Chapter 1: Problem Solving, Expressions, and Equations

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1 CHAPTR Chapter : Problem Solving, xpressions, and quations xercise. Answers will vary for xercises in 0 in 9. Primary: ( 0) in Secondary: ( ) 0 Tertiary: ( ) cm. Primary: ( 0) 90 cm Secondary: ( 90) 0 Tertiary: ( 90). Primary is 7 in. ()? 7. Primary is cm. ()? in. ; so, Vase is ( 7) 8 7 cm. ; so, Vase is ( ) 7. Vase is in. Primary: ( ). Secondary: ( ) Tertiary: ( ) 80 cm in, total length:. 7. in in, total length: 0 in 7. in, total length: 7.. in 9. The secondary stem is of the primary stem, which is of the Vase. of the primary stem of Vase times the height of the Vase. So, the height of the secondary stem is times the height of the Vase.. The two girls will ride out together and one of them will return for Gayle. Gayle will ride to where the other girl is waiting. This girl will return for the second girl and the two of them will return together. Copyright by Houghton Mifflin Company. All rights reserved.

2 Problem Solving, xpressions, and quations Copyright by Houghton Mifflin Company. All rights reserved.. First, fill the -cup container. Then, using the -cup container, fill the 7-cup container. Now there are cups remaining in the -cup container. Next, pour the remaining cups into the tank. Fill up the -cup container again and pour cups into the tank. xercise.. a. Assuming the protected area had 0 mph wind speed, the apparent temperature went from º to -º; º º 8º, the apparent temperature change. b. A 0-mph wind speed has an apparent temperature of 0º; 0º º º, the apparent temperature change. When riding the bicycle the total speed is 0 mph, for an apparent temperature of -7º; 7º º º, the apparent temperature change.. a. Real numbers b. Integers c. Irrational numbers d. Multiplicative inverses e. Additive inverses. a. Distributive of multiplication over addition b. Associative property for addition c. Commutative property for multiplication d. Distributive of multiplication over addition e. Associative property for addition 7. a. Negative b. one c. positive d. one e. zero 9. Integer. Irrational. Natural. Natural numbers 7. a. ( ) 8 ( ) ()( ) 8 ( ) ) ( b. c d. 0.7 ( 0.) ( 0.) (0.7)( 0.) 0. (0.7) ( 0.).7

3 CHAPTR e. 0. (.).9 0. (.) ( 0.)(.) 0.7 ( 0.) (.) 0. f or a. 8 ( ) ( ) 8 b. ( 9) ( 8) 9 8 c.. (.8) (.)..8.. d. 8. (.8) (.) e. f. 7. a. 9 is undefined on the set of real numbers b. 9 c. 9. a. ( ); the opposite of negative three b. ; negative two c. ( ); negative three subtracted from five. a (9 8) 9(00) 900 b (0.) 0 c. 99 ( 00 ) 00 9 d (07 7) 9(00) 900 e a. In the U.S., a decimal would be used instead of a comma. b. In the U.S., we borrow from the 7 and leave the alone. c. U.S. drivers sit on the left and use the right lane. d. In the U.S. we read from left to right. Copyright by Houghton Mifflin Company. All rights reserved.

4 Problem Solving, xpressions, and quations 9. a. π ( ) π ( ) π ( 7) A b. S π π ()(.) A S π π (9) A S 8 π 8π A 89.9cm S π 8.7in c. d ( ) ()( 7) d. x 9 (9 ) 8 d ()( 7) x 9 (7) 0 d 8 x d 9 x 7 8. a. m ( ) m 8 9 c. F ( 00) 900 F 80 e. h ( 0) ( 00) 00 h. 8 b. c c d. C ( ) C ( ) 00. a. d ( ( ) ) ( ( ) ) d () 8 () d 00 0 ( ) b. m ( ) m 8 ( ) ( ) ()( ) c. x () 0 x 8 0 x d. d { } d { } d ( ) d..0. a slope; b Pythagorean Theorem; c Celsius to Fahrenheit temperatures; d Fahrenheit to Celsius temperatures; a Distance Formula between two ordered pairs; b slope; c Quadratic Formula; 9c Discriminant for the Quadratic Formula Copyright by Houghton Mifflin Company. All rights reserved.

5 CHAPTR xercise.. Visualize x columns of dots with one dot missing from the last column.. a. Input, x Output, y 9 b. ; 9 ; 9 c. The rule is y x.. a. Input, x Output, y 8 b. ; 8 ; 8 ; c. We can estimate the rule as y x?. When x, y () or y. The rule is y x. 7. a. In x, the variable is x, the numerical coefficient is, and the constant term is. b. The variable is r and the numerical coefficient is π. There is no constant term. c. The variable is x, the numerical coefficient is (implied by the in front of x), and the constant term is. 9. a. Four subtract the opposite of c. b. The opposite of the cube of z (or z-cubed). c. Negative z-squared, or the opposite of z-squared. d. The output may be positive or negative. Input, z 0 Output, z () 8 () (0) 0 () () 8 e. z will always be negative because z is always positive for any real number z.. a. () ()() 9 b. () ()()() 8 c. ()() 9 d. (x) (x)(x) ( )(x x) 9x e. x ()(x)(x) x f. 0 x x. a. () base is b. () base is c. base is d. (x) base is x e. x base is x f. 0 x base is x Copyright by Houghton Mifflin Company. All rights reserved.

6 Problem Solving, xpressions, and quations. a. (x) (x)(x)(x) 8x b. (x) (x)(x)(x) 8x c. (y) (y)(y)(y)(y) 8y d. (xy) (xy)(xy)(xy)(xy) x y e. (xy) (xy)(xy)(xy)(xy) x y f. 0 (y) (y)(y)(y) (8)y 8y 7. a. b. Multiply x x x x x x () x Factor a b a a a(a) ab a(b) 9. a. (x ) (x) () x b. y 0 (y) () (y ). a. x(x ) x(x) x() x x b. ab bc b(a) b(c) b(a c). a. ( x) ()() ()(x) 8x b. a(b c) (a)(b) (a)(c) ab ac c. x(x x ) (x)(x ) (x)(x) (x)() x x x. a. x ()(x) ()(9); greatest common factor (gcf) is ; (x 9) b. x ()(x) ()(); gcf is ; (x ) c. a 8a (a)(a) (a)(); gcf is a; a(a ) 7. a. ab b (a)(b) (b)(b); gcf is b; b(a b) b. xy x y (xy)() (xy)(x); gcf is xy; xy( x) c. (xy) xy (xy )(x) (xy )(); gcf is xy ; xy (x ) 9. a. ab a ()(ab) ()(a) ()(); gcf is ; (ab a ) b. ac a ()(ac) ()(a) ()(); gcf is ; (ac a ). a. gcf is ; c. gcf is 0; b. gcf is ; a. gcf is be; c. x abe a be a b. gcf is ab; ben be n n cannot be simplified a ab b a ab ab b a b Copyright by Houghton Mifflin Company. All rights reserved.

7 CHAPTR. a. gcf is x; ( y z) xy xz x y z xy x y y b. gcf is x; ( x ) x x x x x x x c. gcf is xy; xy xy y y xy xy 7. a. There are (x ) tiles, (x) tiles, and () tiles; total is x x. b. There are (a ) tiles, (ab) tiles, and (b ) tiles; total is a ab b. 9. a. ac ab ca 7bc ac ac ab 7bc ac( ) ab 7bc 8ac ab 7bc b. x( x) x(x ) x x x x x x x x x 8x. a. (7) (7) 9 b. (7 ) 8. a. (9) (7) 8 9 b. (9 7). a. 9 [(8) ] 9 () b. [(8) ] () 7. a. C 9 [() ] b. C 9 [(0) ] C 9 (0) C 9 (7) C 0 C 0 c. C 9 [(98.) ] C 9 (.) C 7 9. a. V π(. cm) b. V π( cm) V π(.7) cm V π(7) cm V.π cm V π cm V. cm V. cm c. V π( cm) V π() cm V 88π cm V 90.8 cm Copyright by Houghton Mifflin Company. All rights reserved. 7

8 Problem Solving, xpressions, and quations a. S {() [(00) ]()} b. S {() [(00) ]()} S 0[ (99)] S 0[ (99)] S 0( 98) S 0( 98) S 0(00) S 0(0) S 0,000 S 0,00 00 c. S {() [(00) ]()} S 0[0 (99)] S 0(0 9) S 0(0) S,0. a. D D [ ( )] [ ( )] b. D ( 8) () D ( ) [ ( ( ) () )] D D D 00 D 9 D 0 D c. D [( ) )] [ ( )] D ( ) (8) D D 89 D 7. a. A 9. ( T 9.) ( ( S) 0.0S) A 9. ( 9.) ( () 0.0()) A 9. (.) ( ) A 9. (.) (.0) A 9. ( 9.78). F b. A 9. ( 9.) ( (0) 0.0(0)) A 9. (.) ( ) A 9. (.) (.) A 9. ( 8.7) F 8 Copyright by Houghton Mifflin Company. All rights reserved.

9 CHAPTR c. A 9. ( 9.) ( () 0.0()) A 9. (.) ( ) A 9. (.) (.) A 9. ( 89.).8 F d. A 9. ( 9.) ( (0) 0.0(0)) A 9. (.) (0.78) A 9. (.79) 9. 0 F The limitation on this model is with no wind, the apparent temperature is greater than the current temperature. e. A 9. ( 9.) ( (0) 0.0(0)) A 9. ( 9.) ( ) A 9. ( 9.) (.) A 9. ( 8.7) F f. Using Table from section., if T -º and S 0 mph, then the apparent temperature is 0. A 9. ( 9.) ( (0) 0.0(0)) A 9. ( 9.) (0.78) A 9. (.079).08 F This does not match the table. 7. a. One term containing three factors, w, x, and y b. One term containing three factors, x, y, and x ; third factor contains two terms. c. Two terms each containing two factors; is the common factor. d. One term with three factors 9,, and a ; is the common factor. xercise.. Change in x x y 8 Change in y The changes in x and y are constant. Working backwards in the table, when x 0, y. Using the change in y as the coefficient on x, the equation is y x. Copyright by Houghton Mifflin Company. All rights reserved. 9

10 Problem Solving, xpressions, and quations. Change in x x y 7 9 Change in y The changes in x and y are constant. Working backwards in the table, when x 0, y. Using the change in y as the coefficient on x, the equation is y x.. Change in x x y 8 Change in y The changes is x and y are constant. Working backwards in the table, when x 0, y 0. Using the change in y as the coefficient on x, the equation is y x. 7. Change in x x y 0 7 Change in y 7 The change in y is not constant. We can observe that y is close to the value of x, but something more is needed. When x, y, which is more than. Checking a different combination, when x, y 0; again, more than. The equation is y x. 9. Input 0 n Output 0. n. Input 0 n Output n. The difference between x and seven.. The quotient of x and seven. 0 Copyright by Houghton Mifflin Company. All rights reserved.

11 CHAPTR 7. The difference between seven and x. 9. The quotient of x and five.. The quotient of seven and the sum of x and two.. The quotient of the sum of x and two and the difference between x and two.. 0 x y 7. y x 0 9. x y. y 7x. The output is five less than the product of and the input.. The sum of the input and the output is eleven. 7. The difference between two times the input and the output is. 9. The output is the quotient of the input and 8.. y.9x y. 0.0x. y x 8 7. a. 0.7, % b. 0.0, % c % d % 0 9. a. 0% b..% c. 0.00% d. 00% 00. x season ticket cost, y daily cost, % 0.0; y 0.0x. x wages, y amount of tax,.% 0.0; y 0.0x. x amount of loan, y one cost, % 0.0; y 0.0x Copyright by Houghton Mifflin Company. All rights reserved.

12 Problem Solving, xpressions, and quations 7. x amount of wages, y net pay, 7.% 0.07, 0% 0.0, n% n 00 ; x (0.07x 0.0x n 00 x) 9. The group is a woman with her mother and her daughter. Mid-Chapter Test. a. () () () 8 b. ( ) c d a b. (7)() () c. (8)() (0) 0 d. ( )( ) ()()() ()()()() (). a. ()() b. () ()() c. 0 ()() d. 8 (8 ) 8 () 0 e. ( 7) 7 9 f. ( ) ( ) ()( ) () g. ( ( 7)) ( ) 9 ( ) h a b (9 ) 9(0) 90 Copyright by Houghton Mifflin Company. All rights reserved.

13 CHAPTR c. 8(8 8 ) 8(8) 8( 8 ) 7 d..7(9).(9) 9(.7.) 9(0) 90 e f. ( 7) (7 7) a. x will be negative because x is always positive when x is a real number. b. x could be positive or negative, negative x sounds like always negative. c. x could be positive or negative, negative x sounds like always negative. d. x will be negative because x is always positive.. a. (x ) x () x b. (x ) x ()() x c. 7 (x ) 7 x ()() 7 x 0 x 0 7 x d. 8 ( x) 8 ()() ()(x) 8 8 x x 7. a. gcf is ; x 8 (x) ()(9) (x 9) b. gcf is x; x x x(x ) c. gcf is n; mn np n(mn p ) d. gcf is 7xy; x y 9xy 7xy(9x 7y) 8. a. The variable is x, the constant term is, and the numerical coefficient is. b. The variable is x, there is no constant term, and the numerical coefficients are and. 9. a. (x x ) x(x x ) x 9x x x x x x b. a(a ab b ) b(a ab b ) a a b ab a b ab b a a b ab b 0. a. x yz xy z xxyz xyyz x y b. x yz xxyz ( xy) z xyxyz y c. xy yz y( x z) xy xy x z x. a. C x 0.087x or C.087x b. A x 0.0x or A.0x c. C.9x 0.0 Copyright by Houghton Mifflin Company. All rights reserved.

14 Problem Solving, xpressions, and quations. a. # of pairs of pens Total # of panels b. The change in y is constant at. Working backwards in the table, when x 0, y. The equation is y x.. j, x. a, x. g, x. h, 0.x 7. i, x 8. b, x 9. e, x 0. c, x xercise... a. solution set b. evaluate c. scale d. dependent variable e. independent variable. a. (7, 7), J b. (0, 0), c. (7, 98.), G d. (00, ), K 7. a. B (8, 0) b. A, (0, 0) 9. In A s, s is the independent variable and A is the dependent variable.. In A s, s is the independent variable and A is the dependent variable. Copyright by Houghton Mifflin Company. All rights reserved.

15 CHAPTR. A is the independent variable and is the dependent variable.. Independent variable, weight of package; dependent variable, cost of shipping. 7. Independent variable, temperature (a cooler day might bring more kittens); dependent variable, number of kittens. 9. x y x () () 8 () 0 (0) () () () 7.. x y x () 0 () 8 () 0 (0) () () 0 () x y x () () 0 () 0 (0) () () () Copyright by Houghton Mifflin Company. All rights reserved.

16 Problem Solving, xpressions, and quations. x y x x () () () () 8 () () 0 (0) (0) 0 () () () () 0 () () 7. x y x () () () 0 (0) () () () 9. a. 9,, and are straight lines. b. and 7 are parabolas. c. y ax b makes a straight line Copyright by Houghton Mifflin Company. All rights reserved.

17 CHAPTR 9.. On the input axes, use $0 to $00 with a scale of $0; on the output axes, use $0 to $0 with a scale of $.. On the input axes, use 0 to hours with a scale of hours; on the output axes, use low temperature to high temperature with a scale of 0% of the difference. 7. a. b. x y xy ()() ()() ()( ) x y x y () () () () () () c. d. x y x y ()() 8 ()() 8 ()() x y x y () () 7 () 7 e. f. x y x y () () () () () () x y x y () () () xercise.. Guesses will vary. quation is y.07x $.9. When y $0, x $0.79 Copyright by Houghton Mifflin Company. All rights reserved. 7

18 Problem Solving, xpressions, and quations. Guesses will vary. quation is y ($7() $0.0x)0.9. When y $.0, x miles. Guesses will vary. quations are x first, x $0,000 second, and x $0,000 third. x (x $0,000) (x $0,000) $,000,000; shares are $0,000, $0,000, and $0, x y x 0 (0) () () () x when y x when y 9.. x y x () () 0 0 (0) () () 8 () x y 0.x a. 0.() 0 0.(0) b. 0.() () 0. x when y x when y For exercises through, use calculator graphs and tables to solve for x. Answers are given for reference only.. a. x. b. x.. a. x b. x 7. a. x 0 or x b. x or x c. no real number solution d. x 0. 8 Copyright by Houghton Mifflin Company. All rights reserved.

19 CHAPTR 9. a. x or x b. no real number solution c. x or x d. x 0. a. x or x 0 b. x or x c. no real number solution d. x or x. a. {0, } b. {., 0.8} c. {., } d. no real number solutions. 7. Weight (lb) Index I W(70.) H 00 (00)(70.) () 8. 0 (0)(70.) () 0. 0 (0)(70.) ().0 0 (0)(70.) ().8 0 (0)(70.) ().7 Weight (lb) Index I W(70.) H 0 (0)(70.) (70) (0)(70.) (70) 0. 0 (0)(70.) (70). 0 (0)(70.) (70).0 70 (70)(70.) (70). 9. a. W 0 lb b. W 0 lb. a. W 0 lb b. W 70 lb. a. 0 F b F c. 0 F d. 9 0 F e F. Solving the equation x is finding the independent variable. 7. Locating y, given the graph and x, is finding the dependent variable. 9. Locating x, given the graph and y, is finding the independent variable. xercise.7. a. () 0 b. () c. ( ) d e. f. 8 Copyright by Houghton Mifflin Company. All rights reserved. 9

20 Problem Solving, xpressions, and quations. a. () 0 b. ( ) c. () d. 8 (0) 0 e. 7 8 f a. x 8 b. x x x x x 9 x c. x 8 d. x 8 x x x x x e. f. ( )( x 8 ) ( )() )( x 8 ) ( )( ) 8 ( 8 x 8 x g. x h. x 8 ( )( ) ( x ) )( x ) ( )(8) ( x x 7 i. x 8 8 ( )( x ) ( 7) x 0 7. Inverse: take off jacket, take off vest, take off shirt. Dressing and undressing. 9. Inverse is not meaningful. Taking pictures.. Order is not important (unless you want to dig the hole within range of the sprinkler).. a. x 8 b. x x 8 x x x 0 x x 0 x x c. x d. x 0 x x 0 0 Copyright by Houghton Mifflin Company. All rights reserved.

21 CHAPTR x x x x x x. a. 9 (x ) b. 9 (x ) (x ) 9 (x ) 0 x x 8 x x 8 x x 0 c. 9 (x ) d. 9 (x ) (x ) 9 (x ) 0 x 9 x x 9 x x x x 7. x 0 9. x x 0 x x x x x x.. 8 x 8 x 8 x 8 x 8 8 x x x x x. a. is an Identity. b. 8 is a Contradiction. 7. a. x x x is a Contradiction. b. x x x is an Identity. 9. a. x(x ) x is an Identity. Copyright by Houghton Mifflin Company. All rights reserved.

22 Problem Solving, xpressions, and quations x b. x( 0.) is an Identity ( ).. x ( x) 7. x ( x) x 8 x 7 x x x 8 7 x x x x 9 x 8 x 9 x 8 x x 9. x ( x) (9 x). x x x. x 9 x 9. x 9 x x x. x x. x x. 9. 9(x ).. 7. x 0.07x 9x x 9x x.07 9x. x 9x 9. x 9x x...7 x 0.x 0.0x. (x ) x.7.x x x.7..x. x x x x 8 x x x. x 7. (x ) (x ) 9. (x ) x x x x x x x x x x x x x x x x x Copyright by Houghton Mifflin Company. All rights reserved.

23 CHAPTR x x x x x x x. y x x y 7 x y 7 y x x y x 7 x x y y 7 y y x 7 y 7 x x 7 7 y 7 x 7 y y x 7 x y 7 is not equivalent to the other equations. y x is not equivalent to the other equations.. x y 8 y x 8 y x 8 x y x 8 x y x x 8 x y 8 x y x 8 y x 8 y x 8 is not equivalent to the other equations.. D rt 7. y mx b D rt r r y mx mx b mx D t r b y mx 9. πr V. pn V πr pn π π N N V r p π N. A h( a b ). a n a (n )d A ( h( a b )) h h a n (n )d a (n )d (n )d A a a b a h a n (n )d a Copyright by Houghton Mifflin Company. All rights reserved.

24 Problem Solving, xpressions, and quations A b a h a b c A 9. S n(a a n ) ( a b c) S A ( n( a a n )) n n A b c a b c b c S an a an n a A b c a S an a n T T T h c 7. V 0.(T 0) Th T ( T T ) h h c h V 0.(T 0) Th T h T c T h T c T c V 0.( T 0) T c T h T h T h T h V 0 T T c T h T h V 0 T 0. I 77. R 0.V T R R Se 0. V Se I T I R I T Se T 0. V R S e I T a S r r S S r a r r S a S S e n Copyright by Houghton Mifflin Company. All rights reserved.

25 CHAPTR Copyright by Houghton Mifflin Company. All rights reserved. S a r S S a S S S a r or S a r 8. t t D D, D D 8. ) ( b a b a A A, A A 8. T T T c c c T T T c c c ) ( T T T c c c ) ( c c T T ) ( (, Review xercises. Associative properties for addition and multiplication, commutative properties for addition and multiplication, distributive property for multiplication over addition.. Absolute value, braces, brackets, fraction bar, parentheses, square root.. Assumption, condition. 7. Sum, difference, product, quotient. 9. Input-output rule, independent variable, dependent variable.. valuate, simplify, factor, and solve an equation.

26 Problem Solving, xpressions, and quations. Input Input Output Output x y x y x y a b. 7 (7) (7) 0 c. 7 7 y 7 0 y Answers on which property was used may vary on exercise. One possible solution is given. ; Associative property for addition. ( ) ( ) 7. x (x) x ( x) x x x x x x x x 0 9. a. x y x xy x xy y xy y xy x y x x b. ( ) y y x y xy x y xy. ( ) (). π(. in.) π(. in.)( in.) π(. in.)(. in.. in.) π(. in.)(. in.).π in..8 in π 0. π 0 π π 7 π π π 7 9 π π π The ratio is approximately to a. The difference between three and the product of two and a number. b. The product of three and the difference between a number and. x 9. 8 Copyright by Houghton Mifflin Company. All rights reserved.

27 CHAPTR. 9 (x y) (x y) 9 x y 0x y x 0x y y 9 x 7y 9. () (). A π(. in.) A.π in. 7. x y x () () 0 (0) 0 () (). x (.). 0 9 (F ) x 9 (0) 9 [ 9 (F )] x 8 7 F x 0 F. 0 (n )(.7) I Prt 0 (n )(.7) ( n )(.7) n n I Pt I Pt r Ptr Pt 9. C a by C a a by a C a by y y C a y b Copyright by Houghton Mifflin Company. All rights reserved. 7

28 Problem Solving, xpressions, and quations. a. gcf x; x x x(x) x() x(x ) b. gcf x; x x x x x x. a. x b. x x x x x x x x x 0 x x 0. a. x b. x x x x x x x..x. x x 7. a. b. x y 7 x y 0 8 Constant difference on y is. Constant difference on y is 7. When x 0, y 0; y x 0. When x 0, y 7; y 7x x x is the intersection(s) of the two graphs; x and x.. a. Number of quarters; parking time b. Speed; distance traveled b. Size of luggage; cost. escrow balance, x total payments from account, 0. 7 ; 0.7x; For $7.0, $ x $ x 0.7 x $00 8 Copyright by Houghton Mifflin Company. All rights reserved.

29 CHAPTR. Formula π r x S 80 Angle Arc, S (for circle of r 0 in.) 0 0 (π)(0)(0) (π)(0)(80) (π)(0)(90) 80.7 (π)(0)() (π)(0)(7) (π)(0)(8) (π)(0)(7.) (π)(0)(7.) The digits as a single number is the sum of 9 and 9,7. Chapter Test. Another name for additive inverse is opposite.. An ordered pair is used to locate a point on the coordinate graph.. An independent variable is the input, x, or set of numbers on the horizontal axis... a. 7 () 0 7 () 7 (7)() 8 (7) () 9 7 b (0.) (.)(0.) 0.7 (.) (0.) c. ( ) 7 ( ) ( ) ( ) ( ) ( ) ( ) )( ) ( ) )( 8 ( Copyright by Houghton Mifflin Company. All rights reserved. 9

30 Problem Solving, xpressions, and quations. a. (8 9) 0 8 (9 0) ; associative property for addition b ; commutative property for addition 7. a. { [ ( )] } { [ ()] } { [ ()] } { [] } { } {0} 0 b. ()() 9 c. () ()() 9 d. (7 ) (0) e. x (8 x) x 8 x x 8 f. 8. The product of four and the difference between a number and three. 9. a b c h A 0. A ( a b) A a b c A a b h A a c b A a b h. a. x y x x y 9xy x y y gcf xy b. x y 9xy xy(x) xy(y) xy(x y) c. x y 9xy xy x xy y x y. a. graph crosses y 0 (x-axis) at x b. graph intersects y at x c. graphs intersect at x. a. x 0 b. x ( x ) (0) ( x ) ( ) x 0 x 8 0 Copyright by Houghton Mifflin Company. All rights reserved.

31 CHAPTR x 0 x 8 x x x x c. x x ( ) ( x x ) x 0 9x x 0 0 9x 9x 0 9x x x x. Zero is not a positive integer or a natural number... A (..) m A 0.(.0) m A. m. 7. x y x y 9 7 xtending the table gives x 7, Difference in y is a constant. when y. xtending the table backwards, xtending the table backwards, when x 0, y ; equation is y x. when x 0, y 0; equation is y x. Copyright by Houghton Mifflin Company. All rights reserved.

32 Problem Solving, xpressions, and quations 8. a. C cost, x months; C $87x $800x; C $7x b. $0,000 $7x x $0,000 $7; x 8 months or years 8 months c. Costs for apartment and care; amount of savings d. No change in cost; no other costs or income 9. a. b. 7 c. In b, the set of parentheses in the denominator is incomplete, so the calculator assumes a parenthesis at the end of the expression, dividing by instead of by. 0. Formula is:.9() 0.9x 0.07(.9() 0.9x) 0.97() x x x (0) (0) (9) 9.0 Copyright by Houghton Mifflin Company. All rights reserved.