Solutions Key Exponential and Radical Functions

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1 CHAPTER 11 Solutions Key Exponential and Radical Functions xzare YOU READY, PAGE 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 y y x y x y x +. t(t - 1 t t - t 1 6 t r(4r - 4r 4r - 4r 16 r - 0r 11-1 GEOMETRIC SEQUENCES, PAGES CHECK IT OUT! PAGE 767 1a. 80, -160, 0; (-10 -, 0 (-10 -, ( So, the common ratio is -. (-40 (- 80, 80 (- -160, and (-160 (- 0 b. 16, 16, 11.; , , So, the common ratio is , , and a n a 1 r n - 1 a ( 7 a a n a 1 r n - 1 a 10 10,000 ( 4 9 a ; $14.18 THINK AND DISCUSS, PAGE Possible answer: Divide each term after the first by the preceding term. If the quotients are all the same, the sequence is geometric ; ; ; 9. 8; h + 4 h h cm. h h 100 h 10 ft. (m - m - 10m x(8x + 9 x 8x + x 9 4 x + 7x 1. h 1 + h 169 h 1 in.. Possible answer: EXERCISES, PAGES GUIDED PRACTICE, PAGE 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

2 ., 64, 18; 4, 8 4, 16 8 So, the common ratio is. Then, 16, 64, and , 1., 6.; , , So, the common ratio is. Then, 0, 1., and 1, , -97, 916; (-1 4 -, 6 (-1 -, ( So, the common ratio is -. Then, (-108 (- 4, 4 (- -97, and (-97 ( a n a 1 r n - 1 a a 10 1,000,000, ; 16 a n a 1 r n - 1 a 64 ( 4 a 4 6. a n a 1 r n - 1 a a PRACTICE AND PROBLEM SOLVING, PAGES , 60, -1,0; 10 - _ -; -0 -; So, the common ratio is -. Then, 0 (- -10, -10 (- 60, and 60, ( , 4, 64.; 48 ; 7 48 ; _ So, the common ratio is. Then, 108 ( and 4 ( 4, , 04.8, 16.84; _ ; _ ; _ , 16 ( So, the common ratio is 4. Then, 0 ( 4 and 04.8 ( 4 6, 6 ( , , , ; 4 7; _ So, the common ratio is 7. Then, , , 406 and 14, , 84 _ -; _ , -19, 84; - 1 -; So, the common ratio is -. Then, -48 (- 96, 96 (- -19, and -19 ( , _ 18, _ 1 ; So, the common ratio is 4. Then, ( 8 ( 4, ( ( 4 _ 18, and ( _ 18 ( 4 _ a n a 1 r n - 1 a 18 (. - 1 a ; ; ; a a n 1 r n ; 8 4 a a or a m; _ ; _ a n a 1 r n - 1 a ( a , 40, 80, 160; 40, so the common ratio is ; and , 6, 18, 4; 18, so the common ratio is ; 6 and ,, 1, ; 9 ; So the common ratio is ; 1 0., 1, 48, 19, 768; 1 4, so the common ratio is 4; and , 1, 7, 1 49, _ 1 ; The common ratio is 4 7 ; 1 7 and , 100,, 4 ; _ 100, so the common ratio 4 is 4. Then, and 4 4 _. -, 6, -1, 4, -48; 4 -, so the common -1 ratio is -. Then, - (- 6 and 4 ( , -, 1, -, 9; - 1 -; So the common ratio is -. Then, and _. 1, 17, 89, 491; 17 17; So the common ratio is 17. Then, Copyright by Holt, Rinehart and Winston. 46 Holt Algebra 1

3 6. 10 ; 0 ; _ The common ratio is ; yes ; ; 9 The common ratio is ; yes. ; ; There is no common ratio; no. ; -1 - ; - -1 There is no common ratio; no _ 0. 1 ; 6 ; The common ratio is ; yes. 4 ; - -; There is no common ratio; no. a. ; 4 ; Plan is a geometric sequence with common ratio 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 a cm b. a n a 1 r n - 1 a a cm 4. a 1 a ( 1 6 a ( 1 a 4 ( 4. a 1 - a - (4 1-8 a - (4 - a 4 - ( a 1 a ( a (- 0 a 4 ( a 1 a ( 1 4 a ( 8 a 4 ( 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 ( Each term is multiplied by n - 1, where n is the term number. For example, begin with the geometric sequence 4, 1, 6, , 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 ; 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 ; a $99 a $49.0 b ; 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

4 TEST PREP, PAGE D: 10 ; 0 ; 40 ; there is a common 10 0 ratio. 4. J; since r -4 and a 1, ( -8-4; -4; a n (-4 n 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 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 _ 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 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 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 (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 (-0. 9 a 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 (0.4 n - 1 (0.4 6 Then, n n 7 4. Susanna assumed the sequence was geometric with r. She used the formula to find a 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 > b > x x x 4 7. c + < c + - < - c < - 9. x + y > 6 y > -x y < x y x + 1 y -x - 1 Copyright by Holt, Rinehart and Winston. 48 Holt Algebra 1

5 61. Vertical translation of +7; f(x x f(x x Vertical translation of -; f(x x f(x x + 4 Narrowing the graph. f(x a x + 4, where a >. Possible answer: f(x x + 4 THINK AND DISCUSS, PAGE 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 EXPONENTIAL FUNCTIONS, PAGES CHECK IT OUT! PAGES f(x 8 (0.7 x f( 8 (0.7 f( 8( 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 GUIDED PRACTICE, PAGE No; there is no variable in the exponent.. f(x 0,000 (0.97 x f(00 0,000 ( 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 ( 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

6 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, (1.0 x x 6; about 0 (6 years after 1960 PRACTICE AND PROBLEM SOLVING, PAGES f(x 7 ( x f(4 7 ( 4 f(4 7 ( f(4 ; ft 0. y 1. (1.41 x for x 1, y 1. ( y.0;.0 in./min 19. y 4 (0.976 x for x 6, y 4 ( 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 (1. x x 9; after 9 weeks Copyright by Holt, Rinehart and Winston. 440 Holt Algebra 1

7 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. 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 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( f(x 0.4 (10 x f(- 0.4 (10 - f( or a. In 001, n 0 C 000 ( C 000; $000 b. increase n ( (1.08 n - 1 increase 0.08; 8% c. For 006, n C 000 (1.08 C 98.66; $ f(x - (0. x f(1. - (0. 1. f( 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 ( D; a 1, r, hence a n ( n - 1 n CHALLENGE AND EXTEND, PAGE x 64 4 x 4 x 0. x 1 16 x 1 4 x -4 x ( 1. The value of a is the y-intercept. SPIRAL REVIEW, PAGE 778 _ x. 90 x 9. ; x + 10x + (x + 4. x; 4 x + x + 64 (x x ; 9 x + 4x + 49 (x 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

8 CONNECTING ALGEBRA TO GEOMETRY: CHANGING DIMENSIONS, PAGE 779 TRY THIS, PAGE 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 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 _ n 6 -n 1 _ n -8 n 8; 8 cuts 11- EXPONENTIAL GROWTH AND DECAY, PAGES CHECK IT OUT PAGES y a (1 + r t 100 (1.08 t ; In 006, y 100 ( $1904. a. A P ( 1 + r n nt 100 ( t 100( t; After 4 years, A 100 ( $ b. A P ( 1 + r n nt 4000 ( t 4000 (1.00 1t After 8 years, A 4000 ( $ y a (1 - r t 48,000 (1-0.0 t 48,000(0.97 t After 7 years, y 48,000 ( , years 4a. t 0 years 6 A P( 0. t 100( mg b. t _ weeks days 7 A P(0. t 100 ( g THINK AND DISCUSS, PAGE 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 GUIDED PRACTICE, PAGE exponential growth, since > 1. Copyright by Holt, Rinehart and Winston. 44 Holt Algebra 1

9 . y a (1 + r t 1,000 ( t 1,000 (1.06 t After 4 years, y 1,000 ( $1, y a (1 + r t 00 ( t 00 (1.08 t After years, y 00 ( A P ( 1 + r n nt 100 ( t 100 (1.0 t After 4 years, A 100 (1.0 4 $ A P ( 1 + r n nt 400 ( t 400 ( t Ater 6 years, A 400 ( $ y a (1 - r t 18,000 (1-0.1 t 18,000 (0.88 t After 10 years, y 18,000 ( $ y a (1 - r t 10 ( t 10 (0.84 t After 4 hours, y 10 ( 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 y a (1 + r t 149,000 (1.06 t After 7 years, y 149,000 ( $4, y a (1 + r t 1600 ( t 1600 (1.0 t After 10 years, y 1600 ( A P (1 + r nt 700 ( t 700 (1.01 4t After years, A 700 (1.01 4t $ y P (1 + r nt 0 ( t 0 (1.079 t After years, y 0 (1.078 t 47 members 14. A P ( 1 + r n nt 8,000 ( t 8,000 (1.04 t After years, A 8,000 (1.04 $4, A P ( 1 + r n nt _ 7000 ( t 7000 ( t After 10 years, A 7000 ( $ A P ( 1 + r n nt 00 ( t 00 ( t After 4 years, A 00 ( $ A P ( 1 + r n nt 1,000 ( t 1,000 (1.06 t After 1 years, A 1,000 ( $17, y a (1 - r t 18,000 (1-0.0 t 18,000 (0.98 t After 6 years, y 18,000 ( , y a (1 - r t 8 (1-0.1 t 8( 0.9 t After 8 years, y 8 (0.9 8 $ days 0. t 6 hours 144 hours 6 hours 4 A P(0. t 80 (0. 4 g 1. growth; 61%, since 1+ r decay; 90.%, since 1 - r decay; %, since 1 - r 4. growth; 0%, since 1 + r. growth; 10%, since 1 + r decay; 0%, since 1 - r 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 ( ,174, y a (1 + r t,000 (1.07 t After years, y,000 (1.07 $44, Copyright by Holt, Rinehart and Winston. 44 Holt Algebra 1

10 1. y a (1 - r t 800 (1-0.0 t 800 (0.98 t After 7 years, y 800 ( $ y a (1 - r t,000 (1-0.1 t,000 (0.8 t After 6 years, y,000 (0.8 6 $ y a (1 + r t 970 ( t 970 (1.01 t After years, y 970 ( _ 00 years 4. t 700 years 7 A P (0. t 1 ( g. B; possible answer: student B did not subtract the rate from No; possible answer; there is no value for t that would make (0.84 t equal y a (1 + r t ( 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 ( $,4 c. 011 Year Tuition ($ 00 0, , ,76 00, , , , , , , In 10 years: A: 600 ( $977.4 B: 00 (1 + _ ( $ A will have a larger balance. In 0 years: A: 600 (1.0 0 $ B: 00 ( $164. B will have a larger balance 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 G; a -, so as the absolute value of y decreases, y is actually increasing. 47. D; 86 (1.0 $ a. y a (1 + r t 1000 ( t 1000 (1.0 t b (1.0 t t ; about 00 CHALLENGE AND EXTEND, PAGE about 0 years 0. y a (1 + r t (1.04 t t 18 yr for r (1.08 t t 9 yr 1. A P (0. t (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 ( P $,44 4. Month Balance ($ 100 min or 1 h 40 min Monthly Payment ($ (4 8 Remaining Balance ($ 1.% Finance Charge ($ New Balance ($ Copyright by Holt, Rinehart and Winston. 444 Holt Algebra 1

11 b. Table shows balance is paid off in 7 months. c. (6( SPIRAL REVIEW, PAGE h 0 h 16 ft 6. w w 6 in. 7. f(x x f(x x - 4. EXERCISES, PAGES GUIDED PRACTICE, PAGE f(x x f( ( 4 $1.60; ( x x 7 days 1. exponential. quadratic 11-4 LINEAR, QUADRATIC AND EXPONENTIAL MODELS, PAGES CHECK IT OUT! PAGES a. 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 quadratic 9. linear Copyright by Holt, Rinehart and Winston. 44 Holt Algebra 1

12 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, l 6k; linear with m 6 and b 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 Quadratic; for each successive time interval, the height of a ball has a constant second difference of y 0. (4 x 0. y - x 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, $00 is added each year, so For college, 10% is added each year, so (0.1( C; the data is linear since it has a constant change in the y-values for each constant change in the x-values. 8. F; % is a common ratio. CHALLENGE AND EXTEND, PAGE 79 0a. Year Value ($ 0 18, ,10 1, , Year 0 is the year when the car is purchased. d. y 18,000 (0.84 $ e. y 18,000 ( $ 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 ± x x 81 x x ± x ± y - ( x b x 10 - x 0 x 0 8. y 6 x 40. y ( x MULTI-STEP TEST PREP, PAGE 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

13 . y 0( $89.71 READY TO GO ON? PAGE ; 1 ; 4 ; the common ratio is next terms: 4( 48, 48( 96, and 96( ; -; -4 -; the common ratio is - next terms: 8(- -16, (-16(-, and ( ; 1 ; , next terms: , and -7 ( ( ( 4. a , r n-1 a n a 1r a a cm n-1 4. a n a 1r a 8 (( 8-1 a Answers will vary (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 (1.09 x about 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 $ Holt Algebra 1

14 1. A P (0. t _ 00 A 100(0. 0 A 100(0. 10 A 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 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 ; $ SQUARE-ROOT FUNCTIONS, PAGES CHECK IT OUT! PAGES a. y 8 x b. y 8 x 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 GUIDED PRACTICE, PAGE There is no variable under the square-root sign.. c a + b cm. y x + 6 x x -6 Domain: {x x -6}. y x - x 0 x 0 Domain: {x x 0} 7. y x +9 x x - 9 x - Domain: {x x -} 9. f(x x y 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 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

15 11. f(x x f(x 4 - x 1. f(x 4x f( f( 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 (x x + x - Domain: { x x - } x. y 7-8 x x 40 Domain: { x x 40 }. y (x - 9 (x x x 9 Domain: { x x 9 } 1. f(x x f(x x 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 x -1 Domain: { x x -1 }. y (x (x x x -4 Domain: { x x -4 } 4. y (x - 6 (x x -6 0 x Domain: { x x } 6. y (x (x 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 r A π _ cm 9. f(x x 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

16 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. ( - + ( units f(x 9.8x f( f(00 70 m/s 9. v gr Mercury: v m/s Venus: v ,61 m/s Earth: v ,00 m/s Mars: v m/s 40. V π r h r V πh 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 l 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 y x - x - 0 x x Domain: { x x - or x } 0. y x + x + 6 x + x (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 x - 0 and x or x - 0 and x 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 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

17 6. Possible answers: y - x + a + b, where a 0 and b < 0. Example: y - x a., 4; when x or x 4, the expression under the square-root sign is negative. b. for x, y - ( - for x 7, y - ( SPIRAL REVIEW, PAGE y 4x - 8 y x x + 6y 1 6y -x + 1 y - x A P (0. t 1 day t. hours 96 A 0 ( g 4 hours. hours 96 1 TECHNOLOGY LAB: GRAPH RADICAL FUNCTIONS, PAGE 804 TRY THIS, PAGE x -y - 9 y -x (a + b a + ab + b (x - 1 (x + (x(-1 + (-1 9 x - 6x (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 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 A P ( 1 + r n nt _ A 4,000 ( t 4,000 (1.01 4t After years, A 4,000 ( $48, The graph of f(x x 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 RADICAL EXPRESSIONS, PAGES CHECK IT OUT! PAGES a. _ b c d. ( - x - x Copyright by Holt, Rinehart and Winston. 41 Holt Algebra 1

18 a ( 64 8 b. x y x y xy x x x y c. 48 a b 16 a b 4a b b. 6 9 a. c. y _ 4 y 4 y _ 4a _ 7 c. 6 p p 6 q 10 q 10 p q _ 6 x 4 x 4 b. _ z THINK AND DISCUSS, PAGE Method 1: 16( Method : 16( ( 1. Method 1: _ Method : _ x z y y (z z 4 y z z y. c a + b ( ft or 84.9 ft. EXERCISES, PAGES GUIDED PRACTICE, PAGE x - 6 is the radicand ( ( m n m n m 4 n mn m n mn 9. x 4 y 16( x 4 y y 4 x y y a b (100 a b 4. (a + 7 a ( a b 10a b _ _ 7 16 _ _ _ x 1. 4 x 6x 9 x 9 x (6 49 _ 6 7 _ b a 4 _ b c c b c 7a 9 a 9 _ 7a 9 7a (41 _ Copyright by Holt, Rinehart and Winston. 4 Holt Algebra 1

19 ( _ 0 x 169 ( x 169 _ x 169 x 1. c a + b 0 + ( mi mi 0. _ x 6 x 1 6x. _ 7 x 7 18 x 4 x 4 9 x x x x PRACTICE AND PROBLEM SOLVING, PAGES _ a 4 a 9. (x + 1 x ( - x - x 1. (x - x -. 1 ( a b 6 a b 6 6ab 6. 0 r s (64 r s _ _ 64 a 4 8rs _ 16 4 a 6 a _ 16 a 4 a ( ( 4 9 _ 9. _ 14 z 14 9 z 9 _ 14 9 _ ( 81 _ _ 6( 196 x 196 x _ 6 14x _ 6 14x 44. t d 16 _ s;. s ( x 16(x 16 x 1 x x x y _ 1 ( 1 10 x y _ 6 1 x 6 ( 1 x _ x y 6 y ( ( ( x x x y 6 y 6 _ x x y _ s 49s 64( s s 49 8s ( x 6 x 9(7 x 9 7 1x 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( ( 0 _ Copyright by Holt, Rinehart and Winston. 4 Holt Algebra 1

20 _ (4 _ ( _ ( ft; length of missing side ft 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: _ Then simplify by taking the square roots of the perfect squares: 4 7 _ a. v 64h 64 h 8 h ; v ft/s b. Pythagorean Theorem c. d x + h ft 64. Possible answer: The square root of a negative number is not a real number. _ 6. d 6h Sears: d mi; 1.1 mi Empire: d mi; 8.9 mi Aon: d mi; 7. mi 66. s (a + b + c ( A s(s - a(s - b(s - c 14(14-7(14-9( m ; 1. m 67. C: is not divisible by a perfect square. 68. F: C: ( CHALLENGE AND EXTEND, PAGE x (x x + 4 x x - 18 x 9 x (x - 9 x x - x x 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

21 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 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 _ y 6x + b For (, 1, 1 6( + b b - 17 Hence, y 6x exponential 78. quadratic 11-7 ADDING AND SUBTRACTING RADICAL EXPRESSIONS, PAGES CHECK IT OUT! PAGES a b. 8 - c. 4 n + 4 n 8 n d. s - s + 9 s s + 8 s a (6 + 4( b ( - 9( c. 1y + 7y (4y + (9y 4 y + 9 y y + y y. ( b + b ( b 10 b in. THINK AND DISCUSS, PAGE Group 1: 6, , 10 6 Group : 6, - 0 -,. Possible answer: Without simplifying, you cannot tell which terms are like radicals.. Possible answer: EXERCISES, PAGES GUIDED PRACTICE, PAGE Possible answer: any pair of a c and b c where a, b are real numbers and c is nonnegative. Example: 4 6 and a - 9 a -4 a a + 6 a - 4 6a 6a + 6 a ( - 4( ( + ( ( - 9( x - 4x 4(x - 9(x 4 x - 9 x x - x - x 1. 8c + 9 4c 4(7c + 9 4(6c 4 7c c 7c c 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

22 14. P ( + 4( + 9( in. PRACTICE AND PROBLEM SOLVING, PAGES ( n - n -4 n 0. y + y - y y - y (7 + 4( ( - 4( ( - 16( + 9( r + 4r (6r + 9(6r 6r + 9 6r 6r + 6r 8 6r. 6x - 4 7x 9(7x - 4 9(x 9 7x 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 j - 4j 6(j - 9(j 6 j - 9 j 6 j - j j 8. 90c - 40c 9(10c - 4(10c 9 10c c 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 ( mi ab - 10 ab 8 ab ( + 64( ( - 9( x + 00x 9(x + 100(x 9 x x x + 10 x 1 x ( + 16( ( a. section A: 11 ; section B: 11 ; section C: 11 b c. Because the areas found in parts a and b must be equal, the model shows that: ( Copyright by Holt, Rinehart and Winston. 46 Holt Algebra 1

23 40. 40ab - 0ab (ab - (ab ab - ab 1 ab - ab 10 ab ( + ( ( - 9( x - 8x - 70x 100(7x - 4(7x - 70x 100 7x - 4 7x - 70x 10 7x - 7x - 70x 8 7x - 70x (10-16( k + 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 abc 1 6abc ( + 4( + 9( + 9( 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 x x 4 x 8 x 8. x x x 9 x 18 x 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( (4 8 in. 16 in 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( CHALLENGE AND EXTEND, PAGE x - + x - 7 x - 6. x x + x (x x - + x x - + (x - 4 x - + x - 4 x - + x - 9 x - 6. x + 7-4x + 8 x + 7-4(x + 7 x x + 7 x x Copyright by Holt, Rinehart and Winston. 47 Holt Algebra 1

24 66. 4 x + 4 x + x + 6 x 4 x (x x (x x x x x + 6 x x x x + 6 x x x - x + 4x - 4 x (x (x - 1 x x x - 1 x x x - 1 (x + x x + x - x + x (x + - x + x x + - x + x x + - x + (x - 1 x x x + x 9(x x (x A h( b 1 + b (4 ( (4 ( 4( + 9( (4 ( (4 ( + (4 ( (0( 0 cm 9 x x x + x x x + SPIRAL REVIEW, PAGE m AB , m BC _ m CD (- 1, m AD _ 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 (-1 4 ; m YZ 0 - ( ; 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_ y 4x - 4x - 0 4x x Domain: { x x } 76. y 1 + x + 6 x x -6 Domain: { x x -6 } 7. y - x + x + 0 x - Domain: { x x - } 11-8 MULTIPLYING AND DIVIDING RADICAL EXPRESSIONS, PAGES CHECK IT OUT! PAGES a. 10 (10 0 ( b. ( 7 ( 7 ( (7 9(7 6 1c. m 14m m(14m 8 m 4 m (7 4 m 7 m 7 a. 6 ( ( ( b. ( ( ( ( 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

25 d. ( ( ( 10-0 a. ( + ( ( b. (9 + (9 + ( ( c. ( - ( - ( ( d. (4 - ( a. 1 1 ( _ 6 _ 6 c ( 7 7 _ 8 7 ( ( _ 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 GUIDED PRACTICE, PAGE ( 6. ( ( ( ( 1. a 10 a(10 0a 6. 1p p 4 p 9 p ( 9 p 6p 7. 6 ( ( ( ( ( ( - 7( (8 4 4( (4 (4 (4 16 ( 10. ( ( ( ( + 8( y ( 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

26 1. t ( 6t - t t(6t - t(t 1 t - t 4 t ( - t 4 t - t t - t 1. ( + ( (4 + 6 ( ( - 4 ( ( + ( + ( ( 6 - ( 6 - ( (6 - (6 + ( ( (6 + (6 + (6 + _ ( _ 0 4( 8 4( _ ( _ 1 ( _ 6 1. _ 11 _ ( _ 6( _ ( 7 7 _ (7 s s _ 7 s _ 7 _ s ( s s 1s s ( / x _ 1 _ x ( x x _ x x 6. x x ( x x _ x x PRACTICE AND PROBLEM SOLVING, PAGES ((6 90 9( ( ( ( 4 ( 4( d ( d (1 d 6 d 9 d (7 9 d 7 6d 7 8. ( 6 ( 6 1 6(6 1( ( 6 ( 6 (. 4 n ( n ( n 4 (n n 4(n n 10n n. ( ( ( 4-4. ( 6 + ( ( + +. ( 6-10 (6 - ( ( - 4( - 6. ( 8-6 (8-6 ( (6-6 9( f ( + 1 f( + 1 f 9f + 1 f f + 1 f 9 6(6 9( m ( 10 + m 8m(10 + 8m(m 80m + 16 m 16(m + 4m 4 m + 4m 9. (1 + 1 ( Copyright by Holt, Rinehart and Winston. 460 Holt Algebra 1

27 40. ( ( - 7 6( ( ( - ( ( - ( - ( ( + 8 ( + 8 ( ( + 4 ( + 4 ( + 4 4( + 8 ( + 8 ( + 16( _ ( 46. _ (6 _ _ 7 _ 7 x x ( x x 7x x 9(x x x x _ x x x 7 x _ 7 x ( 1. 1y 7 x _ 1y 4y y 4 4( _ 8 _ 8 ( ( 8( _ k 48k ( _ 48(k 16(1k 4 1k 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 ( - ( cm 6. ( 7 ( ( 7 7 6(7 7 _ ( + _ + 4. A ( 6 (6 18 9( 6 m ( ( ( ( _ 6 _ ( _ 10( 0 9. ( - 4( _ 6. 1 ( + 8 4( ( + 8 ( + 8 ( ( ( (4-4 - ( 4-1 Copyright by Holt, Rinehart and Winston. 461 Holt Algebra 1

28 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 ( + x ( + x ( + + (x + (x + x _ + x + x 68. Current W R 80 _ 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 A bh (4-6 - ( + (7 _ - 1 ( 7-6 cm (7 (49( ft 11 ( Possible answer: 1 ; multiply the fraction by. This will rationalize the denominator, since. 74a. t d 16 _ 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 ( H; _ 4 _ 4 ( 77. D; ( 10 (10 0 _ 4 ( _ CHALLENGE AND EXTEND, PAGE ( ( _ + ( - ( + _ ( ( _ ( + ( - _ _ ( ( 10 - ( 10 + ( 10 - (10 - ( 10 - _ ( _ Copyright by Holt, Rinehart and Winston. 46 Holt Algebra 1

29 ( + + ( _ + ( + ( - ( ( - - _ ( - ( + ( - ( - - _ ( _ ( ( ( 8 - _ (8 - (6 8-6 _ ( ( ( _ - ( + ( - _ ( ( _ 6 + ( 6 - ( 6 + _ A 1 lw A lw 4 6 ( 8 ( (6 4 4( 16 4( 8 ft ft A - A ft SPIRAL REVIEW, PAGE 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 (x - (x + 10 (x x + 11x + 6 x + x + 9x + (6 x + x + (9x + x (x (x + 1 (x + 1 (x x - 16 x - 4x + 4x - 16 ( x - 4x + (4x - 16 x (x (x - 4 (x - 4 (x 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 x - 0 x - 1x 4x ( x - x - 4x ( x - 6x + x - 4x ( ( x - 6x + (x - 4x (x (x - + (x - 4x (x + 1 (x ( _ 49 x 49 x 64 y 4 64 y 4 7x 8 y _ ( 16 _ 6 16 _ 6 4 _ Copyright by Holt, Rinehart and Winston. 46 Holt Algebra 1

30 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 x ( x + 7 (4 x 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 x - 6 ( x - ( 6 x - 6 x 11 x 11 a x 6 x - ( x (- x x Check: 11 + x ( ; Hence, no solution. b. x -x - (x ( -x - x -x - x + x + 0 (x+ (x x + 0 or x x - or x -1 Check: x -x - - -( x -x ( ; So, no solution. c. x - x (x - ( x x - 4x + 4 x x - x (x - 1(x x or x x 1 or x 4 Check: _ x - x x - x 4-4 ; The only solution is 4. Copyright by Holt, Rinehart and Winston. 464 Holt Algebra 1

31 6. A lw 1 ( x + 1 ( x + 1 ( ( x x x l x + 1 cm THINK AND DISCUSS, PAGE 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 GUIDED PRACTICE, PAGE No; it does not contain a variable under the radical sign.. x 7 ( x (7 x a 10 ( 0a (10 0a 100 a 6. x x ( x ( x 8. - a ( - a ( - a 9 -a 7 a x - ( x - ( x - 9 x x - 1 ( x - 1 ( x 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 x + 1 ( x + (1 x + 1 x y y ( 4y + 1 (7 4y y 6 y x -10 x ( x ( x 16. -x 0 -x 4 ( -x (4 -x 16 x _ x 6 10 x 1 ( x (1 x 144 x x 9 ( x (9 x x 6 x 4. ( x ( x 4 x _ x x - 7 ( x - 7 x x x x - 1 ( x - 1 ( x x 6. - x 6x - ( - x ( 6x - - x 6x - 7 7x 1 x a 4 a 8 ( a (8 a 64 _ x 4 x 4 ( x (4 x x 8 x 4 ( x (4 x x + 7 x - 19 ( x + 7 ( x - 19 x + 7 x 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

32 8. 0 x - x + x + x ( x + ( x x + x x 9. x x ( x - ( 7 - x x x x 1 x x x + 1 ( -x ( x + 1 -x x + 1 -x 1 x - 1. x x + 0 x + 1 x + ( x + 1 ( x + x + 1 x + x. x x - - ( x - ( x - x 0 Check: x no solution x x ( - 7x (x - 7x 4 x 0 4 x + 7x - 0 (4x - 1 (x + 4x or x + 0 or x - 4 Check: - 7x x x - 7 ( 4 ( x x - 7( ( ; is the only solution. 4. x + x - ( x (- x 4 x 4 Check: x + ( ; no solution. x 1 + x (x ( 1 + x x 1 + x x - x (x - 4 (x + 0 x or x + 0 x 4 or x - Check: x 1 + x x 1 + x is the only solution x Check: _ 6 + x x ( x - 1 ( x x 8 4 no solution x + x 6 - x x - ( 6 - x (x x x - 4x x - x - 0 (x - (x + 1 x - 0 or x x or x -1 Check: 6 - x + x 6 - ( x + x 6 - ( is the only solution. 8. x - - x ( x - ( - x x - 4-4x + x 0 x - x (x - (x - x - 0 or x - 0 x or x Check: _ x - - x _ x - - x is the only solution. Copyright by Holt, Rinehart and Winston. 466 Holt Algebra 1

33 x x - ( x (- x Check: 10 + x no solution 40. A ( b 1 + b h 14 ( x + x + ( ( x + 4 x + 1 x x Check: A ( b 1 + b h x 14 ( ( ; h ( ( + cm PRACTICE AND PROBLEM SOLVING, PAGES x 1 ( x (1 x 144 x a ( -a ( -a a - 4. x ( x - 7 (8 x x x ( 1 - x ( 1 - x -x 4 x x 0 x 6 ( x (6 x x ( ( -x 4 -x - x c (11 ( c 11 c 46. x x 4 ( x (4 x x x ( x + 1 (4 x 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 x 0 x 6 - x ( x ( 6 - x x 6 -x x 6 x. x + x - 4 ( x + ( x - 4 x + x x 6. 4x - x + 4 ( 4x - ( x + 4 4x - x + 4 x 6 7. x x ( x - 6 ( 16-6x x x 11x x 8. 1x - 4x + 9 ( 1x - ( 4x + 9 1x - 4x + 9 8x 96 x 1 9. x ( x + 6 (1 x x -. p 9 p ( p ( p 9 p x 6 x - ( x (- x 9 Check: - x ( no solution Copyright by Holt, Rinehart and Winston. 467 Holt Algebra 1

34 61. x x + 1 (x ( x + 1 x x + 1 x - x (x - (x + 0 x - 0 or x + 0 x or x - Check: x x + 1 ( + 1 x x ( is the only solution. 6. 6x + 9 Check: 6x + 9 6x -7 6 ( ( 6x ( x x 49 6 no solution x x ( 4 - x (x 4 - x x 0 x + x (x + 4 (x - 1 x or x x -4 or x 1 Check: 4 - x x 4 - ( x x 4 - ( is the only solution. 64. x + 4 x - 4 ( x + 4 (x - 4 x + 4 x - 8x x -1x (x - 1 (x - 1 x or x x 1 or x 1 Check: x + 4 x - 4 ( x + 4 x - 4 ( is the only solution. 6. x + x ( x + (x x + 4 x 0 x - x (x + 1 (x - 1 x or x x - or x 1 Check: x + x ( - x + x + ( - (1 + ( is the only solution. 66. x x + - ( x + (- x + 9 x 6 Check: x 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 x - 4 x - 4 x 7 ( x (7 x x - 4 x - 4 ( x - (4 x - 16 x 19 Copyright by Holt, Rinehart and Winston. 468 Holt Algebra 1

35 71. x x + 6 ; x x + 6 (x ( x + 6 x x + 6 x - x (x - (x + 0 x - 0 or x + 0 x or x - Check: _ x x + 6 _ x x is the only solution. 7. P (l + w l ( + x x m 4 x + 7 (4 ( x x x Dimensions: m by 4 m 7. P (b + h 8 ( x x x + ( ( x + 9 x + 6 x b x in. Dimensions: in. by 1 in. 7a. v Em m 8 E( E E.9 E 0.8 ( ( E _ 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 d d 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 y 4 In (, 6 y 4 y 4 ( y (4 y 16 Subst. y 16 into (1 x x x ( x ( x Therefore, x and y 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

36 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 ( J; x x But the square root of any real, positive number is always positive. 90. G; check: x + 1 x A; check: x - x - ( but 1-1 CHALLENGE AND EXTEND, PAGE x + x + 1 ( x + (x + 1 x + x + x x + x - 0 (x + (x - 1 x + 0 or x x - or x 1 Check: _ x + x + 1 b. v 8 d d 61.6 (8 d d d 9.9 ft 89. C; check: x 1 - x 1-9 _ x + x is the only solution. 9. x - 1 x - 1 ( x - 1 (x - 1 x - 1 x - x x - x + 0 (x - (x - 1 x - 0 or x x or x 1 Check: _ x - 1 x - 1 _ x - 1 x , are both possible solutions. 94. x - 1 x + 6 (x - 1 ( x + 6 x - x + 1 x + 6 x - 4x - 0 (x - (x x - 0 or x x or x -1 Check: x - 1 x + 6 x - 1 x ( ( 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 a. (x + ( x + x + 4 x + 4x + 4 x + x 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

37 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 x x 1. mi x 10. _ 1. x 1 48 x 1.(48 x 600 in 0 ft 10. Number of PINs , Number of samplers 6 C 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 D 11 h km. y x - x - 0 x Domain: { x x }. ( m. y x - 7 x 0 x 0 Domain: { x x 0 } 4. y x - 6 x x 6 x Domain: { x x } MULTI-STEP TEST PREP, PAGE C πd. r d.14(1 4.9 m _ m. t 0 min v 1800 s 0.001r 0.001(67. v d t m/s 4. Differences are due to rounding m/s. 1 m; the required distance is the diameter of the wheel a b a b b a b b ab b 1. 16( _ 16 _ b 81 4 b 81 b ( 9. _ x y 49 y (x _ 49 y x 7y x ( 11 _ _ _ 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

38 16. diagonal in x + x 6 x ( + ( ( + 49( + 49 ( ( x + 18x - 00x 49(x + 9(x - 100(x 49 x + 9 x -10 x 7 x + x - 10 x ( x x 4 1x(x 4 6 x 4(6x 4x 4. 8 (8 4 4( ( - ( _ ( 7 ( _ _ 9. 6b 6b 8 8 b 4 _ b 4 _ b 1. x 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 x x 0 4x x ( 4x - ( 4 - x 4x x x 4 x x x ( 0 + x (x 0 + x x 0 x - x (x - (x + 4 x - 0 or x x or x -4 Check: 0 + x x 0 + x x is the only solution. 6. 4x x - ( 4x (- 4x 4 x 1 Check: _ 4x ( no solution Copyright by Holt, Rinehart and Winston. 47 Holt Algebra 1