Chapter 8. Chapter Opener. Pre-Algebra 273 Chapter 8 Solutions Key. 6y y y 24

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1 Chapter Chapter pener Math in the Real World (p. 99) The bike trail that rises feet over a horizontal distance of feet is steeper. Sample answer: Make a ratio of vertical change to horizontal change for each trail. First trail: Second trail:. rise horizontal change rise horizontal change So, the first trail rises feet over a horizontal distance of feet and the second trail rises. feet over a horizontal distance of feet. So, the first trail is steeper. Prerequisite Skills Quiz (p. ). Sample answer: An equation is a mathematical sentence formed b placing an equal sign between two epressions, while an inequalit is a mathematical sentence formed b placing an inequalit smbol (>, <,, or ) between two epressions. While a solution of an equation like is a single number, the solution of an inequalit like >, <,, or is all numbers greater or less than a number, and ma or ma not include the number itself.. Let the cost of the trip. Cost of the trip Difference in amounts Amount saved The trip costs $.. ( t) t t t t t Check: ( t) [ ()]. (w ) w w w w w Check: (w ) ( ) Check: 9 () 9 (). 9 ( f ) 9 f f f f f f Check: 9 ( f ) 9 ( ). <. 9. < <.. n p n p n <. m > m > m > 9 9 Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

2 Lesson.. Checkpoint (pp. ). The domain of the relation is the set of all inputs, or -coordinates. The range is the set of all outputs, or -coordinates. Domain:,,, Range:,,. The domain of the relation is the set of all inputs, or -coordinates. The range is the set of all outputs, or -coordinates. Domain:,, Range:,,,. (, ) (, ) (, ) (, ) (, ) Input utput The relation is a function because ever input is paired with eactl one output.. Input utput (, ) (, ) (, ) (, ) The relation is not a function because the input is paired with two outputs, and.. Guided Practice (p. ). A relation is a function if for each input there is eactl one output.. Input utput Sample answer: Each element of the domain can be paired with either or both of the elements of the range.. Domain:,,,,. Domain:,,, Range:,,,, Range:,,.. (, ) (, ) (, ) (, ) (, ) Input utput The relation is not a function because the input is paired with two outputs, and. (, ) (, ) (, ) (, ) (, ) Input utput The relation is a function because ever input is paired with eactl one output.. Sample answer: The relation (, ), (, ), (, ), (, ) is a function because ever input is paired with eactl one output.. Practice and Problem Solving (pp. ). Domain:,,, 9. Domain:, Range: 9,,, Range:,, 9. The relation consists of the ordered pairs (, ), (, ), (, ), (, ), and (, ). Domain:,,, Range:,. The relation consists of the ordered pairs (.,.), (.,.), (.,.), (.,.9), and (.,.). Domain:.,.,. Range:.,.9,.,.. A relation is sometimes a function.. (, ) (, ) (, ) (, ) (, ) Input utput The relation is not a function because the input is paired with two outputs, and. Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

3 . (, ) (, ) (, ) (, ) (, ) Copright Holt McDougal Input utput The relation is a function because ever input is paired with eactl one output.. Input utput (, ) (, ) (, ) (, ) (, ) The relation is a function because ever input is paired with eactl one output.. Input utput (, ) (, ) (, ) (, ) (, ) The relation is not a function because the input is paired with two outputs, and.. a. Yes. Sample answer: The ordered pairs (age, height) represent a function because each age is paired with eactl one height. b. No. Sample answer: The ordered pairs (height, age) do not represent a function because some heights will be paired with more than one age. This is because the height of an adult remains the same for man ears.. The relation is not a function because the vertical line passes through more than one point. 9. The relation is a function because no vertical line passes through more than one point.. The relation is not a function because the vertical lines,, and pass through more than one point.. a. Domain:,,, Range:,,, 99, b. Input utput 99 c. No; the relation is not a function because the input is paired with two outputs, and.. a. Yes. Sample answer: Each advisor number input can be paired with onl one wind speed output. The relation also passes the vertical line test. b. pal qualified as a hurricane for advisories.. The mapping diagram more clearl shows whether a relation is a function. Sample answer: It can quickl be determined how man outputs an input is paired with.. a. As a skdiver falls, the atmospheric pressure increases. The reading on the skdiver s altimeter decreases. b. The domain of the relation is the altitude of the skdiver. The range of the relation is the atmospheric pressure at each altitude. c. Yes. Sample answer: Each altitude input corresponds to onl one atmospheric pressure output. The relation also passes the vertical line test. d. An atmospheric pressure of about 9 lb/ft will trigger the alarm.. Sample answer: The relation (, ), (, ), (, ), (, ) is a function because each input is paired with eactl one output. The inverse (, ), (, ), (, ), (, ) is not a function because the input is paired with two outputs, and.. a. Mass (grams) Cowbird Growth Vireo Gnatcatcher Age (das) b. Sample answer: The growth is the same in that for both the vireo and the gnatcatcher, the cowbird s growth is not too fast the first two das, then is more rapid the net several das before slowing and almost stopping. It is different in that the growth for the cowbird raised b the gnatcatcher decreases and levels off with the cowbird at an earlier stage and at a much lower mass than the cowbird raised b the vireo.. Mied Review (p. ). When and ; (). When and ; () 9. When and ; () () ()() () Pre-Algebra Chapter Solutions Ke

4 . When and ; () (). So, is a solution.. a () So, is not a solution.. m () So, is not a solution.. u So, is a solution. (). I Prt ()(.)() $ $ $ The interest is $, and the balance is $.. I Prt ()(.)(.) $ $ $ The interest is $, and the balance is $.. Standardized Test Practice (p. ). a. Yes. Sample answer: Each merchandise cost input is paired with eactl one shipping cost output. b. No. Sample answer: Each shipping cost input is paired with man merchandise costs output. Lesson.. (, ), (, ), (, ), (, ), (, ). (, ), (, ), (, ), (, ), (, ). (, ), (, ), (, ), (, ), (, ). Checkpoint (pp. 9).. () () () () (, ) is not a solution. (, ) is a solution... () () () (9) (, ) is not a solution. (, 9) is a solution. Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

5 . (, ), (, ), (, ), (, ), (, ).. () () (, ) is not a solution. (, ) is a solution.. (, ), (, ), (, ), (, ), (, ) 9.. The horizontal line is a function. The vertical line is not a function Guided Practice (p. ). An equation whose graph is a line is called a linear equation.. No. Sample answer: The equation is not in function form because the equation is solved for, not. The equation in function form is... () () (, ) is a solution. (, ) is not a solution. Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

6 . () d t Distance (m) t d () Sojourner Trip d t () t t Time (h). t It would take Sojourner about hours to reach its maimum distance from the lander.. Practice and Problem Solving (pp. ).. 9 () 9 (, ) is not a solution. (, ) is a solution... () (9) () (, ) is a solution. (9, ) is not a solution... The equation is a function.. The equation is a function. 9. The equation is not a function.. The equation is a function. The equation is a function. Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

7 .. The equation is a function.. The equation is not a function.. The equation is a function.... Copright Holt McDougal Pre-Algebra 9 Chapter Solutions Ke

8 (9) 9, The weight of the whale is 9, pounds....(). The capacit of the can is. liter...9.9(,),., Iowa has an area of about, square kilometers.. a () a a. a a a a a. 9 () a 9 a 9 a 9 a a a. (a ) () a a a a a Pre-Algebra Chapter Solutions Ke a Copright Holt McDougal

9 9. a. f.t..()... The fork length of the bigee thresher is about centimeters. f.t..() The fork length of the scalloped hammerhead is about 9 centimeters. f.9t..9()... The fork length of the white shark is about centimeters. b. Bigee thresher:. % Scalloped hammerhead: 9. % White shark:.9 9% c. Bigee thresher. Sample answer: The bigee thresher has the shortest bod relative to its total length, so it must have the longest tail relative to its bod length.. a. a.9d..9(9) Suiko is about 9. million ears old. b. a.9d...9d....9d d d d Midwa is about kilometers from Kilauea.. a. f.s.9 f.9.s.9.9 f.9.s f..9. s. f.9 s. b. s f.9. s The speed of the platpus is about. meter per second. Copright Holt McDougal. a. b. 9 9 (, 9) (, ) (, ) (, ) (, 9) (, ) (, ) c. No; es. Sample answer: is not a linear equation because the graph is a curve, not a straight line. is a function because its graph passes the vertical line test.. Mied Review (p. ). Check: (). c c c c c Check: c (). w w w w w Check: w () Pre-Algebra Chapter Solutions Ke

10 . n n 9 Y=-.X+ Y=-.+ n p n p n Check: n % of p p p p X=. Y=- X=-. (., ) (.,.). C.g. Y=+.X X=9 Y=. Y= % of p p 9 p p 9. % of p p p p. % of p p p 9 p. Domain:,,,. Domain:, Range:,,, Range:,,. Domain:. Domain:,,, Range:,,, 9 Range:,,,. Standardized Test Practice (p. ). B; () (9) (, 9) is not a solution.. I. Technolog Activit (p. ).. Y=-X Y=X- (9,.) You can rent 9 games for $.. Lesson.. Checkpoint (p. ). () The -intercept is, and the -intercept is. (, ) (, ). () () The -intercept is, and the -intercept is. X=. Y=. X=. (.,.) (.,.) Y=-. (, ) (, ) Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

11 . () The -intercept is, and the -intercept is. (, ) (, ). Guided Practice (p. ). For the line that passes through the points (, ) and (, ), the -intercept is and the -intercept is.. Sample answer: To find the -intercept, substitute for in the equation and solve for. To find the -intercept, substitute for in the equation and solve for.. The -intercept is, and the -intercept is.. The -intercept is, and the -intercept is.. The -intercept is, and the -intercept is... (, ) (, ) (, ) 9. Let the amount of ground beef, and let the amount of chicken. Cost of Amount Cost of ground p of ground chicken p Amount Total of chicken cost beef beef () () Chicken (lb) Barbecue Food (, ) (, ) Ground beef (lb). Practice and Problem Solving (pp. ). () The -intercept is, and the -intercept is. (, ) (, ). (, ) (, ) (, ). () The -intercept is, and the -intercept is. (, ) (, ) Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

12 . () () The -intercept is, and the -intercept is. (, ) (, ). () () The -intercept is, and the -intercept is. (, ) (, ). () () The -intercept is, and the -intercept is. (, ) (, ). () () 9 The -intercept is 9, and the -intercept is. CNTINUED. CNTINUED (9, ) (, ). () The -intercept is, and the -intercept is. (, ) (, ). The -intercept is, and the -intercept is. (, ) (, ) () The -intercept is, and the -intercept is 9. (, ) 9 (, 9) Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

13 9. a. Let the amount of canned food, and let the amount of dr food. Calories in canned p food Amount of canned food Calories in dr food p Amount of dr food Total calories b. () () The -intercept is, and the -intercept is. Dr food (oz) Beagle Food (, ) (, ) Canned food (oz) c. Sample answer: You can feed our beagle ounce canned food, and ounces dr food, or ounces canned food and ounces dr food, or ounces canned food and ounce dr food.. a. () 9 The -intercept is 9, and the -intercept is. Gas remaining (gal) A Tank of Gas (, ) (9, ) 9 Driving time (h) b. Sample answer: The -intercept represents the number of hours until the fuel tank is empt. The -intercept represents the amount of fuel the tank can hold. CNTINUED. CNTINUED c. () p p p After hours of driving, tank of gas is left ()..9() The -intercept is, and the -intercept is. (, ) (, ) ()..() The -intercept is, and the -intercept is. (, ) (, ).....(). The -intercept is, and the -intercept is. CNTINUED 9 Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

14 . CNTINUED (, ) (, ). () The -intercept is, and the -intercept is. (, ) (, ). () () The -intercept is, and the -intercept is. (, ) (, ). () The -intercept is, and the -intercept is. CNTINUED. CNTINUED (, ) (, ). Sample answer: has no -intercept. It is a horizontal line with -intercept. has no -intercept. It is a vertical line with -intercept.. The line slants upward from left to right. Sample graph: 9. a. Let the number of hours for single-engine airplanes, and let the number of hours for twin-engine airplanes. Cost for singleengine Hours for Cost for Hours p singleenginenginengine twin- p for twin- Total fees 9 b. 9 9 () 9 () The -intercept is, and the -intercept is. Twin-engine (h) Airplane Rental (, ) (, ) 9 Single-engine (h) c. The single-engine planes must be rented for hours. d. 9 () Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

15 . a. P l w b. () () The -intercept is, and the -intercept is. Width (in.) Rectangle Dimensions 9 (, ) (, ) 9 Length (in.) c. Sample answer: and, and, and d. No. Sample answer: The - and -intercepts do not represent possible side lengths. For the -intercept, and for the -intercept,, and neither the length nor the width of a rectangle can be.. Sample answer: c Let c,, and. The intercepts are common multiples of the coefficients of and.. a. r increases.. CNTINUED Walking time (h) Decreasing Distance (, ) (, 9) 9 (, ) (, ) (, ) (, ) 9 Running time (h) b. Sample answer: The -intercept stas the same, but the -intercept moves closer to the origin, resulting in the graph getting steeper. c. Sample answer: The -intercept stas the same, but the -intercept moves closer to the origin, resulting in the graph getting less steep. d. Sample answer: Both the - and -intercepts move farther from the origin together in such a wa that the steepness of the line does not change for different distances.. a b a b a b b a Walking time (h) Increasing Running Speed (, 9) 9 9 (, ) (, ) (, ) 9 Running time (h) w increases. Walking time (h) d increases. CNTINUED Increasing Walking Speed (, 9) 9 9 (, ) 9 (, ) 9 (, ) 9 Running time (h) Copright Holt McDougal The -intercept is b a. a b a() b b The -intercept is b. b a b The -intercept is, and the -intercept is.. Mied Review (p. ). ( ) 9. ( ). 9 ( 9 ). ( ( ) ) 9. increase; Amount of increase Amount of original % Pre-Algebra Chapter Solutions Ke

16 9. increase;. decrease;. decrease; Amount of increase Amount of original Amount of decrease Amount of original Amount of decrease Amount of original. 9 () 9 9 (, 9) is a solution.. () (, ) is not a solution.. () (, ) is not a solution.. () () (, ) is a solution. % 9 9 % 9 %. Standardized Test Practice (p. ). B; The -intercept is.. I; () The -intercept is.. Let the number of basic washes, and let the number of delue washes. Cost of basic wash p Number Cost of of basic delue washes wash p Number of delue Total sales washes () 9 () The -intercept is, and the -intercept is. CNTINUED. CNTINUED Delue washes Car Washes 9 (, ) (, ) Basic washes Sample answer: Three possible combinations are basic washes and delue washes, basic washes and delue washes, or basic washes and delue washes. Lesson.. Concept Activit (p. 9) Investigate Check student s setup. Draw Conclusions. The steeper ramp has a larger slope than the other ramp.. When the slope is, the rise and of a ramp are equal. Let the rise and of a ramp equal. slope r is ru e n. When the rise increases and the stas the same, the slope increases.. Checkpoint (pp. ). m r ise difference of -coordinates. m r ise difference of -coordinates () Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

17 . m r ise difference of -coordinates 9 9. m r ise difference of -coordinates. m r ise difference of -coordinates The slope is positive.. m r ise difference of -coordinates The slope is undefined.. m r ise difference of -coordinates () The slope is zero.. m r ise difference of -coordinates The slope is negative.. Guided Practice (p. ). The vertical change between two points on a line is called the rise, and the horizontal change is called the.. Sample answer: The denominator of the slope ratio for a vertical line is alwas because the -coordinate of ever point on a vertical line is the same, and division b is undefined.. Sample answer: The - and -coordinates need to be used in the same order. If ou subtract the second -coordinate from the first -coordinate to obtain the denominator, then ou should subtract the second -coordinate from the first -coordinate to obtain the numerator. So, m.. The slope is positive. m r ise difference of -coordinates (). The slope is positive. m r ise difference of -coordinates () Copright Holt McDougal Pre-Algebra 9 Chapter Solutions Ke

18 . The slope is zero. m r ise difference of -coordinates (). slope r ise Sample answer:. and., the ramp in Eample has a greater slope. Therefore, it is steeper.. Practice and Problem Solving (pp. ). The slope is positive. m r ise difference of -coordinates () 9. The slope is negative. m r ise difference of -coordinates ( ). The slope is undefined. m r ise difference of -coordinates () (). (, ), (, ) m r ise difference of -coordinates. (, ), (, ) m r ise difference of -coordinates (). (, ), (, ) m r ise difference of -coordinates (). (, ), (, ) m r ise difference of -coordinates 9 Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

19 . (, ), (, ) m r ise difference of -coordinates. (, ), (, ) m r ise difference of -coordinates The slope is undefined. difference of -coordinates. a. m b. Sample answer: The cheetah s speed in meters per second. c. Sample answer: It would also start at the origin, but rise less steepl because the gazelle s speed of meters per second is less than the cheetah s speed of meters per second, and the speed is indicated b the slope.. Sample answer: 9. Sample answer:. m r ise difference of -coordinates. m r ise difference of -coordinates. m r ise difference of -coordinates The slope is undefined.. m r ise difference of -coordinates () () 9. m r ise difference of -coordinates. Sample answer:. Sample answer: Copright Holt McDougal Pre-Algebra 9 Chapter Solutions Ke

20 . m r ise difference of -coordinates (). m r ise difference of -coordinates ( ) 9. m r ise difference of -coordinates (). m r ise difference of -coordinates ( ) () The slope is undefined.. m r ise difference of -coordinates ( ) ( ). m r ise difference of -coordinates. m r ise difference of -coordinates ( ) The slope is undefined.. Sample answer: A line with zero slope is a horizontal line, and a line with undefined slope is a vertical line.. Let the. slope r ise p p foot inches inches in ches feet The length of ground the ramp covers is feet.. a. Gradient.. The gradient between A and B is feet per mile. b. Gradient... The gradient between B and C is feet per mile. c. Gradient.. The gradient between A and C is feet per mile.. a. No. Sample answer: First, find the slope of the road. m r ise.% The road has a grade of.% which is less than %, so no warning sign should be posted. CNTINUED 9 Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

21 . CNTINUED b. Let the rise. m r ise 9%.9 (.9) p 9 The road rises 9 feet.. Trail A: m r is ru e n. Trail B: m r is ru e n. Because. >., trail B is steeper. Therefore, the instructor should take trail A. 9. Sample answer: a. A and B: m r ise difference of -coordinates () () B and D: m r ise difference of -coordinates () C and E: m r ise difference of -coordinates Conclusion: The slope does not depend on which two different points are chosen. CNTINUED 9. CNTINUED b. Q and R: m r ise difference of -coordinates ( ) R and S: m r ise difference of -coordinates ( ) Q and T: m r ise difference of -coordinates ( ) 9 Conclusion: The slope does not depend on which two different points are chosen.. Sample answer: Use the point P(, ). m r ise difference of -coordinates 9 Let and. 9 9 So, the line through P(, ) and (, ) has a slope of 9.. Mied Review (p. ). Check: Copright Holt McDougal Pre-Algebra 9 Chapter Solutions Ke

22 . Check:. Check: m. () m () m m Check:. p p p p p The GCF of and is.. p p p p p p p p The GCF of and is.. p p p p The GCF of and is.. p p p p The GCF of and is. 9. () The -intercept is, and the -intercept is. (, ) () 9() 9 9 The -intercept is, and the -intercept is 9. 9 (, 9) (, ). () () The -intercept is, and the -intercept is. (, ) (, ). Standardized Test Practice (p. ). D; m r ise difference of -coordinates ( ) ( ). G; m r ise difference of -coordinates (, ) 9 Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

23 Focus on Graphing Practice (p. ). Sample answer: Water is poured into the glass, then someone drinks the water in four gulps, pausing between gulps.. Sample answer: The swimmer climbs the diving board, pauses, then leaps into the air and plunges into the water. The swimmer s descent through the air is slightl faster than the descent through the water. After swimming at the same elevation for a while, the swimmer rapidl surfaces.. Distance traveled (miles) Lesson.. Checkpoint (pp. ). The line has a slope of and a -intercept of. (, ) (, ).. Temperature ( C) Time (minutes) 9 () The line has a slope of and a -intercept of. (, ) (, ) Elapsed time (minutes) Sample answer: The water cools at successivel slower rates over time. Student Reference: Parallel, Perpendicular, and Skew Lines Checkpoint (p. 9). Lines a and b are parallel.. Lines a and c are perpendicular.. Lines d and b are perpendicular.. Lines c and d are parallel.. Lines k and m are not skew because the lie in the same plane and intersect.. Lines k and j are not skew because the intersect.. Lines j and m are skew because the do not lie in the same plane and do not intersect.. CE ^&(, AG ^&(, and EF ^&( are perpendicular to GE ^&(. 9. GE ^&( and BD ^&( are parallel to AC ^&(.. GE ^&( and ^&( JH are skew to CD ^&(.. The line has a slope of and a -intercept of. (, ) (, ). The slope of a parallel line is, and the slope of a perpendicular line is.. The slope of a parallel line is, and the slope of a perpendicular line is. Copright Holt McDougal Pre-Algebra 9 Chapter Solutions Ke

24 . The slope of a parallel line is, and the slope of a perpendicular line is.. Guided Practice (p. ). An equation of the form m b is written in slope-intercept form.. Parallel. Sample answer: The lines and both have a slope of and different -intercepts. Because their slopes are equal and the have different -intercepts the lines are parallel.. The line has a slope of and a -intercept of. (, ) (, ). The line has a slope of and a -intercept of. (, ) (, ). () The line has a slope of and a -intercept of. (, ) (, ) 9 Pre-Algebra Chapter Solutions Ke. The slope of a parallel line is, and the slope of a perpendicular line is.. 9 The slope of a parallel line is, and the slope of a perpendicular line is.. The slope of a parallel line is, and the slope of a perpendicular line is. 9. () () The line has a slope of and a -intercept of. Scarf length (in.) Scarf Knitting (, ) Da () It will take about das to finish the scarf.. Practice and Problem Solving (pp. ). C. A. B. Sample answer:,, and are parallel to.. The line has a slope of and a -intercept of. (, ) (, ). The line has a slope of and a -intercept of. (, ) (, ) Copright Holt McDougal

25 . () The line has a slope of and a -intercept of.. (, ) () The line has a slope of and a -intercept of. (, ). (, ) The line has a slope of and a -intercept of. (, ) 9. (, ) The line has a slope of and a -intercept of. (, ) (, ). Let the number of minutes, and let the distance in feet. Distance traveled Feet per minute p Number of minutes The line has a slope of and a -intercept of. Distance (ft) 9 Robot Travel 9 Time (min) The robot could reach the end of the tunnel in about minutes.. a. Y=-X X= Y= It takes the paramotorist minutes to reach the ground. b. The line has a slope of and a -intercept of. The slope represents the rate at which the paramotorist descends in feet per minute, and the -intercept represents the beginning height in feet.. The slope of a parallel line is, and the slope of a perpendicular line is.. 9 The slope of a parallel line is, and the slope of a perpendicular line is.. The slope of a parallel line is, and the slope of a perpendicular line is.. The slope of a parallel line is, and the slope of a perpendicular line is. Copright Holt McDougal Pre-Algebra 9 Chapter Solutions Ke

26 . The slope of a parallel line is, and the slope of a perpendicular line is.. The slope of a parallel line is, and the slope of a perpendicular line is.. m r ise difference of -coordinates The slope of a parallel line is, and the slope of a perpendicular line is. 9. m r ise difference of -coordinates The slope of a parallel line is, and the slope of a perpendicular line is.. m r ise difference of -coordinates () The slope of a parallel line is, and the slope of a perpendicular line is.. a. Let the number of das, and let the unharvested area of the larger field. Unharvested area Total area Acres harvested p Number per da of das b. Let the number of das, and let the unharvested area of the smaller field. Unharvested area Total area Acres harvested p Number per da of das c. In part (a), the slope of the line is and the -intercept is. In part (b), the slope of the line is and the -intercept is. Unharvested area (acres) Corn Harvesting (, ) 9 (, ) Time (das) d. The graphs are parallel because both lines have the same slope,, and different -intercepts. e. It takes das to harvest the corn in the larger field. It takes das to harvest the corn in the smaller field.. a. Let the number of miles, and let the amount of mone. Donor Amount per mile Fied amount Equation Janette None $ Ben $ $ Salil $ None Mar $ $ b. ( ) ( ), or. c. The equation from part (b) has the greatest slope because the slope is equal to the sum of the slopes in part (a). Sample answer: The slope represents how much mone is earned per mile. The equation from part (b) is the sum of the slopes from parts (a). So, the equation from part (b) has the greatest slope. 9 Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

27 . a. m b m b m() b m() b b m b (, b) is a solution. (, m b) is a solution. b. (m b) b m b b m The difference of the -coordinates is m. The difference of the -coordinates is. c. m r ise difference of -coordinates m m So, the slope of m b is m.. Mied Review (p. ). ( ) Check: ( ) ( ). ( z) z z z z z Check: ( z) [ ()]. a a a a a Check: a a (). c c c c c c c Check: c c () (). a p% p b % p. p is % of. 9. a p% p b % p. p is % of.. a p% p b. a p% p b % p b p% p. p b. p% b % p% is % of. is % of.. m r ise difference of -coordinates. m r ise difference of -coordinates. m r ise difference of -coordinates Copright Holt McDougal Pre-Algebra 99 Chapter Solutions Ke

28 . m r ise difference of -coordinates () Mid-Chapter Quiz (p. ). (, ) (, ) (, ) (, ) Input utput. Standardized Test Practice (p. ). D. Let the number of weeks, and let the remaining calling time. Remaining Total Minutes used p Number calling time minutes per week of weeks The line has a slope of and a -intercept of. Minutes remaining Phone Card Weeks Focus on Graphing Practice (p. ). The graph on the left represents direct variation. The pressure from the water varies directl with the depth of the dive. The constant of variation k is.. It is the slope of the graph and represents the rate of change in the pressure of the water per meter of depth. The graph on the right does not represent direct variation because the line does not pass through the origin and the ratios for the labeled points on the graph are not equal.. a.. The relation is not a function because the input is paired with four outputs,,,, and. (, ) (, ) (, ) (, ) Input utput The relation is a function because ever input is paired with eactl one output.. 9 The equation is a function.. Cost (Dollars) The equation is not a function. Perimeter of Frame (Inches) The slope of the graph is., which represents the cost per inch of the frame. b. Answers ma var. A reasonable answer would be a picutre that measures inches b inches. Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

29 . The equation is a function.. 9 The equation is a function.. () () The -intercept is, and the -intercept is. (, ) (, ). () The -intercept is, and the -intercept is. (, ) (, ) 9. () The -intercept is, and the -intercept is. (, ) (, ). () () The -intercept is, and the -intercept is. (, ) (, ). m rise } difference of -coordinates Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

30 . m rise } difference of -coordinates. m rise } difference of -coordinates (). m } rise difference of -coordinates ( ) The slope is undefined.. Let the number of plas, and let the total cost. Total cost Cost per pla p Number Registration of plas fee The line has a slope of and a -intercept of. Total cost ($) Drama Festival 9 Number of Plas Brain Game (p. ) (, ) states had quarters issued each ear. Lesson.. Checkpoint (pp. 9 ). m b. m ( ) b (). A graph. Sample answer: A table shows discrete input and output values, while a graph can show those values and intermediate values. A graph also makes it easier to determine whether or not the points lie on a nonvertical line, whereas ou cannot tell immediatel if a function is linear when looking at a table of values.. Guided Practice (p. ). The line that lies as close as possible to the data points in a scatter plot is called the best-fitting line.. Sample answer: First, find the slope using the two points. 9 m () Find the -intercept. The line crosses the -ais at (, 9), so b 9. Write an equation of the form m b. 9. m 9 b m b. m () b m b Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

31 . m () b m b (). The slope of the given line is, so the slope of the perpendicular line is. The -intercept is. (). () Sample answer: Butter Clams Copright Holt McDougal Length (mm) 9 9 Width (mm) () Sample answer: Using (, ) and (, ): m. The line intersects the -ais at.... ()...(). 9 The length of the butter clam is about 9 millimeters.. Practice and Problem Solving (pp. ). m b 9. m b. m b. m b () (). m b m b. m () b m b (). m () b m b. m 9 b 9 m b 9. m ( ) b m b (). m ( ( ) ) b m b (). The slope of the given line is, so the slope of the parallel line is also. The -intercept is. 9. The slope of the given line is, so the slope of the parallel line is also. The -intercept is.. The slope of the given line is, so the slope of the parallel line is also. The -intercept is. (). The slope of the given line is, so the slope of the perpendicular line is. The -intercept is.. The slope of the given line is, so the slope of the perpendicular line is. The -intercept is. () Pre-Algebra Chapter Solutions Ke

32 . The slope of the given line is, so the slope of the perpendicular line is. The -intercept is... (, ) (, ) (, ) (, ) (, ) m The -intercept is. m b (, ) (, ) (, ) (, ) (, ) m The -intercept is. m b (). a. (,.), (,.), (,.), (,.), (,.) Area (km ) CNTINUED Kilimanjaro Glaciers 9 Years since 9. CNTINUED b. Sample answer: Using (, 9.) and (, ): 9. m.. The line intersects the -ais at.... c The glaciers will disappear in about.. k. k k k() k k 9. k. k k() k k() k. Lisa: no; John: es. Sample answer: Let the annual sales. Let the total earnings. Lisa: Total Percent earnings commission p Annual Salar sales., John: Total Percent earnings commission p Annual sales. For Lisa, annual sales and annual earnings do not show direct variation because of the constant term. For John, annual sales and annual earnings do show direct variation with k... a. Spring Stretching Length (mm) (, ) (, ) (, ) (, ) (, ) Mass (g) The points lie on a nonvertical line, so the table represents a linear function. CNTINUED Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

33 . CNTINUED b. m The -intercept is. m b. a. Boston Marathon Winning time (min) Years since 9 b. Sample answer: Using (, ) and (9, ): m 9 9 The line intersects the -ais at. c. () The men s winning time in will be about minutes. d. No. Sample answer: The equation predicts a winning time of minutes eventuall, which is impossible. I would epect the winning times eventuall to level off and decrease ver little, if an.. First, find the slope. m () Substitute m into the equation m b. b To find the -intercept, substitute (, ) into the equation and solve for b. () b b b So, the -intercept is. The equation is () or.. Mied Review (p. ). Check: () (). Check: () (). (m ) m m m m m m m m m m Check: (m ) m ( ) (). ( n) n n n No solution 9.. %...%.. %. 9. %. The line has a slope of and a -intercept of. (, ) (, ) Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

34 . The line has a slope of and a -intercept of. (, ) (, ). The line has a slope of and a -intercept of. (, ). (, ) The line has a slope of and a -intercept of. (, ) (, ). Standardized Test Practice (p. ). D; m b m b. F; The slope of the given line is, so the slope of the parallel line is also. The -intercept is. m b (). Technolog Activit (p. ) ().. In, there will be about, female phsicians in the United States.. The best-fitting line for the data is.9 9. Focus on Functions (p. ).... The function is discrete. The range is,,,. The function is continuous. The range is. The function is continuous. The range is The function is discrete. The range is,,,,. Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

35 . Let represent the number of dogs that ou wash. Let represent the profit in dollars. The cost of supplies is $, and each dog ou wash brings in $, so the equation for the profit is given b. You cannot wash part of a dog, so the domain consists of the whole numbers,,,,... So the function is discrete. 9 9 So ou need to wash dogs to have a profit of $9.. Let t represent the number of ears since the tree is measured to be feet tall. Let h represent the height of the tree in feet. The current height of the tree is feet tall, and each ear the tree grows at the rate of. foot per ear, so the equation for the height is given b h.t. Time is continuous, so the domain is the positive unit of time after the tree is measured. So the function is continuous. h.... So the tree will be feet tall in ears.. Let V represent the volume of water in quarts. Let W represent the total weight of the bucket with the water in pounds. The bucket weighs pound when it is empt, and quart of water weights about pounds, so the equation for the total weight is given b W V. You can have a fraction of a quart of water in the bucket. So the function is continuous. W V 9 V 9 V V V So the bucket with quarts of water weighs 9 pounds. Lesson.. Checkpoint (pp. 9). g() g() () When, g().. g() g() (). g() 9 When g() 9,.. f() The -intercept is. The slope is. (, ) (, ). g() The -intercept is. The slope is. (, ). h() (, ) The -intercept is. The slope is.. (, ), (, 9) (, ) m 9 b f() m b f() Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

36 . (, ), (, ) m ( ) b f() m b f() () f() 9. (, ), (, ) m () b g() m b g() () g(). (, ), (, ) m () b r() m b r() r(). Guided Practice (p. ). f(). Sample answer: The given values of f() mean that the graph of f passes through (, ) and (, ). Now use the definition of slope. difference of -coordinates m So, the slope of f is.. f() f() () When, f().. f() f() (). f() 9 When f(), 9. Pre-Algebra Chapter Solutions Ke. f() The -intercept is. The slope is. (, ) (, ). g() The -intercept is. The slope is. (, ) (, ). h() The -intercept is. The slope is. (, ) (, ) 9. (, ), (, ) m () b f() m b f() f(). Let t the number of ears since 9. Let f(t) the monthl cost of basic cable TV. Monthl cost Increase per ear p Number Cost in of ears 9 f(t).t 9.. Practice and Problem Solving (pp. ). f() f() () When, f().. g() g() () When, g(). Copright Holt McDougal

37 . f() When f(),.. g(). When g(),... f() f() (). f() f() () g() g() () f() g() (). C. A 9. B. f() The -intercept is. The slope is. (, ). g() (, ) The -intercept is. The slope is. (, ). h() (, ). CNTINUED (, ) (, ). The slope of the given line is, so the slope of the parallel line is also. The -intercept is. g() m b g() g(). (, ), (, ) m b f() m b f(). (, ), (, ) m () b g() m b g() g(). (, ), (, ) m b h() m b h(). (9, ), (, ) m () (9) 9 b r() m b r() () r() The -intercept is. The slope is. CNTINUED Copright Holt McDougal Pre-Algebra 9 Chapter Solutions Ke

38 . a. m(b) b m() () The mass of the squid is about grams. b. m(b) b b b. b The lower beak of the arrow squid is about. millimeters long. 9. a. Total Cost per Number of Fied p costs birdhouse birdhouses costs c() b. Price of Number of Income p birdhouse birdhouses i() c. p() i() c() ( ) d. p() p() () Your profit is $. e. p() You will break even when ou make and sell birdhouses.. a. s(d).d... Y=-.X+. X=9 Y=. b. The speed of the current decreases as ou go deeper below the river s surface. c. s(d).d. s(9).(9).. The speed of the current is. foot per second.. a. The dimensions of the nth rectangle are (n ) b n. b. A lw A(n) (n )n n n c. P l w P(n) (n ) n n n n CNTINUED. CNTINUED d. A(n) n n A() () P(n) n P() () The area is square units, and the perimeter is units.. Mied Review (p. ). p. n p n p p n p n p p n n. a a a a 9 9 c c. c c c. %. % % 9. %. The slope of the given line is, so the slope of the perpendicular line is. The -intercept is. m b (). The slope of the given line is, so the slope of the 9 perpendicular line is 9. The -intercept is. m b 9. Standardized Test Practice (p. ). D; f() f() (). F; (, ), (, ) m (). w(p).p Find w(p) when p,. w(,).(,),. About, tons of solid waste was disposed of in Marion Count during 99. Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

39 Lesson.. Concept Activit (p. ) Draw Conclusions. The ordered pair represented b the student with both hands raised satisfies both equations, so it is the solution to the linear sstem.. right hand raised: (, ), (, ), (, ) left hand raised: (, ), (, ), (, ), (, ), (, ) both hands raised: (, ). right hand raised: (, ), (, ), (, ) left hand raised: (, ), (, ), (, ), (, ) both hands raised: (, ). right hand raised: (, ), (, ), (, ), (, ) left hand raised: (, ), (, ), (, ), (, ), (, ) both hands raised: (, ). right hand raised: (, ), (, ), (, ), (, ) left hand raised: (, ), (, ), (, ), (, ), (, ) both hands raised: (, ). Let represent the amount of mone saved in dollars. Let represent time in weeks. Then the linear sstem is as follows: Ashln: Caleb: right hand raised: (, ), (, ), (, ), (, ), (, ) left hand raised: (, ), (, ), (, ), (, ), (, ) both hands raised: (, ) So in weeks the will have the same amount of mone saved.. Checkpoint (p. ). (, ). The sstem has no solution.. ne. Sample answer: If two lines in a plane are not parallel (and are not the same line), the must intersect in one point. Two lines in a plane with different slopes are not parallel, so the must intersect in one point. In the drawing, lines p and q are parallel and will never intersect. Line r has a different slope from either p or q, and will clearl intersect each in a single point. p q. Guided Practice (p. ) r. A solution of a sstem of linear equations in two variables is an ordered pair that is a solution of each equation in the sstem.. If the graphs of the two equations in a sstem are parallel lines, the linear sstem has no solution.. (, ) The solution is (, ).. Copright Holt McDougal The sstem has infinitel man solutions. The solution is (, ).. (, ) The solution is (, ). Pre-Algebra Chapter Solutions Ke

40 . The sstem has no solution.. Let the tpes of court shoes, and let the tpes of ning shoes. Tpes of Tpes of Total court shoes ning shoes tpes Tpes of ning shoes p Tpes of court shoes Intersection X= Y= The solution is (, ). So, the store manager should displa tpes of court shoes and tpes of ning shoes.. Practice and Problem Solving (pp. ). () () () () (, ) is not a solution.. () () (, ) is a solution. 9. () () () (, ) is a solution.. The solution is (, ).. The solution is (, ).. The solution is (, ).. (, ) The solution is (, ).. (, ) The solution is (, ).. The sstem has infinitel man solutions.. (, ) The solution is (, ). Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

41 . The sstem has no solution.. (, ) The solution is (, ). 9.. (, ) The solution is (, ).. Let the number of pairs of skates, and let the number of biccles. Pairs of skates Number of biccles Total rentals Rent per pair of skates p Pairs of skates Rent Number per p of Total income biccle biccles. (, ) Intersection X= Y= The solution is (, ).. The sstem has infinitel man solutions. The solution is (, ). The owner rented pairs of skates and biccles.. Let the number of newspaper ads, and let the number of radio ads. Newspaper ads Radio ads Total ads Cost of Number of p newspaper ad newspaper ads Cost of radio ad CNTINUED p Number of radio ads Total budget,, Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

42 . CNTINUED Intersection X= Y= The solution is (, ). You should newspaper ads and radio ads each month.. (, ) (, ) (, ) The triangle s vertices are (, ), (, ), and (, ).. a. Let the number of pages printed, and let the total cost. b. Inkjet: Total cost Laser: Total cost Cost per page. Cost per page. p Pages Cost of printed printer p Pages Cost of printed printer. CNTINUED c. Writing the equation in one variable based on the verbal model suggested gives the following:..... d. The method used in (c) gives a concise algebraic epression when the total cost of printing with both printers is equal as the verbal model suggests. The graphing method gives the same solution, but also allows a visual representation of costs at points when the are not equal to revenue. This is useful if ou want to decide which printer is more cost effective given the number of pages ou are epecting to print.. a. m b For there to be one solution, the lines should have different slopes. Sample answer: Let m and b. (, ) b. m b For there to be no solution, the lines should be parallel, which means that the must have the same slope but not be the same line. Sample answer: Let m and b. Intersection X= Y= The solution is (, ). After pages, the total cost of the printers are equal. CNTINUED CNTINUED Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

43 . CNTINUED c. m b For there to be infinitel man solutions, the lines must be the same. Sample answer:. a. Let l the length, and let w the width of the pool. A lw lw l w l w l w b. The ordered pair (, ) satisfies both equations. The length of the pool should be feet, and the width of the pool should be feet.. Mied Review (p. ). > 9 > 9 > 9.. t t t. n < p n < p n < , (, ), (, ) m b f() m b f(). (, ), (, ) m ( ( ) ) b m b h() () h(). Standardized Test Practice (p. ). C; () () (, ) is a solution. 9. F; 9 () () 9() 9 (, ) is not a solution.. Technolog Activit (p. 9). According to the table shown above, when, that is after months, the will each have songs.. (, ) Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

44 . (, ). (, ) Lesson.9.9 Checkpoint (pp. ). > Graph using a dashed line. Test (, ). > ()? > >/ Shade the half-plane that does not contain (, ). >. Graph using a solid line. Test (, ). Shade the half-plane that contains (, ).. < Graph using a dashed line. Test (, ). < < Shade the half-plane that contains (, ). <. Let the fluid ounces of orange juice, and let the fluid ounces of grapefruit juice. Vitamin C in orange juice p Fluid ounces of orange juice Vitamin C in p grapefruit juice Fluid ounces of grapefruit juice Graph using a solid line. Test (, ). () ()? / Shade the half-plane that does not contain (, ). Grapefruit juice (fl oz) Vitamin C Sources range juice (fl oz).9 Guided Practice (p. ) Total amount of vitamin C. The graph of a linear inequalit in two variables is called a half-plane.. Sample answer: When graphing a linear inequalit in two variables, test a point in one of the half-planes to determine whether it is a solution. If the test point is a solution, shade the half-plane that contains the point. If not, shade the other half-plane.. >. > ()? > ()? > >/ (, ) is not a solution. > (, ) is a solution. Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

45 . >. > () ()? > ()? > > >/ (, ) is a solution. (, ) is not a solution.. < Graph using a dashed line. Test (, ). <? < () < Shade the half-plane that contains (, ). <. Graph using a solid line. Test (, ). () ()? Shade the half-plane that contains (, ). 9. > Graph using a dashed line. Test (, ). > > Shade the half-plane that contains (, ). >. Graph using a solid line. Test (, ). / Shade the half-plane that does not contain (, ).. () Let the number of matinee tickets, and let the number of evening tickets. Number Number Cost of Amount Cost of matinee p of of evening p of gift matinee evening show certificate tickets tickets () Graph using a solid line. Test (, ). () ()? Shade the half-plane that contains (, ). Evening tickets Movie Tickets 9 Matinee tickets () Sample answer: matinees and evening shows, matinees and evening shows, matinees and evening show.9 Practice and Problem Solving (pp. ). Sample answer: Because the inequalit is >, the line should be dashed, not solid. Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

46 . Sample answer: The wrong half-plane is shaded. The half-plane to the right and below the boundar should be shaded.. No. Sample answer: The test point (, ) is on the line. Whether or not a point on the boundar line is a solution of an inequalit has no bearing on which halfplane is shaded.. Sample answer: The point (, ) is a solution of, but is not a solution of <. <?? < </. 9? () 9 (, ) is a solution.. < <? () </ (, ) is not a solution.. / (, 9) is not a solution. 9. () ()? (, ) is a solution.. < Graph using a dashed line. Test (, ). <? < < Shade the half-plane that contains (, ).. > Graph using a dashed line. Test (, ). >? > () > Shade the half-plane that contains (, ). >. Graph using a solid line. Test (, ).? () Shade the half-plane that contains (, ).. Graph using a solid line. Test (, ).? () / Shade the half-plane that does not contain (, ). < Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

47 . Graph using a solid line. Test (, ).? Shade the half-plane that contains (, ).. Graph using a solid line. Test (, ). ()? Shade the half-plane that contains (, ).. > Graph using a dashed line. Test (, ). > () ()? > >/ Shade the half-plane that does not contain (, ).. < Graph using a dashed line. Test (, ). < () ()? < </ Shade the half-plane that does not contain (, ). <. > Graph using a dashed line. Test (, ). > > Shade the half-plane that contains (, ). > 9. Graph using a solid line. Test (, ). / Shade the half-plane that does not contain (, ). > Copright Holt McDougal Pre-Algebra 9 Chapter Solutions Ke

48 . < Graph using a dashed line. Test (, ). < </ Shade the half-plane that does not contain (, ). < Pre-Algebra Chapter Solutions Ke. Graph using a solid line. Test (, ). / Shade the half-plane that does not contain (, ).. a. Let the number of -ticket rides, and let the number of -ticket rides. Number of tickets p -ticket rides Number of tickets p -ticket rides Total tickets b. Graph using a solid line. Test (, ). ()? Shade the half-plane that contains (, ). -ticket rides CNTINUED Carnival Rides -ticket rides. CNTINUED c. Sample answer: four -ticket and eight -ticket rides, ten -ticket and five -ticket rides, fourteen -ticket and three -ticket rides. a. > Graph using a dashed line. Test (9, ). > >? (9) >/ Shade the half-plane that does not contain (9, ). Width (in.) Widescreen Format b. Let. > > () Height (in.) > If the height of a widescreen image is inches, then the width is greater than inches.. a. Kite A: A p bh bh ( )9 p 9 square inches square hes inc p square feet Kite B: A p bh s bh s p square inches square hes inc p square feet CNTINUED square foot square hes inc square foot square hes inc Copright Holt McDougal

49 . CNTINUED b. Let the number of kite A, and let the number of kite B. Area of Number Area of Number kite A p of kite B p of Total area kite A kite B Graph using a solid line. Test (, ). () ()? Shade the half-plane that contains (, ). Number of kite B Making Kites Number of kite A c. Points that represent solutions where ou use up all our paper lie on the boundar line. Points that represent solutions where ou have paper left over lie inside the shaded region, but not on the boundar line.. a. < <?? () < (, ) is not a solution. / b. <? <? () < (, ) is a solution. c. <? <? () </ (, ) is not a solution.. < Graph using a dashed line. Graph using a solid line. Use the test points in Eercise. w. Sample answer: It is the intersection of two half-planes, and consists of all points that are below and to the right of the line and that are also on or above and to the right of the line..9 Mied Review (p. ). p p p p 9. (.)(.)(.) (.). p p p p p p.. a b b a. 9m n 9 m n. The solution is (, ). (, ). (, ) The solution is (, ).. (, ) The solution is (, )..9 Standardized Test Practice (p. ). D; 9? 9() / < Copright Holt McDougal Pre-Algebra Chapter Solutions Ke

50 . I;. (, ) (, ) (, ) Input utput Brain Game (p. ) (, ) is a solution of all of the inequalities. < > <? > () > < () <? 9 () ()? Chapter Review (pp. 9) <. Sample answer: The domain of a relation is the set of inputs, or -coordinates. The range of a relation is the set of outputs, or -coordinates.. Sample answer: m b } The slope is } and the -intercept is.. Sample answer: The line s slope is the ratio of the rise and between two points... f() (, ) (, ) (, ) (, ) Input utput (, ) (, ). () (, ) is a solution of.. () () (, ) is not a solution of. 9. () () The -intercept is, and the -intercept is.. () The -intercept is, and the -intercept is.. () () The -intercept is, and the -intercept is.. m r ise difference of -coordinates () Pre-Algebra Chapter Solutions Ke Copright Holt McDougal

51 . m r ise difference of -coordinates m r ise difference of -coordinates. The line has a slope of and a -intercept of.. () The line has a slope of and a -intercept of The line has a slope of and a -intercept of.. Because the slope of the given line is, the slope of the parallel line is also. The -intercept is. 9. Because the slope of the given line is, the slope of the parallel line is also. The -intercept is. (). Because the slope of the given line is 9, the slope of the parallel line is also 9. The -intercept is. 9. g() g() () When, g().. g() When g(),.. g() g() (). (, ) The solution is (, ).. (, ) The solution is (, ).. (, ) The solution is (, ).. Graph using a solid line. Test (, ). () Shade the half-plane that contains (, ). Copright Holt McDougal Pre-Algebra Chapter Solutions Ke