGES 776 778 18. f(x 7 ( x f(4 7 ( 4 f(4 7 ( 16 81 f(4 ; ft 0. y 1. (1.41 x for x 1, y 1. (1.41 1 y.0;.0 in./min 19. y 4 (0.976 x for x 6, y 4 (0.976 6 y 89; 89 ft 1. Yes; as the x-values change by a constant amount, the y-values are multiplied by a constant amount.. No; as the x-values change by a constant amount, the y-values are not multiplied by a constant amount.. No; as the x-values change by a constant amount, the y-values are not multiplied by a constant amount. 4. Yes; as the x-values change by a constant amount, the y-values are multiplied by a constant amount. 1. y 4 ( 1_ x. y 0. (0. x 4. f(x 4 (1.41 x 1,000 4 (1.41 x x 9; about 009. y - ( 1_ x. y (.1x + 7 is not exponential since there is no variable in the exponent. For y ( (6 x,y 7. for x and y 4. for x, hence y ( (6 x does not generate 8.4. For y 4.8 ( x, y 8.4 for x ; ans. y 4.8 ( x 6a. f(x 0 (1. x f( 0( 1. f( 8.8; $8.80 b. f(x 0 (1. x 100 0 (1. x x 9; after 9 weeks Copyright by Holt, Rinehart and Winston. 440 Holt Algebra 1
c. f(x 0 (1. x f(0 0 (1. 0 f(0 0; $0 f(n + 1 d. increase _ - 1 f(n n + 1 0 (1. increase _ 0 (1. n - 1 increase.;. or 0% 7. If the value of b were 1, the function would be constant. If the value of a were 0, the function would be the constant function y 0. 8. Possible answer: The graphs have the same basic shape and the same y-intercept; each graph is steeper than the one before it. 9. Possible answer: The graphs have the same basic shape and the same y-intercept; each graph is steeper than the one before it. 40. f(x 4 x f( 4 f( 64 4. f(x 0.4 (10 x f(- 0.4 (10 - f(- 0.0004 or 4 10-4 4a. In 001, n 0 C 000 (1.08 0 C 000; $000 b. increase n + 1 000 (1.08 000 (1.08 n - 1 increase 0.08; 8% c. For 006, n C 000 (1.08 C 98.66; $98.66 41. f(x - (0. x f(1. - (0. 1. f(1. -0.1 44. Possible answer: The following table shows how much money you could earn with each plan. Year Salary Plan A Salary Plan B 0 $0 $10,000 1 $0,000 $0,000 $40,000 $40,000 $60,000 $80,000 Choose plan B because plan A doesn t pay anything for the first year and because after years, plan B pays more money. 4. C; the other graphs do not increase exponentially. 46. G; f(4 1 (1.4 9.4 47. D; a 1, r, hence a n ( n - 1 n CHALLENGE AND EXTEND, PAGE 778 48. 4 x 64 4 x 4 x 0. x 1 16 x 1 4 x -4 x -4 49. ( 1. The value of a is the y-intercept. SPIRAL REVIEW, PAGE 778 _ 88 + 89 + x. 90 x 9. ; x + 10x + (x + 4. x; 4 x + x + 64 (x + 8. 9 x ; 9 x + 4x + 49 (x + 7 6. a n 4 ( n - 1 a 1 4 ( 11 a 1 708,88 x 1 7 -x - -x - x Copyright by Holt, Rinehart and Winston. 441 Holt Algebra 1
CONNECTING ALGEBRA TO GEOMETRY: CHANGING DIMENSIONS, PAGE 779 TRY THIS, PAGE 779 1. widths: 8, 4,, 1; common ratio: lengths: 16, 8, 4, ; common ratio: heights:, 16, 8, 4; common ratio: volumes: 4096, 1, 64, 8; common ratio: 8. heights: 8, 4, 7; common ratio: edge of bases:, 9, 7; common ratio: volumes: 4, 648, 17,496; common ratio: 7 ALBEGRA LAB, PAGE 780 TRY THIS, PAGE 780 1. doubles. 0, 1,,, 4,. number of regions ( n - 1 n 4. n 8; number of regions 8 6. n 1 n 9 n 9; 9 folds 6. is divided in half 7. 0, -1, -, -, -4, - 8. a n ( n - 1 a n ( n a n -n 9. a 7-7 _ 1 10. -n 6 -n 1 _ 1 18 8 -n -8 n 8; 8 cuts 11- EXPONENTIAL GROWTH AND DECAY, PAGES 781 788 CHECK IT OUT PAGES 781 784 1. y a (1 + r t 100 (1.08 t ; In 006, y 100 (1.08 6 $1904. a. A P ( 1 + r n nt 100 ( 1 + 0.0 4 4t 100(1.0087 4t; After 4 years, A 100 (1.0087 16 $179.49 b. A P ( 1 + r n nt 4000 ( 1 + 0.0 1 1t 4000 (1.00 1t After 8 years, A 4000 (1.00 96 $08.47. y a (1 - r t 48,000 (1-0.0 t 48,000(0.97 t After 7 years, y 48,000 (0.97 7 8,78 180 years 4a. t 0 years 6 A P( 0. t 100( 0. 6 1.6 mg b. t _ weeks days 7 A P(0. t 100 (0. 7 0.781 g THINK AND DISCUSS, PAGE 784 1. Possible answers: interest earned on an investment, population growth or decline, radioactive decay. increasing; by % per year. An exponential growth function has the form y a (1 + r t. The base (1 + r corresponds to the base b. The exponent t corresponds to the exponent x. An exponential decay function has the form y a (1 - r t. The base (1- r corresponds to the base b. The exponent t corresponds to the exponent x. 4. EXERCISES, PAGES 78 788 GUIDED PRACTICE, PAGE 78 1. exponential growth, since > 1. Copyright by Holt, Rinehart and Winston. 44 Holt Algebra 1
. y a (1 + r t 1,000 (1 + 0.06 t 1,000 (1.06 t After 4 years, y 1,000 (1.06 4 $1,149.7. y a (1 + r t 00 (1 + 0.08 t 00 (1.08 t After years, y 00 (1.08 441 4. A P ( 1 + r n nt 100 ( 1 + 0.0 1 t 100 (1.0 t After 4 years, A 100 (1.0 4 $171.8. A P ( 1 + r n nt 400 ( 1 + 0.08 4 4t 400 (1.007 4t Ater 6 years, A 400 (1.007 4 $496.4 6. y a (1 - r t 18,000 (1-0.1 t 18,000 (0.88 t After 10 years, y 18,000 (0.88 10 $01.0 7. y a (1 - r t 10 (1-0.16 t 10 (0.84 t After 4 hours, y 10 (0.84 4 4.98 mg 8. t _ 1 hr 9. t 16 days 0 min days A P (0. t A P (0. t 0 (0. 44 (0..7 g. g PRACTICE AND PROBLEM SOLVING, PAGES 78 787 10. y a (1 + r t 149,000 (1.06 t After 7 years, y 149,000 (1.06 7 $4,040.91 11. y a (1 + r t 1600 (1 + 0.0 t 1600 (1.0 t After 10 years, y 1600 (1.0 10 10 1. A P (1 + r nt 700 (1 + 0.01 4t 700 (1.01 4t After years, A 700 (1.01 4t $770.09 1. y P (1 + r nt 0 (1 + 0.078 t 0 (1.079 t After years, y 0 (1.078 t 47 members 14. A P ( 1 + r n nt 8,000 (1 + 0.04 t 8,000 (1.04 t After years, A 8,000 (1.04 $4,066.8 1. A P ( 1 + r n nt _ 7000 ( 1 + 0.0 4 4t 7000 (1.007 4t After 10 years, A 7000 (1.007 40 $948.44 16. A P ( 1 + r n nt 00 ( 1 + 0.018 1 1t 00 (1.001 1t After 4 years, A 00 (1.001 48 $761.09 17. A P ( 1 + r n nt 1,000 (1 + 0.06 t 1,000 (1.06 t After 1 years, A 1,000 (1.06 1 $17,6.66 18. y a (1 - r t 18,000 (1-0.0 t 18,000 (0.98 t After 6 years, y 18,000 (0.98 6 1,94 19. y a (1 - r t 8 (1-0.1 t 8( 0.9 t After 8 years, y 8 (0.9 8 $4.97 6 days 0. t 6 hours 144 hours 6 hours 4 A P(0. t 80 (0. 4 g 1. growth; 61%, since 1+ r 1.61. decay; 90.%, since 1 - r 0.098. decay; %, since 1 - r 4. growth; 0%, since 1 + r. growth; 10%, since 1 + r 1.1 6. decay; 0%, since 1 - r 0.8 7. growth; %, since 1 + r 4 8. decay; 0%, since 1 - r 9. y a (1 + r t 8,000,000 (1.001 t After years, y 8,000,000 (1.001 8,174,174 0. y a (1 + r t,000 (1.07 t After years, y,000 (1.07 $44,881.66 Copyright by Holt, Rinehart and Winston. 44 Holt Algebra 1
1. y a (1 - r t 800 (1-0.0 t 800 (0.98 t After 7 years, y 800 (0.98 7 $7118.6. y a (1 - r t,000 (1-0.1 t,000 (0.8 t After 6 years, y,000 (0.8 6 $948.74. y a (1 + r t 970 (1 + 0.01 t 970 (1.01 t After years, y 970 (1.01 100 _ 00 years 4. t 700 years 7 A P (0. t 1 (0. 7 9.8 g. B; possible answer: student B did not subtract the rate from 1. 6. No; possible answer; there is no value for t that would make (0.84 t equal 0. 7. y a (1 + r t 600 00( 1 + 0.04 t 1.04 t t 18 years 8a. y a (1 + r r 0,000 (1.09 t b. In 008, t 6, hence y 0,000 (1.09 6 $,4 c. 011 Year Tuition ($ 00 0,000 00 1,800 004,76 00,900.8 006 8,1.6 007 0,77.48 008,4.00 009 6,60.78 010 9,81. 011 4,47.87 9. In 10 years: A: 600 (1.0 10 $977.4 B: 00 (1 + _ 0.06 4 40 00 (1.01 40 $907.01 A will have a larger balance. In 0 years: A: 600 (1.0 0 $191.98 B: 00 (1.01 80 $164. B will have a larger balance. 40. 0 h; 1h 41. The graph when r is 0% rises faster than when r is 10%. The greater the value of r, the faster the graph will rise. 4. Possible answer: $400 is invested at a rate of 8% compounded annually. 4. Possible answer: The population is 800 and decreasing at a rate of 4% per year. 44. No; possible answer: the sample doubles every minute, so the container is half full 1 minute before it is full. This would be after min. 4. D; y a (1 -r t a 00, 1 - r 1-0.01 0.99 46. G; a -, so as the absolute value of y decreases, y is actually increasing. 47. D; 86 (1.0 $1001. 48a. y a (1 + r t 1000 (1 + 0.0 t 1000 (1.0 t b. 100 1000 (1.0 t t ; about 00 CHALLENGE AND EXTEND, PAGE 788 49. about 0 years 0. y a (1 + r t 1000 00 (1.04 t t 18 yr for r 0.08 1000 00 (1.08 t t 9 yr 1. A P (0. t 10 80 (0. t t So, half-life _ 00 t. A P (0. t 6 1 P (0. P 10 g. A P ( 1 + r n nt 0,000 P (1 + 0.01 P $,44 4. Month Balance ($ 100 min or 1 h 40 min Monthly Payment ($ (4 8 Remaining Balance ($ 1.% Finance Charge ($ New Balance ($ 1 00 0 170. 17. 17. 0 14..14 144.69 144.69 0 114.69 1.7 116.41 Copyright by Holt, Rinehart and Winston. 444 Holt Algebra 1
4 116.41 0 86.41 1.0 87.71 87.71 0 7.71 0.87 8.8 6 8.8 0 8.8 0.4 9.01 7 9.01 9.01 0 0 0 b. Table shows balance is paid off in 7 months. c. (6(0 + 9.01-00 9.01 SPIRAL REVIEW, PAGE 788. 1. 1. h 0 h 16 ft 6. w 1 10 0 w 6 in. 7. f(x x + 1 8. f(x x - 4. EXERCISES, PAGES 79 79 GUIDED PRACTICE, PAGE 79 9. f(x x -1 60. f(4 0.10 ( 4 $1.60; 1.80 0.10 ( x x 7 days 1. exponential. quadratic 11-4 LINEAR, QUADRATIC AND EXPONENTIAL MODELS, PAGES 789 79 CHECK IT OUT! PAGES 790 79 1a. exponential b. quadratic. Quadratic; for every constant change in the x-values of +1, there is a constant second difference of -6 in the y-values.. The oven temperature decreases by 0 F every 10 minutes; y -x + 7; 7 F THINK AND DISCUSS 1. No; most real-world data probably will not fit exactly into one of these patterns.. No; this is just a prediction based on the assumption that the observed trends will continue, which they may or may not do.. linear 4. Quadratic; for every constant change of +1 in the x-values, there is a constant second difference of -1 in the y-values.. Exponential; for every constant change of +1 in the x-values, there is a constant ratio of. 6. Linear; for every constant change of +1 in the x-values, there is a constant change of + in the y-values. 7. Grapes cost $1.79/lb; y 1.79x; $10.74 PRACTICE AND PROBLEM SOLVING. PAGES 79 79 8. quadratic 9. linear Copyright by Holt, Rinehart and Winston. 44 Holt Algebra 1
10. exponential 11. Linear, for every constant change of +1 in the x-values, there is a constant change of -1 in the y-values. 1. Quadratic, for every constant change of +1 in the x-values, there is a constant second difference of - in the y-values. 1. Exponential, for every constant change of +1 in the x-values, there is a constant ratio of 0. in the y-values. 14. The company s sales are increasing by 0% each year; y,000 (1. x ; $14,79.41 1. l 6k; linear with m 6 and b 0 16. Linear; for every weekly interval, the height of the plant has a constant increase of 0. inches. 17. Linear; for each successive year, the number of games has a constant change of 0. 18. Quadratic; for each successive time interval, the height of a ball has a constant second difference of -0.8. 19. y 0. (4 x 0. y - x + 4 1. linear. quadratic. Possible answer: (0,, (1,6, (,1, (,4; for a constant change in x of +1, there is a common ratio of. 4. Possible answer: the first differences are constant, so there is no need to check the second differences. A linear function would best model the data.. Possible answer: make a table of ordered pairs and see whether the y-values show a pattern of constant second differences or constant ratios. 6a. college 1: linear because it has constant changes of $00 each year; college : exponential because it has a constant yearly ratio of 1:1.1. b. college 1: y 00x + 000; college : y 000 (1.1 x c. Both have the same tuition ($000 in 004. d. For college 1, $00 is added each year, so 000 + 00 00. For college, 10% is added each year, so 000 + (0.1(000 00. 7. C; the data is linear since it has a constant change in the y-values for each constant change in the x-values. 8. F; % is a common ratio. CHALLENGE AND EXTEND, PAGE 79 0a. Year Value ($ 0 18,000 1 1,10 1,700.80 10,668.67 4 8961.68 Year 0 is the year when the car is purchased. d. y 18,000 (0.84 $6899.6 e. y 18,000 (0.84 8 $4461.77 b. exponential, for each successive year, the value decreases by 16%, the common ratio. c. y 18,000 (0.84 x 1a. Possible answer: quadratic; the second differences are approximately constant at -. b. about 48 kg c. No; this quadratic model will begin to decrease although the dog s weight will either continue to grow or eventually remain constant. SPIRAL REVIEW, PAGE 79. n; she would run km n times. _. 14 g. 4 x 100 x x ± x ± 7. 16 x + 86 16 x 81 x 81 16 x ± 81 16 x ± 9 4 9. y - ( x 4. 74 - b 6. 10 - x 10 - x 0 x 0 8. y 6 x 40. y ( x MULTI-STEP TEST PREP, PAGE 796 1. y 0 (1.09 x where y tuition is the dependent variable and x years since 1980 is the independent variable. 9. C; For every constant change of +1 in the x-values, there is a constant change of + in the y-values. Copyright by Holt, Rinehart and Winston. 446 Holt Algebra 1
. y 0(1.09 6 $89.71 READY TO GO ON? PAGE 797 6 ; 1 ; 4 ; the common ratio is 1. 6 1 next terms: 4( 48, 48( 96, and 96( 19 8 -; -; -4 -;. -1-4 the common ratio is - next terms: 8(- -16, (-16(-, and (- -64-600 -00-100 1 ; 1 ; 1. -400-100 -600 1 1-7, next terms: -00-10, -10 1-7. and -7 ( ( ( 4. a 1 1000, r n-1 a n a 1r 4 7-1 a 7 1000 a 7 6.144 cm n-1 4. a n a 1r a 8 (( 8-1 a 8 474. Answers will vary. 4. 700 0(1.09 x x 8; about 1988 ( 6. f(x (1.1 x 7. y x 4 f(4 (1.1 f(4 4.9 in y x 8. y ( x 9. y -(4 x y y å x x. 1000 0(1.09 x about 199-199 10. y -(0. x 11. f(x 40(0.8 x y x x 40(0.8 x 14; after about 14 h 1. y a(1 + r x 0,000(1.0 x; After 10 years, y $40,17.49 nx 1. y a(1 + r n 1x; 000(1.007 After years, y $88.0 Copyright by Holt, Rinehart and Winston. 14. y a(1 - r x 100(0.8 x After 4 years, y $491. 447 Holt Algebra 1
1. A P (0. t _ 00 A 100(0. 0 A 100(0. 10 A 0.098 mg 16. quadratic 17. exponential. The graph of f(x x + 8 is the graph of f(x x translated 8 units to the left.. The graph of f(x x + 8 is the graph of f(x x translated 8 units to the left, while the graph of f(x x + 8 is the graph of f(x x translated 8 units up. 4. 18. linear; for every constant change of +1 in the x-values, there is a constant change of +1 in the y-values. 19. exponential: for every constant change of +1 in the x-values, there is a common ratio of in the y-values. 0. The value of the stamp is increasing by 0% each year; y (1. x ; $7.1 11- SQUARE-ROOT FUNCTIONS, PAGES 798 80 CHECK IT OUT! PAGES 798 800 1a. y 8 x b. y 8 x 8 8 1 40.00 ft/s 0.98 ft/s a. y x - 1 x -1 0 x 1 x Domain: { x x } b. y x - x - 0 x x Domain: { x x } a. f(x x + b. f(x x + EXERCISES, PAGES 801 80 GUIDED PRACTICE, PAGE 801 1. There is no variable under the square-root sign.. c a + b 14 + 8 16.1 cm. y x + 6 x + 6 0 x -6 Domain: {x x -6}. y x - x 0 x 0 Domain: {x x 0} 7. y x +9 x + 9 0 x - 9 x - Domain: {x x -} 9. f(x x - 1 4. y 4 - - x - x 0 -x - x Domain: {x x } 6. y x + x + 0 x - Domain: {x x -} 8. y x + x - x - 0 x Domain: {x x } 10. f(x - x THINK AND DISCUSS, PAGE 800 1. Possible answer: Set the expression under the square-root sign greater than or equal to zero and solve. Copyright by Holt, Rinehart and Winston. 448 Holt Algebra 1
11. f(x x + 1 1. f(x 4 - x 1. f(x 4x f(104 4 104 f(104 49.96 mi/h 17. y 4 - x 0 x 0 Domain: { x x 0 } 19. y -x + -x + 0 -x - x Domain: { x x } x 1. y (x + - 1 (x + - 1 0 x + x - Domain: { x x - } x. y 7-8 x - 8 0 x 40 Domain: { x x 40 }. y (x - 9 (x - 9 0 x - 9 0 x 9 Domain: { x x 9 } 1. f(x x - 1 14. f(x x +4 16. y 8 - x 8 - x 0 -x -8 x 4 Domain: { x x 4 } 18. y x + x + 0 x - Domain: { x x - } 0. y x + 1 x + 1 0 x -1 Domain: { x x -1 }. y (x + 4 - (x + 4 0 x + 4 0 x -4 Domain: { x x -4 } 4. y (x - 6 (x - 6 0 x -6 0 x Domain: { x x } 6. y (x + 7-6 (x + 7-6 0 x + 7 x -4 Domain: { x x -4 } 7. y 4 + x + x + 0 x - Domain: { x x - } 8. f(x x - 0. f(x -1 - x. f(x x - 6 4. r A π _ 60.14 4.7 cm 9. f(x x - 4 1. f(x x - 4. f(x x + 4 a. b. For each function, x must be real, hence x 0 Domain: { x x 0 } c. x 0 for all values of x in the domain. Range: { y y 0 } d. Possible answer: it has a minimum value of 0 and curves to the right. As a increases, the curve becomes steeper. 6a. Copyright by Holt, Rinehart and Winston. 449 Holt Algebra 1
b. For each function, x must be real, hence x 0 Domain: { x x 0 } c. x 0 for all values of x in the domain and the coefficients in all the functions are negative. Range: { y y 0 } d. Possible answer: it has a maximum value of 0 and curves to the right. As a decreases, the curve becomes steeper. 7. d (w - x + (z - y 8. ( - + ( - 1 1.61 units f(x 9.8x f(00 9.8 00 f(00 70 m/s 9. v gr Mercury: v.7.4 10 6 414 m/s Venus: v 8.8 6.1 10 6 10,61 m/s Earth: v 9.8 6.4 10 6 11,00 m/s Mars: v.7.4 10 6 016 m/s 40. V π r h r V πh 11.14 10 6.1 in 41. Set the expression under the square-root sign greater or equal to 0 and solve; the square root of a negative number is not a real number so the domain cannot be all real numbers. 4. Since the domain is x, the value of y is 0 when x. 4. No; the domain of a square-root function is limited to values that make the value under the square-root sign non-negative. A function with a limited domain cannot have a range of all real numbers. 44a. T π l b. T π l l 0.14 80 l 0 9.9 s Domain: { l l 0 } c. No; 9.9 seconds is too fast for the ride to make one complete swing back and forth. This is for a pendulum that is under the influence of gravity only. This is not true for the ride. 4. A; the graph of x is shifted units left. 46. J; x would make x - a nonnegative number 47. C; y. seconds 48. g(x 4x - 1 g(9 4(9-1 g(9 CHALLENGE AND EXTEND, PAGE 80 49. y x - x - 0 x x Domain: { x x - or x } 0. y x + x + 6 x + x + 6 0 (x + (x + 0 x + 0 and x + 0 or x + 0 and x + 0 Domain: { x x - or x - } 1. y x + x - 1 x + x -1 0 (x - (x + 4 0 x - 0 and x + 4 0 or x - 0 and x + 4 0 Domain: { x x or x -4 }. y - x + x + 0 x - and y Domain: { x x - } Range: { y y } 4. y 6 - x 0 x 0 and y 6 Domain: { x x 0 } Range: { y y 6 } x. y 4 - - x - x 0 x and y 4 Domain: { x x } Range: { y y 4 }. Possible answers: y x + b, where b > 0 Example: y x + 6 Copyright by Holt, Rinehart and Winston. 40 Holt Algebra 1
6. Possible answers: y - x + a + b, where a 0 and b < 0. Example: y - x - 1-1 7a., 4; when x or x 4, the expression under the square-root sign is negative. b. for x, y - ( - for x 7, y - (7 - - 1 SPIRAL REVIEW, PAGE 80 8. y 4x - 8 y x - 4 9. x + 6y 1 6y -x + 1 y - x + 68. A P (0. t 1 day t. hours 96 A 0 (0. 1 1.8 g 4 hours. hours 96 1 TECHNOLOGY LAB: GRAPH RADICAL FUNCTIONS, PAGE 804 TRY THIS, PAGE 804 1.. 60. x -y - 9 y -x - 9 61. (a + b a + ab + b (x - 1 (x + (x(-1 + (-1 9 x - 6x + 1 6. (a - b(a + b a - b (x - (x + (x - ( 4 x - 6. (a + b a + ab + b (a - b c a + (a(- b c + (- b c a - a b c + b 4 c 64. (a + b a + ab + b ( x + y ( x + ( x (y + (y x 4 + 4 x y + 4 y 6. (a - b(a + b a - b (r - s(r + s (r - (s 9 r - 4 s 66. (a - b(a + b a - b ( a b - c 4 ( a b + c 4 ( a b - ( c 4 a 6 b 4 - c 8 67. A P ( 1 + r n nt _ A 4,000 ( 1 + 0.0 4 4t 4,000 (1.01 4t After years, A 4,000 (1.01 1 $48,71.69. The graph of f(x x + 1 + 4 will be the graph of f(x x shifted 1 unit left and 4 units up. 4. The graph of f(x x will have a steeper curve. 11-6 RADICAL EXPRESSIONS, PAGES 80 810 CHECK IT OUT! PAGES 80 807 1a. _ 6 4 64 b. 40 + 9 49 7 8 c. + 1 + 144 169 1 d. ( - x - x Copyright by Holt, Rinehart and Winston. 41 Holt Algebra 1
a. 18 64( 64 8 b. x y x y xy x x x y c. 48 a b 16 a b 4a b 1 7 4 b. 6 9 a. c. y 6 4 9 6 _ 4 y 4 y _ 4a. 0 49 0 49 4 49 _ 7 c. 6 p p 6 q 10 q 10 p q _ 6 x 4 x 4 b. _ z THINK AND DISCUSS, PAGE 808 1. Method 1: 16(9 144 1 Method : 16(9 16 9 4( 1. Method 1: _ 100 4 Method : _ 100 4 100 4 10 6 x z y y (z z 4 y z z y. c a + b 60 + 60 ( 60 60 ft or 84.9 ft. EXERCISES, PAGES 808 810 GUIDED PRACTICE, PAGE 808 1. x - 6 is the radicand. 81 9. 98 49 7. 180 (6 6 6 7. 648 (4 18 8. m n m n m 4 n mn m n mn 9. x 4 y 16( x 4 y y 4 x y y 10. 00 a b (100 a b 4. (a + 7 a + 7 6. 40 (410 4 10 10 100 a b 10a b 11. 17 _ 17 1. 7 16 _ 7 16 _ 17 7 4 _ 1. 6 49 6 49 6 7 _ x 1. 4 x 6x 9 x 9 x 17. 108 49 (6 49 _ 6 7 _ 6 7 14. b 16. 7 a 4 _ b c c b c 7a 9 a 9 _ 7a 9 7a 18. 04 (41 _ 4 1 1 Copyright by Holt, Rinehart and Winston. 4 Holt Algebra 1
19. 1 81 6( 81 6 81 16 9 1. _ 0 x 169 ( x 169 _ x 169 x 1. c a + b 0 + (16 + 41 41 mi mi 0. _ 1 1 6 x 6 x 1 6x. _ 7 x 7 18 x 4 x 4 9 x x x x PRACTICE AND PROBLEM SOLVING, PAGES 809 810 _ 4. 100 10. 800 400 0 6. + 4 7. 7 81 9 8. a 4 a 9. (x + 1 x + 1 0. ( - x - x 1. (x - x -. 1 ( 4. 16 a b 6 a b 6 6ab 6. 0 r s (64 r s 6. 1 64 1 64 _ 1 8 8. _ 64 a 4 8rs _ 16 4 a 6 a _ 16 a 4 a. 4000 10(400 0 10 7. 4 4 9( 4 9 _ 9. _ 14 z 14 9 z 9 _ 14 9 _ 14 40. 18 81 18 81 64( 81 _ 8 9 4. 10 _ 6( 196 x 196 x _ 6 14x _ 6 14x 44. t d 16 _ 160 16 10 s;. s 46. - 80-16( - 16-4 48. 48x 16(x 16 x 1 x 0. 1. 1 x x y _ 1 ( 1 10 x y _ 6 1 x 6 ( 1 x _ x y 6 y 4. 18 8 18(8 144 1 6. 8 14 8(14 11 16(7 4 7 41. x x x y 6 y 6 _ x x y _ 4. 19 s 49s 64( s 49 64 s 49 8s 7 4. -4 7-4 ( -4-0 47. x 6 x 9(7 x 9 7 1x 7 49. x 4 x 4 ( x x 1. x x 81 x 4 x x 81 x x 4 x 9 x x 9 x x. 1 1( 6 6. 10 10( 0 _ 7. 11 11 Copyright by Holt, Rinehart and Winston. 4 Holt Algebra 1
_ 8. 4 4 1 (4 _ 60. 7 7 9 9 8 4( _ 9. 60 60 0 4( 61. 4 ft; length of missing side 10 + 14 17. ft 10 + 14 + 17. 41. ft, rounded up to 4 ft. 6. Possible answer: Use the Quotient Property of Square Roots: 8 49 _ 8 49 Then use the Product Property of Square Roots in the numerator: _ 8 4 7 4 7 49 49 49 Then simplify by taking the square roots of the perfect squares: 4 7 _ 7 49 7 6a. v 64h 64 h 8 h ; v 8 17 9.6 ft/s b. Pythagorean Theorem c. d x + h 10 + 17 171.4 ft 64. Possible answer: The square root of a negative number is not a real number. _ 6. d 6h Sears: d 6 140 8700 100 87 10 87 mi; 1.1 mi Empire: d 6 10 700 00 0 mi; 8.9 mi Aon: d 6 116 6816 16 46 4 46 mi; 7. mi 66. s (a + b + c (7 + 9 + 1 14 A s(s - a(s - b(s - c 14(14-7(14-9(14-1 14 7 14 14 m ; 1. m 67. C: is not divisible by a perfect square. 68. F: 1 4 1 4 1 60 69. C: 10 + 10 ( 10 10 CHALLENGE AND EXTEND, PAGE 810 70. 4x + 16 4(x + 4 4 x + 4 x + 4 7. 9 x - 18 x 9 x (x - 9 x x - x x - 71. x + x x (x + 1 7a. x x b. x 4 x c. x 6 x d. x 8 x 4 e. x 10 x x x+1 x x + 1 Copyright by Holt, Rinehart and Winston. 44 Holt Algebra 1
f. x n (since any number to an even power is always positive; x n (since any negative number to an odd power is always negative SPIRAL REVIEW, PAGE 810 74. yes; possible answer: the equation is y 6x and is of form y kx, with k 6 7. no; possible answer: the equation is y x - 8 which is not of y kx form and the _ y value is not x the same for each (x, y. 76. y mx + b m _ - - 1 - -6-1 6 y 6x + b For (, 1, 1 6( + b b - 17 Hence, y 6x - 17 77. exponential 78. quadratic 11-7 ADDING AND SUBTRACTING RADICAL EXPRESSIONS, PAGES 811 81 CHECK IT OUT! PAGES 811 81 1a. 7-6 7-7 b. 8 - c. 4 n + 4 n 8 n d. s - s + 9 s s + 8 s a. 4 + 4 9(6 + 4(6 9 6 + 4 6 6 + 6 6 b. 4 7-18 4 9( - 9( 4 9-9 1 - c. 1y + 7y (4y + (9y 4 y + 9 y y + y y. ( b + b ( b 10 b in. THINK AND DISCUSS, PAGE 81 1. Group 1: 6, 600 10 6, 10 6 Group : 6, - 0 -,. Possible answer: Without simplifying, you cannot tell which terms are like radicals.. Possible answer: EXERCISES, PAGES 81 81 GUIDED PRACTICE, PAGE 81 1. Possible answer: any pair of a c and b c where a, b are real numbers and c is nonnegative. Example: 4 6 and - 6. 14-6 8. 9 + 10 4. 6 + - 1-4. 7 + 7 + 6. a - 9 a -4 a 7. 9 6a + 6 a - 4 6a 6a + 6 a 8. - 8 16( - 4( 16-4 4-9. 4 1 + 7 4 4( + ( 4 4 + 8 + 1 10. + 1-7 + 4( - 9( + 4-9 +10-9 11. 0x - 4x 4(x - 9(x 4 x - 9 x x - x - x 1. 8c + 9 4c 4(7c + 9 4(6c 4 7c + 9 4 6c 7c + 18 6c 1. 0t - 1t + t (t - 4(t + t t - 4 t + t t - 4 t + t 8 t - 4 t Copyright by Holt, Rinehart and Winston. 4 Holt Algebra 1
14. P 0 + 8 + 18 + 8 ( + 4( + 9( + 4 + 9 + 4 + 1 in. PRACTICE AND PROBLEM SOLVING, PAGES 81 81 1. 4 + 6 16. 7-1 6( - 1 6-1 -1 17. 11 + 11-6 11-11 18. 6 7 + 7 6 6 7 + 7 6 19. - n - n -4 n 0. y + y - y y - y 1. 17 + 8 (7 + 4(7 7 + 4 7 7 + 7 7 7. 80-0 16( - 4( 16-4 8-6. 8 - + 18 4( - 16( + 9( 4-16 + 9 10-4 + 6 1 4. 10r + 4r (6r + 9(6r 6r + 9 6r 6r + 6r 8 6r. 6x - 4 7x 9(7x - 4 9(x 9 7x - 4 9 x 7x - 1 x 6. 48p + 18p - 7p 16(p + 9(p - 9(p 16 p + 9 p - 9 p 4 p + 9 p - 6 p 9 p - p 7. 180j - 4j 6(j - 9(j 6 j - 9 j 6 j - j j 8. 90c - 40c 9(10c - 4(10c 9 10c - 4 10c 9 10c - 10c 7 10c 9. 7m - 1m - 108m (m - 4(m - 6(m m - 4 m - 6 m 10 m - m - 6 m m 0. P 1 + 8 + + 1 + + + 4( + + 4 + + + 4 mi 1. 7 + 7 7 1 7. 18 ab - 10 ab 8 ab. - + 0 4. 98 + 18 49( + 64( 49 + 64 7 + 8 1. 00-7 100( - 9( 100-9 10-7 6. 4x + 00x 9(x + 100(x 9 x + 100 x x + 10 x 1 x 7. 8 + 8. 6 18-4( + 16( 4 + 16 + 7 6 9( - 6 9-0 - 9a. section A: 11 ; section B: 11 ; section C: 11 b. 10 11 c. Because the areas found in parts a and b must be equal, the model shows that: 11 + 11 + 11 ( + + 11 10 11 Copyright by Holt, Rinehart and Winston. 46 Holt Algebra 1
40. 40ab - 0ab (ab - (ab ab - ab 1 ab - ab 10 ab 41. 1 + 1 + 4( + ( + 4 + + + + 4. 8-18 169( - 9( 169-9 1-10 4. 700x - 8x - 70x 100(7x - 4(7x - 70x 100 7x - 4 7x - 70x 10 7x - 7x - 70x 8 7x - 70x 44. - 90-160 - 9(10-16(10-9 10-16 10-9 10-1 10-1 10 4. 7 80k + 0k + 4k 7 16(k + 4(k + 9(k 7 16 k + 4 k + 9 k 8 k + 4 k + k k 46. 4abc + 600abc 4(6abc + 100(6abc 4 6abc + 100 6abc 1 6abc 47. 1 + 0 + 7 + 4 4( + 4( + 9( + 9( 4 + 4 + 9 + 9 + + + + 48. A and C are incorrect. In A, the radicands were added. In C, the radicals were not like radicals but they were incorrectly combined by subtracting the radicands. 49. Possible answer: Like radicals have the same number, variable, or numbers and variables under the radical sign; examples: and ; nonexamples: and. 0. ab + x - a 7 ab - a x 7 ab - ab x ab x ab 1. 4 x - yx x - y x x - 4 x y x x y y 9. - x + 4 x + - 4 x x 4 x 8 x 8. x + 8 11 x x 9 x 18 x 18 4. + + x 9 x 4 x 16 x 48 x 48. x - y -4x - y -6x y 6 x y 6 x b. Pythagorean Theorem 6a. d r 0 r r 1 ft 7. A s P 4s P 4s 4( 48 4( 1 4( 16( 4( 4( 4( 16 4 4 4(4 8 in. 16 in. 16 + 8 4 in. 8. The radical is similar to a variable. To add or subtract, combine coefficients. 9. B; the radicands have no common factors and are hence not like radicals. 60. F; - 7x + 6 7x 7x 61. A; 18-9( - 9 - - CHALLENGE AND EXTEND, PAGE 81 6. x - + x - 7 x - 6. x x + x (x + 64. 4 x - + x - 7 4 x - + (x - 4 x - + x - 4 x - + x - 9 x - 6. x + 7-4x + 8 x + 7-4(x + 7 x + 7-4 x + 7 x + 7 - x + 7 0 Copyright by Holt, Rinehart and Winston. 47 Holt Algebra 1
66. 4 x + 4 x + x + 6 x 4 x (x + 6 + x (x + 6 4 x x + 6 + x x + 6 x x + 6 + x x + 6 x x + 6 67. x - x + 4x - 4 x (x - 1 + 4(x - 1 x x - 1 + 4 x - 1 x x - 1 + x - 1 (x + x - 1 68. x + x - x + x (x + - x + x x + - x + x x + - x + (x - 1 x + 69. 9x + 9 - x + x 9(x + 1 - x (x + 70. A h( b 1 + b (4 ( 0 + 4 (4 ( 4( + 9( (4 ( 4 + 9 (4 ( + (4 ( (0( 0 cm 9 x + 1 - x x + x + 1 - x x + SPIRAL REVIEW, PAGE 81 71. m AB 4-1 4-1 1, m BC _ - 4 - - 4 6 m CD 0 - - - (- 1, m AD _ 0-1 - - 1 6 Since m AB m CD, AB CD. Since m BC m AD, BC AD. Since both pairs of opposite sides are parallel, ABCD is a parallelogram. 7. m XZ 4-0 - (-1 4 ; m YZ 0 - (- -1 - - 4 ; Since the product of the slopes is -1, XZ YZ, XYZ is a right triangle. 7. P(roll 6 and toss heads 1_ 6 1_ 1_ 1 74. y 4x - 4x - 0 4x x Domain: { x x } 76. y 1 + x + 6 x + 6 0 x -6 Domain: { x x -6 } 7. y - x + x + 0 x - Domain: { x x - } 11-8 MULTIPLYING AND DIVIDING RADICAL EXPRESSIONS, PAGES 816 81 CHECK IT OUT! PAGES 816 818 1a. 10 (10 0 ( b. ( 7 ( 7 ( 7 9 7 7 9 7(7 9(7 6 1c. m 14m m(14m 8 m 4 m (7 4 m 7 m 7 a. 6 ( 8-6 8-6 6(8-6 48-6 (16-6 16-6 4-6 b. ( 10 + 4 10 + 4 (10 + 4 ( 0 + 4 1 ( + 4 1 + 4 1 + 4 1 c. 7k ( 7-7k 7-7k 7(7k - 7k 49k - 7k 49 k - 7k 7 k - 7k Copyright by Holt, Rinehart and Winston. 48 Holt Algebra 1
d. (-4 + 6-0 + 0-0 + 0 ( -0 + 0-0 + 0( 10-0 a. ( + (8-4 - + 8-4 + - ( 4 + - 9 4 + - 1 + b. (9 + (9 + (9 + 81 + 9 + 9 + 81 + 18 + ( 81 + 18 + 4 81 + 18 + 8 + 18 9 - - + c. ( - ( - ( - 9-6 + ( 9-6 + 4 9-6 + 11-6 d. (4 - ( + 4 + 0 - - 4a. 1 1 ( _ 6 _ 6 c. 80 16( 7 7 _ 8 7 ( 7 7 8 49 8 7 0 - ( - 0-9 - 0 - - 17 - _ THINK AND DISCUSS, PAGE 818 b. 7a 7a 1 4( _ 7a _ 7a ( 1a 9 1a 6 1. is equal to 1, so multiplying by does not change the value of the original expression.. Possible answer: EXERCISES, PAGES 819 81 GUIDED PRACTICE, PAGE 819 1. ( 6. ( ( ( ( 1. a 10 a(10 0a 6. 1p p 4 p 9 p ( 9 p 6p 7. 6 ( + 7 6 + 6 7 6 + 6(7 6 + 4 8. ( - - - ( - 9-9. 7 ( - 7-7 7( - 7( - 1. 8 (8 4 4(6 4 6 6 4. (4 (4 (4 16 ( 10. ( 10 + 8 10 + 8 (10 + 8 ( 0 + 8 4 4( + 8( 4 + 16 + 16 11. y ( 1 + 4 y(1 + 4 y 7y + 4 y (y + 4 y y + 4 y y + 4 y 16 4 Copyright by Holt, Rinehart and Winston. 49 Holt Algebra 1
1. t ( 6t - t t(6t - t(t 1 t - t 4 t ( - t 4 t - t t - t 1. ( + ( + 10 + + + 1 + 7 14. (4 + 6 ( - 6 1-4 6 + 6-6 6-6 1. ( - 4 ( + + - 4-8 - - 16. ( + ( + ( + + + + 8 + 10 17. ( 6 - ( 6 - ( 6-6 - (6 - (6 + ( 6-18 - 18 + 7 81-10 18 81-10 9( 81-0 18. (6 + (6 + (6 + _ 19. 1 6 + 18 + 18 + 9( 6 + 6 + 18 4 + 6 0. _ 0 4( 8 4( _ ( _ 1 ( _ 6 1. _ 11 _ 11 6 6 ( _ 6( _ 18. 7 7 ( 7 7 _ 7 7 10. 8 4(7 s s _ 7 s _ 7 _ s ( s s 1s s 4. 6 6 ( 6 6 6. 1/ x _ 1 _ x ( x x _ x x 6. x x ( x x _ x x PRACTICE AND PROBLEM SOLVING, PAGES 819 81 7. 6 ((6 90 9(10 10 9. ( ( ( 4 ( 4( 8 1. 1d ( d (1 d 6 d 9 d (7 9 d 7 6d 7 8. ( 6 ( 6 1 6(6 1(6 90 0. ( 6 ( 6 (. 4 n ( n ( n 4 (n n 4(n n 10n n. (4-10 4 - (10 4-0 4 - ( 4-4. ( 6 + (6 + 1 + 4( + +. ( 6-10 (6 - (10 1-0 4( - 4( - 6. ( 8-6 (8-6 (6 4-6 18 4(6-6 9( 6 6-18 7. f ( + 1 f( + 1 f 9f + 1 f f + 1 f 9 6(6 9(6 4 8. 8m ( 10 + m 8m(10 + 8m(m 80m + 16 m 16(m + 4m 4 m + 4m 9. (1 + 1 (4 + 1 60 + 1 1 + 4 1 + 1 7 + 19 1 6 Copyright by Holt, Rinehart and Winston. 460 Holt Algebra 1
40. ( 6 + 4 ( - 7 6( - 7 6 + 4-8 1-7 6 + 4-8 4( - 7 6 + 4-8 - 7 6 + 4-8 41. ( - (4 + 1 + - 4-10 - 4. ( - ( - ( - - - + 0-10 + 8 4. ( + 8 ( + 8 ( + 8 + 8 + 64 67 + 16 44. ( + 4 ( + 4 ( + 4 4( + 8 ( + 8 ( + 16( _ 4. 7 7 9 + 16 1 ( 46. _ 4 8 10 (6 _ 6 47. _ 7 _ 7 x x ( x x 7x x 9(x x x x _ x x 49. 49x 7 x _ 7 x ( 1. 1y 7 x _ 1y 4y y 4 4( _ 8 _ 8 ( ( 8( _ 10 16 48. 48k 48k ( _ 48(k 16(1k 4 1k 0. 7 7 b b ( b b 7b b _ 9(b b 9 b b. 1t 1t 6 6 t. A (6 (6 6( 180 in. A (6-6 ( - (6 10 - cm 6. ( 7 ( 7 6 7 ( 7 7 6(7 7 _ 4 7 8. 6 + 18 + 18 + 9( + _ + 4. A ( 6 (6 18 9( 6 m 7. 1 10 10 60. (6 + 1 6 + (1 6 + 4 6 + 4(6 6 + 6 61. 1 + 1 + 6 6 ( _ 6 _ 6. 1 + 10 1 + 10 1 + 10 + 10 ( _ 10( 0 9. ( - 4( + + - 4-8 - - _ 6. 1 ( + 8 4( ( + 8 ( + 8 ( + 8 + 8 + 64 (67 + 16 14 + ( 14 + 96 64. (4-4 - ( 4-1 Copyright by Holt, Rinehart and Winston. 461 Holt Algebra 1
6. ( x - y ( x - y ( x - y x - x y - x y + y x - xy + y 66. ( x - ( x + 7 (x + 7 x - 1 x - x - 8 x - 67. ( + x ( + x ( + + (x + (x + x _ + x + x 68. Current W R 80 _ 80 170 amps 1.0 amps 70. A bh ( ( 6 (6 18 9( yd 7. A bh ( - ( - x 69. P π l π π _ ( π ( 16( π _ ( 4 π π ( π 6 ( π 6 s 1.9 s 4 71. A bh (4-6 - ( + (7 _ - 1 ( 7-6 cm (7 (49(11 69. ft 11 (7 11 7. Possible answer: 1 ; multiply the fraction by. This will rationalize the denominator, since. 74a. t d 16 _ 100 16 100 16 10 4. s b..6s; it takes more than twice as long to go up the tower as it does to come down. 7. B; ( 1 7 ( 1 76. H; _ 4 _ 4 ( 77. D; ( 10 (10 0 _ 4 ( _ CHALLENGE AND EXTEND, PAGE 81 78. 4 4 - - ( + + 4 ( _ + ( - ( + _ + 4 4-4 + 4 79. 8 8 + + ( - - 8 ( _ - 80. 10 + ( + ( - _ - 8 8 - _ 8-8 - -4 + 4 10 + ( 10-10 - ( 10 - ( 10 + ( 10 - (10 - ( 10 - _ ( - 1 7 _ - 1 7 Copyright by Holt, Rinehart and Winston. 46 Holt Algebra 1
81. + + - - ( + + ( _ + ( + ( - ( + + + + - + 6-1 - - 6 8. + + ( - - _ ( - ( + ( - ( - - _ 6 - -1-6 8. 8 + 6 8 + 6 ( 8-6 8-6 _ ( 8-6 6 ( 8 + 6 ( 8 - _ (8 - (6 8-6 _ 16-1 4-4( - 84. 6 6 + + ( - - 6 ( _ - ( + ( - _ - 6 6-6 - 6 8. 6-6 - ( 6 + 6 + ( _ 6 + ( 6 - ( 6 + _ 6 + 6-6 + 86. A 1 lw A lw 4 6 ( 8 ( 4 1 16 (6 4 4( 16 4( 8 ft ft A - A 1-8 4 ft SPIRAL REVIEW, PAGE 81 87. translation of 4 units down 88. rotation about (0, 0 (or vertical stretch, steeper 89. x + 7x - 0 x - x + 10x - 0 ( x - x + (10x - 0 x (x - + 10 (x - (x + 10 (x - 90. 6 x + 11x + 6 x + x + 9x + (6 x + x + (9x + x (x + 1 + (x + 1 (x + 1 (x + 91. x - 16 x - 4x + 4x - 16 ( x - 4x + (4x - 16 x (x - 4 + 4 (x - 4 (x - 4 (x + 4 9. x + 0x + 7 ( x + 10x + ( ( x + x + (x + (x (x + + (x + (x + (x + (x + 9. x 4-18 ( x 4-9 ( x 4 - x + x - 9 ( ( x 4 - x + ( x - 9 ( x ( x - + ( x - ( x - ( x + 94. 8 x - 0 x - 1x 4x ( x - x - 4x ( x - 6x + x - 4x ( ( x - 6x + (x - 4x (x (x - + (x - 4x (x + 1 (x - 9. 60 6(10 6 10 6 10 97. _ 49 x 49 x 64 y 4 64 y 4 7x 8 y _ 6 96. 7 16 7 16 6( 16 _ 6 16 _ 6 4 _ Copyright by Holt, Rinehart and Winston. 46 Holt Algebra 1
98. _ 0 a 7 _ 0 a 4 9 a 9 0 a 4 9 a 4 ( 9 a 11-9 SOLVING RADICAL EQUATIONS, PAGES 8 89 CHECK IT OUT! PAGES 8 8 1a. x 6 ( x (6 x 6 c. x 1 ( x (1 x 1 x b. x + 7 ( x + 7 ( x + 7 x 18 c. x + 7-1 x + 7 4 ( x + 7 (4 x + 7 16 x 9 x a. x x 11 ( x 11 x 11 c. _ x 4 x 10 ( x (10 x 100 4a. x + x + 6 ( x + ( x + 6 x + x + 6 x 4 x b. 9 7x (9 ( 7x 81 7x x a. x - 1 x ( x ( x 9 b. x 4 8 x (8 ( x x 64 b. x - - 6 0 x - 6 ( x - ( 6 x - 6 x 11 x 11 a. 11 + x 6 x - ( x (- x x Check: 11 + x 6 11 + ( 6 11 + 6 16 6 ; Hence, no solution. b. x -x - (x ( -x - x -x - x + x + 0 (x+ (x + 1 0 x + 0 or x + 1 0 x - or x -1 Check: x -x - - -(- - - 6 - - 4 - x -x - -1 -(-1 - -1 - -1 1-1 1 ; So, no solution. c. x - x (x - ( x x - 4x + 4 x x - x + 4 0 (x - 1(x - 4 0 x - 1 0 or x - 4 0 x 1 or x 4 Check: _ x - x 1-1 -1 1 x - x 4-4 ; The only solution is 4. Copyright by Holt, Rinehart and Winston. 464 Holt Algebra 1
6. A lw 1 ( x + 1 ( x + 1 ( ( x + 1 9 x + 1 8 x l x + 1 cm THINK AND DISCUSS, PAGE 86 1. Possible answer: Method 1 is preferable because 1 is easily divided by and dividing by first keeps the numbers small.. Subtract from both sides. After doing this, square both sides to eliminate the radical.. Possible answer: EXERCISES, PAGES 86 89 GUIDED PRACTICE, PAGE 86 1. No; it does not contain a variable under the radical sign.. x 7 ( x (7 x 49 4. 0a 10 ( 0a (10 0a 100 a 6. x + 6 11 x ( x ( x 8. - a ( - a ( - a 9 -a 7 a -7 10. x - ( x - ( x - 9 x 11 1. x - 1 ( x - 1 ( x - 1 4 x. 4 -y (4 ( -y 16 -y -8 y. 1 -x (1 ( -x 144 -x -144 x 7. x - 7 ( x - (7 x - 49 x 4 x 7 9. x - 7 x 10 ( x (10 x 100 x 0 11. x + 1 ( x + (1 x + 1 x - 1. 4y + 1-1 6 4y + 1 7 ( 4y + 1 (7 4y + 1 49 4y 6 y 9 14. - x -10 x ( x ( x 16. -x 0 -x 4 ( -x (4 -x 16 x -16 18. 0. _ x 6 10 x 1 ( x (1 x 144 x x 9 ( x (9 x 81. 1 x 6 x 4. ( x ( x 4 x _ x - 7 1 x - 7 ( x - 7 x - 7 9 x 16. 4 x - 1 1 x - 1 ( x - 1 ( x - 1 9 x 6. - x 6x - ( - x ( 6x - - x 6x - 7 7x 1 x 1. 17. a 4 a 8 ( a (8 a 64 _ x 4 x 4 ( x (4 x 16 19. x 8 x 4 ( x (4 x 16 1. 7. x + 7 x - 19 ( x + 7 ( x - 19 x + 7 x - 19 6 x 1 x _ x 1 ( x x ( x 4 9. x x 10 ( x (10 x 100 Copyright by Holt, Rinehart and Winston. 46 Holt Algebra 1
8. 0 x - x + x + x ( x + ( x x + x x 9. x - 7 - x ( x - ( 7 - x x - 7 - x x 1 x 6 0. -x x + 1 ( -x ( x + 1 -x x + 1 -x 1 x - 1. x + 1 - x + 0 x + 1 x + ( x + 1 ( x + x + 1 x + x. x - + 0 x - - ( x - ( x - x 0 Check: x - + 0 0 - + 0 + 0 + 0 10 0 no solution 4. - 7x x ( - 7x (x - 7x 4 x 0 4 x + 7x - 0 (4x - 1 (x + 4x - 1 0 or x + 0 or x - 4 Check: - 7x x x - 7 ( 4 ( 4 1 4-7x x - 7( ( - 14 4-1 4 ; is the only solution. 4. x + x - ( x (- x 4 x 4 Check: x + ( 4 + 4 + + 7 ; no solution. x 1 + x (x ( 1 + x x 1 + x x - x - 1 0 (x - 4 (x + 0 x - 4 0 or x + 0 x 4 or x - Check: x 1 + x x 1 + x 4 1 + 4-1 - 4 16-9 4 4-4 is the only solution. 6. 6 + x - 1 4 Check: _ 6 + x - 1 4 x - 1-6 + - 1 4 ( x - 1 (- 6 + 4 4 x - 1 4 6 + 4 x 8 4 no solution 7. 6 - x + x 6 - x x - ( 6 - x (x - 6 - x x - 4x + 4 0 x - x - 0 (x - (x + 1 x - 0 or x + 1 0 x or x -1 Check: 6 - x + x 6 - ( + 0 + 6 - x + x 6 - (-1 + -1 9 + -1 + -1-1 is the only solution. 8. x - - x ( x - ( - x x - 4-4x + x 0 x - x + 6 0 (x - (x - x - 0 or x - 0 x or x Check: _ x - - x - - 0 0 0 0 _ x - - x - - 1-1 1-1 is the only solution. Copyright by Holt, Rinehart and Winston. 466 Holt Algebra 1
9. 10 + x x - ( x (- x Check: 10 + x 10 + 10 + 1 no solution 40. A ( b 1 + b h 14 (4 + 10 x + x + ( ( x + 4 x + 1 x x Check: A ( b 1 + b h x 14 (4 + 10 + 14 7 4 14 7( 14 14 ; h ( ( + cm PRACTICE AND PROBLEM SOLVING, PAGES 87 89 41. x 1 ( x (1 x 144 x 48 4. -a ( -a ( -a a - 4. x - 7 8 ( x - 7 (8 x - 7 64 x 71 47. 1 - x ( 1 - x ( 1 - x -x 4 x -8 49. x 0 x 6 ( x (6 x 6 4. -x ( ( -x 4 -x - x 44. 11 c (11 ( c 11 c 46. x - 4 0 x 4 ( x (4 x 16 48. x + 1 + 6 x + 1 4 ( x + 1 (4 x + 1 16 x _ x 0. 4 x 8 ( x (8 x 64 x 1. -x 0 -x 4 ( -x (4 -x 16 x -16. x - 1 x + ( x - 1 ( x + x - 1 x + x 16 x 8 4. x - 6 - x 0 x 6 - x ( x ( 6 - x x 6 -x x 6 x. x + x - 4 ( x + ( x - 4 x + x - 4 9 x 6. 4x - x + 4 ( 4x - ( x + 4 4x - x + 4 x 6 7. x - 6 16-6x ( x - 6 ( 16-6x x - 6 16-6x 11x x 8. 1x - 4x + 9 ( 1x - ( 4x + 9 1x - 4x + 9 8x 96 x 1 9. x + 6 1 ( x + 6 (1 x + 6 1 x -. p 9 p ( p ( p 9 p 60. - x 6 x - ( x (- x 9 Check: - x 6-9 6 -( 6-6 6 no solution Copyright by Holt, Rinehart and Winston. 467 Holt Algebra 1
61. x x + 1 (x ( x + 1 x x + 1 x - x - 1 0 (x - (x + 0 x - 0 or x + 0 x or x - Check: x x + 1 ( + 1 x x + 1 - (- + 1-9 - is the only solution. 6. 6x + 9 Check: 6x + 9 6x -7 6 ( 49 6 + 9 ( 6x (-7 49 + 9 6x 49 7 + 9 x 49 6 no solution 16 6. 4 - x x ( 4 - x (x 4 - x x 0 x + x - 4 0 (x + 4 (x - 1 x + 4 0 or x - 1 0 x -4 or x 1 Check: 4 - x x 4 - (-4-4 16-4 4-4 4 - x x 4 - (1 1 1 1 1 1 1 is the only solution. 64. x + 4 x - 4 ( x + 4 (x - 4 x + 4 x - 8x + 16 0 x -1x + 1 0 (x - 1 (x - 1 x - 1 0 or x - 1 0 x 1 or x 1 Check: x + 4 x - 4 (1 + 4 1-4 64 8 8 8 x + 4 x - 4 (1 + 4 1-4 9 - - 1 is the only solution. 6. x + x ( x + (x x + 4 x 0 x - x - 1 0 (x + 1 (x - 1 x + 1 0 or x - 1 0 x - or x 1 Check: x + x ( - x + x + ( - (1 + (1-1 + -1 4 1-1 1-1 1 is the only solution. 66. x + + 10 7 x + - ( x + (- x + 9 x 6 Check: x + + 10 7 6 + + 10 7 9 + 10 7 + 10 7 1 7 no solution 67. A bh 60 (10( x 1 x (1 ( x 144 x; 1 in. 68. x 9; x 9 ( x (9 x 81 x 7 69. x - 4 x - 4 x 7 ( x (7 x 49 70. x - 4 x - 4 ( x - (4 x - 16 x 19 Copyright by Holt, Rinehart and Winston. 468 Holt Algebra 1
71. x x + 6 ; x x + 6 (x ( x + 6 x x + 6 x - x - 6 0 (x - (x + 0 x - 0 or x + 0 x or x - Check: _ x x + 6 _ x x + 6 + 6 - - + 6 9-4 - is the only solution. 7. P (l + w l 9 + 7 18 ( + x + 7 16 9 + x + 7 4 m 4 x + 7 (4 ( x + 7 16 x + 7 9 x Dimensions: m by 4 m 7. P (b + h 8 ( x + + 1 4 x + + 1 x + ( ( x + 9 x + 6 x b x + 6 + 9 in. Dimensions: in. by 1 in. 7a. v Em m 8 E(0.14 0.14.9 0.8E.9 0.8 E.9 E 0.8 (.9 0.8 ( E _ 1.664 E 0.8 E 4.88 joules 74. P (b + h 0 ( x + x 1 x x ( ( x 9 x b x 9 9 cm h x 9 6 cm Dimensions: 9 cm by 6 cm b. v Em m 0 Em m 0 Em 0 m E m 0 or E 0 m 0 since m 0; m is in the denominator. Then, E 0 joules. _ 76. t d 16 _ 1 d 16 d 1 16 16 d d 14.70 mi 77. v.r 6.r 6. r 6 r. ( 6. ( r 4. r r 1690 ft 78. Radical equations may have extraneous solutions. x + y 81 79. 6 y 4 In (, 6 y 4 y 4 ( y (4 y 16 Subst. y 16 into (1 x + 16 81 x + 4 9 x ( x ( x Therefore, x and y 16. 80. always 81. Sometimes; for a b, the statement is true. For a and b -, the statement is false. 8. Sometimes; for the equation x x -, the value of x must be nonnegative in order for the left side to be defined, so the statement is true. For the equation 7 - x, the solution is - and the statement is false. Copyright by Holt, Rinehart and Winston. 469 Holt Algebra 1
8. Student B made an error going from - x x + 9 to 4 x. The student should have added x to both sides and subtracted 9 from both sides to get -4 x. 84. m 8. x 0 since the square root is only defined for nonnegative values. k 0 since the value of the square root must be nonnegative. 86a. 4 mi 4(80 ft 1 hr 600 s 61.6 ft/s 87. A; check: 8 - x - 8 - (-4-16 - 4-88. J; x + 1 + 1 0 x + 1-1 But the square root of any real, positive number is always positive. 90. G; check: x + 1 x - 11 1 + 1 1-11 1 91. A; check: x - x - (1-1 - 1-1 1-1 but 1-1 CHALLENGE AND EXTEND, PAGE 89 9. x + x + 1 ( x + (x + 1 x + x + x + 1 0 x + x - 0 (x + (x - 1 x + 0 or x - 1 0 x - or x 1 Check: _ x + x + 1 b. v 8 d 61.6 8 d 61.6 (8 d 794.6 64d d 9.9 ft 89. C; check: x 1 - x 1-9 _ x + x + 1 1 + 1 + 1 - + - + 1 1-1 4 1-1 1 is the only solution. 9. x - 1 x - 1 ( x - 1 (x - 1 x - 1 x - x + 1 0 x - x + 0 (x - (x - 1 x - 0 or x - 1 0 x or x 1 Check: _ x - 1 x - 1 _ x - 1 x - 1-1 - 1 1-1 1-1 1 1 0 0 1 1 0 0 1, are both possible solutions. 94. x - 1 x + 6 (x - 1 ( x + 6 x - x + 1 x + 6 x - 4x - 0 (x - (x + 1 0 x - 0 or x + 1 0 x or x -1 Check: x - 1 x + 6 x - 1 x + 6-1 ( + 6-1 - 1 (-1 + 6 4 16-4 4 4 - is the only possible solution. 9. x + x + 11 x + ( x + x + 11 (x + x + x + 11 x + 6x + 9 x 96. x + 9x + 14 x + 4 ( x + 9x + 14 (x + 4 x + 9x + 14 x + 8x + 16 x 97. x + x + x + 4 98a. (x + ( x + x + 4 x + 4x + 4 x + x + 4 0 x b. The equation has no solution. This is clear from the graphs since they do not intersect. Copyright by Holt, Rinehart and Winston. 470 Holt Algebra 1
99a. b. The solution is x, which is where the graphs intersect. _ 100. y 4 x - x - > 0 ( x - > (0 x - > 0 x > x > ; x cannot equal because the denom. cannot equal 0. SPIRAL REVIEW, PAGE 89 101... x 40 18.x 1. mi x 10. _ 1. x 1 48 x 1.(48 x 600 in 0 ft 10. Number of PINs 10 10 10 10 10,000 104. Number of samplers 6 C 4 1 6. When the passenger is at point P, the distance d is the hypotenuse of the right triangle shown, so d r by the Pythagorean Theorem; d r READY TO GO ON? PAGE 81 1. D 11 h 11 0. 61.9 km. y x - x - 0 x Domain: { x x }. ( 67. 9.46 m. y x - 7 x 0 x 0 Domain: { x x 0 } 4. y x - 6 x - 6 0 x 6 x Domain: { x x } 6. 10. 107. 106. MULTI-STEP TEST PREP, PAGE 80 1. C πd. r d.14(1 4.9 m _ 1 67. m. t 0 min v 1800 s 0.001r 0.001(67. v d t 4.9 1800 0.4 m/s 4. Differences are due to rounding. 0.067 0.6 m/s. 1 m; the required distance is the diameter of the wheel. 7. 10. a b a b b a b b ab b 1. 16( _ 16 _ 4 14. 4 b 81 4 b 81 b 9 8. 7 ( 9. _ 00 100 10 11. 98x y 49 y (x _ 49 y x 7y x 1. 18 11 64( 11 _ 64 11 _ 8 11 1. _ 7 a 9 _ ( a 6 49 a 49 a 6 ( 49 a 6 49 a 7 Copyright by Holt, Rinehart and Winston. 471 Holt Algebra 1
16. diagonal 19. + 14.4 68.64 + 07.6 76 4 in. 17. 1 7-7 7 7 18. x + x 6 x 19. 1 + 7 4( + ( 4 + + 7 0. 0 + 98 ( + 49( + 49 ( + 7 + 7 1. 4-4 4 - ( 4-6. 98x + 18x - 00x 49(x + 9(x - 100(x 49 x + 9 x -10 x 7 x + x - 10 x 0. 6 11 6(11 66. 4 1x x 4 1x(x 4 6 x 4(6x 4x 4. 8 (8 4 4(6 4 6 6 6. ( - ( + 1 + - - 1 - - 1 - _ 14 7. 19 19 19( 7 ( _ 8. 14 8 8 7 4 7 4 7 _ 9. 6b 6b 8 8 b 4 _ b 4 _ b 1. x - 4 1 x ( x ( x 6. _ x 40 x 16 ( x (16 x 6 0. _ 7 _ 7 _ t t ( t t _ 7(t t 81t t _ 9 t t _ t t. - x -1 x 4 ( x (4 x 16 4. 4x - - 4 - x 0 4x - 4 - x ( 4x - ( 4 - x 4x - 4 - x x 4 x 9. 0 + x x ( 0 + x (x 0 + x x 0 x - x - 0 0 (x - (x + 4 x - 0 or x + 4 0 x or x -4 Check: 0 + x x 0 + x x 0 + 0-4 -4 16-4 4-4 is the only solution. 6. 4x + 1 10 4x - ( 4x (- 4x 4 x 1 Check: _ 4x + 1 10 4(1 + 1 10 + 1 10 14 10 no solution Copyright by Holt, Rinehart and Winston. 47 Holt Algebra 1