Selected Answers. numbers; a person's weight can be a decimal such as 83.5 pounds.

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1 Houghton Mifflin Harcourt Publishing ompan UNIT 1 MULE 1 LESSN _ _.. 1 _ 7. = ± 1. = ± 1 9. = 10. = _ _ _ _ _ ; 0. _ ; 9; ; _ _ ; 0. _ ; 99; ; _ ; 0. _ ; 999; ; 1. 17; ; ± ; _. 9. _. 1_ 101 mi cent 9. = ± _ 1 ±.7 1. = ± _ 1 = ±1. His estimate is low because 1 is ver close to 1, so _ 1 is ver close to _ 1, or. better estimate would be. or.9.. feet 7. = _ = _; 1 1 = _ 9 = 1 _; 1 9 = _ 7 = _; a = 9 _ a_ b ; _ b _ a _ b = _ a b LESSN rational, real. irrational, real. False. Ever integer is a rational number, but not ever rational number is an integer. Rational numbers such as _ and - _ are not integers.. False. Real numbers are either rational or irrational numbers. Integers are rational numbers, so no integers are irrational numbers.. Real numbers; the amount can be an number greater than 0.. Rational numbers; a person's weight can be a decimal such as. pounds. 1. rational, real. whole, integer, rational, real. irrational, real. rational, real. whole, integer, rational, real. integer, rational, real 7. rational, real. integer, rational, real 9. True. Whole numbers are a subset of the set of rational numbers and can be written as a ratio of the whole number to True. Whole numbers are rational numbers. 11. Integers; the change can be a whole dollar amount and can be positive, negative, or zero. 1. Rational numbers; the ruler is marked ever 1 th inch whole, integer, rational, real 17. rational, real 19. whole, integer, rational, real 1. Integers; the scores are counting numbers, their opposites, and zero.. Whole; the diameter is π π = 1 mile.. rational number 7. Sample answer: If the calculator shows a terminating decimal, the number is rational. therwise, ou cannot tell because ou see onl a few digits. LESSN 1.. >. <. _, _, _ 7, π, 10 7 π _ mi,. _ mi, 10 mi, _ 10 mi 1. <. >. <. <. >. < 7. >. > ; 1.; 1.7;.; 1.; _ ; π 10. ( 1 + π_ ) km,. km, 1 km, ( _ 17 -) km 1. π, _ 10, , 9_, _, 17a. _ 0 7.7, = 7., 7. _ 7., 7 _ = 7.0, so the average is 7. km. b. The are nearl identical. _ is approimatel Sample answer: _ 1 1a. between _ 7. and _. b. between _ 9 = and _ ; rational numbers can have the same location, and irrational numbers can have the same location, but the cannot share a location. MULE LESSN _ = = = , When multipling powers with the same base, ou add the eponents. When dividing powers with the same base, ou subtract the eponents. When raising a product to a power, ou raise each factor to that power. When raising a power to a power, ou multipl the eponents The eponents cannot be S1

2 UNIT 1 (cont d) added because the bases are not the same. 9. Earth to Neptune;, or 10,, times greater kg, or 1000 kg 7. oth epressions equal, so 7 - = 7. When multipling powers with the same base, ou add eponents; 7 + (-) =. When dividing powers with the same base, ou subtract eponents; 7 - =. In cases like this, n -m = n. m 9. ; LESSN km. 7,0,000,000 9., ,000,000 g ,000. 1,9,900, ,0, , ,000,000,000 1.,000 s 1. 7,00,000 cans lb lb lb. 10 1_ hours or 10 hours and 0 minutes.. 10 lb 7a. None of the girls has the correct answer. b. Poll and Samantha have the decimal in the wrong place; Esther miscounted the number of places the decimal moved. 9. The speed of a car because it is likel to be less than Is the first factor greater than 1 and less than 10? Is the second factor a power of 10? LESSN m m cm cm cm. 7 cm = 0.07 m, 7 cm = cm; 0.07 m = m The first factors are the same; the eponents differ b.. If the eponent on 10 is nonnegative, the number is greater than or equal to Negative, because a ladbug would weigh less than 1 ounce ,90,000.,97, m, m, m, m, m 7. The result will be greater than the number with the positive eponent because the divisor is less than 1. LESSN more people miles minutes. 7.E. E 7..7E ; 10 ; 0.;.; ; 10 ;.;.; 0.10; E E 11. E about 000 as man tons 1. Plastics. about 7 people per square mile. 1 ears, months,. das 7. about $ 10, or $0,000 per person 9. The student is off b a power of 10. The correct product is , or Houghton Mifflin Harcourt Publishing ompan S

3 Houghton Mifflin Harcourt Publishing ompan UNIT MULE 1 MULE LESSN.1. = 1. miles hiked in hours. = _ 1. is. constant of proportionalit a. The pairs (weeks, das) are (, 1), (, ), (, ), (10, 70). b. the time in weeks; the time in das; = 7. The pairs (ogen atoms, hdrogen atoms) are (, 10), (17, ), (10, 0); =. = 0 7. No; the ratios of the numbers in each column are not equal. 9a. Sample answer: The account had a balance of $100 to begin with. b. Sample answer: Have Ralph open the account with no mone to begin with and then put $0 in ever month. 11. = 10 1a. The pairs (time, distance) are (1, 10), (, 0), (, 0), (, 0), (, 0). b. = 10, where is the distance in inches and is the time in minutes. c.. minutes 1. For S = 1, P = and = 1; For S =, P = and = ; For S =, P = 1 and = 9; For S =, P = 1 and = 1; For S =, P = 0 and =. a. Yes. The ratio of the perimeter of a square to its side length is alwas. b. No. The ratio of the area of a square to its side length is not constant. LESSN. 1., 1, -10; variable. +; +; _ 1. constant. variable. variable. constant. 00; 1; 00; 1; ft per min _ miles per hour 1a. 1 gallon ever minutes, or 0. gal/min b. minutes a. slope _ = -1; slope _ = 1_ ; slope _ = -1; slope _ = 1_ b. The slopes of the opposite sides are the same. c. Yes; opposite sides still have the same slope. 17. Sample answer: ne line has a positive slope and one has a negative slope. The lines are equall steep, but one slants upward left to right and the other slants downward left to right. The lines cross at the origin. LESSN.. His unit rate and the slope of a graph of the ride both equal _ mi/min. Tomas s Ride 10 istance (mi) 10 Time (min). : 7, 7 mi/h; :, mi/h; is fling faster. 1. slope = unit rate = _ mi/h. slope = unit rate = _ mi/h. lark is faster. From the equation, Henr s rate is equal to 0., or 1_ mile per hour. lark s rate is the slope of the line, which is _, or 1. miles per hour.. = 1. = _ 7a. The pairs (time, distance) are (, ), (, ), (1, 9), (1, 1), (0, 1). b. Migration Flight istance (mi) Time (min) c. _ ; The unit rate of migration of the goose and the slope of the graph both equal _ mi/min. 9a. Machine 1: slope = unit rate = 0. 1 = 0. gal/s; Machine : slope = unit rate = _ = 0.7 gal/s b. Machine is working at a faster rate since 0.7 > slope = unit rate =.7. If the graph of a proportional relationship passes through the point (1, r), then r equals the slope and the unit rate, which is $.7/min. 1. gallons; Sample answer: The unit rate is = 1 gal/min. So, 1 1_ min after 1 min, an additional 1 1 1_ = 7 gal will be pumped in. The total is = gal. S

4 UNIT (cont d) MULE LESSN.1 1. Sample answer: (, 0), (, ), (, ), (, ). (-1, ), (0, 1), (1, -1), (, -) b. Total cost ($) 0 1 Magazine Subscription osts 1. fter parking 1 cars; John earns a fied weekl salar of $00 plus $ for each car he parks. He earns the same in fees as his fied salar for parking 00 = 0 cars. LESSN (-,1), (-1, ), (0, ), (1, 7), (, 9). (-, -), (0, -), (, -), (1, 1), (, ). Undefined,.,.7,.,.7; The ratio _ is not constant.. The graph is a line, but it does not pass through the origin.. (-, -), (-1, -), (0, -1), (1, 0), (, 1) Set of unconnected points; ou cannot bu a fractional part of a lunch. 9a. Sample answer: For (, ) where is number of ears renewed and is total cost in dollars: (0, 1), (1, 0), (, ), (, ), (, ) 10 Number of ears renewed c. The graph does not include the origin. lso, the ratio of the total cost and number of ears is not constant. d. No; the number of ears must be a whole number, so total cost goes up in $ increments. 11. Sample answer: In a table, the ratios _ will not be equal; a graph will not pass through the origin; an equation will be in the form = m + b, where b t most one. line representing a proportional relationship must pass through the origin. line parallel to it cannot also pass through the origin. LESSN. 1. m = ; b = 1. m = 7; b = ; 1. ; -1. _ ; -. -; 9. ; 1. -; 10 9a. $ to park; $1 per hour b. $.0; (. hours $1 per hour + $) = $ Rate of change is constant from 1 to to, but not from to. 1. Epress the slope m between a random point (, ) on the line and the point (0, b) where the line crosses the -ais. Then solve the equation for... alories remaining Time (h). The new graph has the same -intercept but a slope of -00 instead of The calories left to burn will decrease more slowl with each hour of eercise, so it will take longer for Ken to meet his goal. 7. The -intercept would not change, but the slope would become -00, which is much steeper. The line would intersect the -ais when = hours. Houghton Mifflin Harcourt Publishing ompan S

5 Houghton Mifflin Harcourt Publishing ompan 1. 1_ ; ; a. Slope = ; -intercept = ; ou start with cards and add cards each week. aseball cards Weeks b. The points with coordinates that are not whole numbers; ou will not bu part of a baseball card and ou are buing onl once a week. a. Spring length (in.) 1 1 Weight (lb) b. The slope, 0.7, means that the spring stretches b 0.7 inch with each additional pound of weight. The -intercept, 0., is the unstretched length of the spring in inches. c. 1.7 inches; no; the length with a -pound weight is. in., not. in. 7. (0, ), (1, 7), (, ), (, ) 9. (0, -), (1, -1.), (, 0), (, 1.) 11. (0, -), (, -), (, -1), (9, 1) 1a. Yes; since the horizontal and vertical gridlines each represent units, moving up gridlines and right 1 gridline represents a slope of 7, or. b. m = so $ is the charge per visit; b = 0 so the membership fee is $0. ost ($) Pool visits c. 0 visits 1. Yes; plot the point and use the slope to find a second point. Then draw a line through the two points. LESSN. 1. nonproportional. proportional. proportional. nonproportional 7. nonproportional. nonproportional 9. nonproportional 10. proportional 11. Test-Prep enter s charges are proportional, but s are not. enter offers a coupon for an initial credit, but its hourl rate, $, is higher than enter s hourl rate of $0. So, enter will cost more in the long run. 1. Proportional; the line includes the origin.. Nonproportional; the line does not include the origin.. Nonproportional; when the equation is written in the form = m + b, the value of b is not 0.. Proportional; when the equation is written in the form = m + b, the value of b is 0.. Proportional; the quotient of and is constant,, for ever number pair.. No; the quotient of and is not constant for ever number pair. 7. Sample answer: The rating is proportional to the number of households watching: the quotient of the rating and the number of households is alwas a. Nonproportional; the graph does not pass through the origin, so b 0. b. m = 0., b = 10; each cup of sports drink weighs a half pound. The empt cooler weighs 10 pounds. 11. Proportional; this equation has the form = m + b, where b = 0. 1a. No; from Equation, the -intercept is 7.1, not 0, so the graph does not include the origin. From Table, the quotient of K and is not constant. b. No; Equation is in the form = m + b, with F instead of and instead of. The value of b is, not 0, so the relationship is not proportional. S

6 UNIT (cont d) MULE LESSN.1. = = a. the length of the necklace in inches b. the total number of beads in the necklace c. = = -00 = -0; 00; = temperature; chirps per minute; - 9 = = ; 100 = ; -10; = = 0 7. m = 0.1; the diver ascends at a rate of 0.1 m/s 9. = = m = 00; b = The amount of mone in the savings account increases b $00 each month. 17. The rate of change would not be constant. Using different pairs of points in the slope formula would give different results. LESSN. 1. m = 1,000; b = 0; = 1,000 Volume (m ) 00,000 00, ,000 Water Released from Hoover am Time (s). p = 7n + 0. c = 0.0d m = -1.; b = 0; = mount left on pass ($) us Pass alance Number of rides 1-9. m = = = b = 9. = = -0.00(000) + 9 = 9 F 7. m = ; b = ; = t + 9a. = b. The number of dollars left decreases as the number of car washes increases. c. 0; after 0 washes there is no mone left on the card. 11. = - + 1a. No, the change between weeks is constant, but the change in the amount of rain is not constant. b. No; there is no apparent pattern in the table. 1. 0; Jaíme s graph contained (0, 0). Since Jala s data were the same, but with and switched, her graph also contained (0, 0). LESSN. 1. = + 0. = 0. $0 7. $.7. $00 1. = 0. =. +. = 0 + 0; $10. Yes, because the graph has a constant rate of change.. No, because the graph does not have a constant rate of change. 7. Yes, because the rate of change is constant. 9. Linear; the rate of change is the cost of a V, which is constant. 11. Not linear; the rate of change in the area of a square increases as the side length increases. 1. The relationship is linear; the equation of the linear relationship is = 0.1, so the Mars Rover would travel 7. feet in 0 seconds. 1. Sample answer: ecause = lies halfwa between = and =, the -value should lie halfwa between the corresponding -values. 17. Find the equation of the linear relationship using the slope and given point, and then insert an -value to find a -value on the graph of the line. MULE LESSN.1. Function; each input value is paired with onl one output value.. Not a function; the input value is paired with more than one output value. 7. Function; each input value is paired with onl one output value.. Not a function; the input value is paired with more than one output value. 10. Not a function; input values are paired with more than one output value; (70, 1) and (70, 17) 1. 0; 00. _ ; 1..; Function; each input value is paired with onl one output value. Not a function; the input value is paired with more than one output value.. Yes; each input value is paired with onl one output value. 9. Not a function; the input value is paired with more than one output value. 11a. There is onl one number of bacteria for each number of hours, so each input is paired with onl one output. Houghton Mifflin Harcourt Publishing ompan S

7 Houghton Mifflin Harcourt Publishing ompan b. Yes. Each input value would still be paired with onl one output value. 1. Yes. Each input value (the weight) is paired with onl one output value (the price). 1. It does not represent a function. For the input values to be paired with all four output values, at least one of the input values would be paired with more than one output value. LESSN.. proportional (, ) = (0, 0), (, ), (, ), (9, ); linear; proportional Making Soda mount (gal) Time (min) 1. (-1, 7), (1, ), (, -1), (, -); linear (-, -), (-1, 1), (0, ), (1, 1), (, -); nonlinear No; the equation cannot be written in the form = m + b, and the graph of the solutions is not a line.. Yes; the equation can be written in the form = m + b, and the graph of the solutions is a line. 7. No. The relationship is not linear because is squared, so it will not be proportional. 9a. Yes. The solutions lie in a line. Total cost ($) rill Team Uniforms Number of uniforms b. $ isagree; the equation can be written in the form = m + b where m is 0, and the graph of the solutions is a horizontal line. 1. The relationship is linear if the points all lie on the same line and proportional if it is linear and a line through the points passes through the origin. 1. ppling the istributive Propert gives + = +, or =. This is in the form = m + b with b = 0, so it is linear and proportional. LESSN. 1. uing at the bookstore is more epensive. 1. The second method (19 bpm vs. 10 bpm) gives the greater heart rate.. Heart rate and age are nonproportional for each method.. Students pa a $0 fee and $ per hour.. Tutoring Fees ost ($) Time (h). With both plans, it costs $0 for hours of tutoring.. Plan ($90 vs. $10) is cheaper for 10 hours of tutoring. 7. ost and time are proportional for Plan 1 and nonproportional for Plan. 9. Scooter (1 gallons vs. 1 gallons) uses fewer gallons of gas. 11. the first plan 1. The camera at the second store; the cost at the first store is $90 and the cost at the second store is $0. 1. Since the rate per visit is the same, the monthl cost of Gm is alwas more than that of Gm. 17. = - + is changing more quickl because even though - is less than -1, the absolute value of - is greater than the absolute value of -1. S7

8 UNIT (cont d) LESSN. 1. The graph is increasing quickl. This shows a period of rapid growth.. The number of bacteria is decreasing.. Graph. Graph. 9. Graph Regina left the rental shop and rode for an hour. She took a half-hour rest and then started back. She changed her mind and continued for another half hour. She took a half-hour break and then returned to the rental shop Population Fo Population t Time istance bove or elow Water 0 istance from Edge of Pool. increasing where surfacing; decreasing where diving; linear where walking and swimming; nonlinear where diving Speed (mi/h) :0 :1: 1. : to : Time : :: Houghton Mifflin Harcourt Publishing ompan S

9 Houghton Mifflin Harcourt Publishing ompan UNIT MULE 7 LESSN 7.1. weeks 1. = -. =. b = 9. h = -. = -. a = 7. n =. p = 9. personal training sessions hours 11. Sample answer: Xavier has $100 in his lunch account. He spends $ for lunch each da. Zack has $10 in his lunch account. He spends $10 each da. fter how man das will the bos have the same amount in their accounts? 1a. 1 + = 1 + ; = ; hours b. arlene s og Sitting; the cost would be $, as opposed to $7 at errick s og Sitting = + 10; = = + 1; = = ; = ; 7 chairs 1. + = + ; = ; laps LESSN 7.. k = -. = = ;. Ib 1a = 7.9 b. = ; months. n =. b = 0. m =. t = -0.. w = 1 7. p = tiles 1a. 100 mi b. $0 17. = 1. + ; -0 F = -0 LESSN = -1. =. b = -. t = 7. $, ; ; ; ; ; ; ; ; ; ; ; ; = 1. ; ; ; -1; 1; ; -0; +; 1; -1; -7; -1; -7; -1; -1; =. =. = 7. = -1. = 7. = 9. = - 9. = = ( +,000) =,00; $, a. + 1 b. Joe s age in ears: + ; Martina s age in ears: + 19 c. ( + ) = + 19 d. Joe: ears old; Martina: 1 ears old 1. It is not necessar. In this case, distributing the fractions directl results in whole number coefficients and constants. 17. Table first row: 0., 0.; table second row: 100 -, 0.1, 0.1(100 - ); table third row: 0.19, 19 a. The milliliters of acid in the % solution plus the milliliters of acid in the 1% solution equals the milliliters of acid in the miture. b (100 - ) = 19 c. The chemist used 0 ml of the % solution and 0 ml of the 1% solution. 19. Use the istributive Propert to distribute both and inside the square parentheses on the left side. ombine like terms inside the square parentheses. Then use the istributive Propert again to distribute. ombine like terms on the left side and use inverse operations to solve the equation. = 1 LESSN 7.. = ; one solution. 7 = 7; infinitel man solutions. -9 = ; no solution. You started with a false statement and performed balanced operations on both sides of the equation. This does not change the true or false nature of the original statement.. Sample answer: = ; true. - = 1; false. none. n value of will result in a true statement; infinitel man solutions. ne solution. Infinitel man solutions 7. true; same variable; same constant; like; 10; 10 + ; ; 1 + = = 0; infinitel man solutions 1. = ; no solution a. Yes; because the perimeters are equal, ou get the equation ( - ) + ( + 1) + + ( + 1) = ( 9) + ( + 1) + ( + ) +, or =. Since = is a true statement, there are an infinite number of values for. b. The condition was that the two perimeters are to be equal. However, a specific number was not given, so there are an infinite number of possible perimeters. c. 1; Sample answer: I used the trapezoid and wrote the equation ( - ) + ( + 1) + + ( + 1) = 0. Solving this gives = No; setting the epressions equal to each other and solving gives = 0 +, or 100 = 0, which is false. 1. Matt is incorrect. He applied the istributive Propert to the right side incorrectl. orrectl simplified, the equation is 0 = -7, which is false, meaning no solution. S9

10 UNIT (cont d) MULE 1. (, ) LESSN.1. (-1, ) -. (1, ) a. + = and + = 0; = - + and = b. Games of laser tag Games of bowling c. Marquis will bowl games and pla games of laser tag. -. (, 0) a. = b. = c. Vocabular questions Spelling questions d. 10 spelling questions and vocabular questions. sstem of equations 7a. =.0 + ; = + b. The solution is (, 1). The cost at both alles will be the same for games bowled, $1. ost ($) 1 1 ost of owling (, 1) Games 11. Infinitel man; rearranging the left side of the nd equation and subtracting a from both sides gives -a + a = -a. ividing both sides b -a gives - =. The equations describe the same line. LESSN.. (, ). (-, ). (-9, -7) Estimate: (, 1) Solution: ( 10, _ ) The solution is reasonable because 10 is close to the estimate of and _ is close to the estimate of 1.. arlos: + 10 = 10 Vanessa: + 0 = 0 (0, 0.); 0 represents the cost per da: $0; 0. represents the cost per mile: $0. Houghton Mifflin Harcourt Publishing ompan 1. (, ). (, -1). (, 1). (, 1). Estimate: (1, -); Solution: ( 7_, - ) S10

11 . Estimate: (-1, ); Solution: ( -1, 9_ ) 7. Estimate: (, -); Solution: ( 1,- ). Estimate: (-, 1); Solution: ( - 9_, _ ) 9. a. Hensons cost: + = 1; Garcias cost: + = 17 b. adult ticket price: $; child ticket price: $ Gupp: inches; plat: inches 1. Labor fee: $1.9; quart of oil: $ adult tickets; 9 student tickets 17. a. Jenn substituted her epression for into the same equation she used to find. She should substitute her epression into the other equation. b. Yes; adding the equations would have resulted in = 9, easil giving = after dividing each side b. Substitution requires man more steps. second equation b. oth -term coefficients would be. Solve b eliminating the -terms using subtraction. c. (9, -) LESSN.. no solution 7. (10, -); one solution. infinitel man solutions 1. Step 1: are parallel; intersect; are the same line Step : no; 1; infinitel man. infinitel man solutions. no solution. (-, -); one solution Houghton Mifflin Harcourt Publishing ompan The graph shows that the -coordinate of the solution is negative, so Zach s solution is not reasonable nickels and 0 dimes 1. ( _, - 10) 17. The substitution method has the advantage of alwas giving an eact answer. Graphing produces an eact answer onl if the solution is an ordered pair whose coordinates are integers. LESSN.. (, -). (, -). (-1, ). (0, -) 9. (7, -) 10. ( 7, 1_ ) 11. bag of roasted almonds: $1.9; juice drink: $1. 1. Step 1: 0; -10; ; -10; -;. Step : ; (-, ). (, -). (, ). (7, -7). (-, ). (, ) 7. (-, -). a. Ton: +. = ; Rae: + = 0 b. Minimum speed limit: mi/h; maimum speed limit: 70 mi/h LESSN.. (-, 1). (-1, ). ( 1_, -1 ) 7. (, 1). (-, -1) 9. ( 1_, ) 10. ontestants run 0.7 hour and bike 0. hour. 1. Step 1: 1; ; ; 0; ; ; 10. Step : -; (, -). (, -1). (-, ). ( 7_, 7_ ). (, -). (, -1) 7. (-, ). a. First store: =.; second store: =. b. Number of apples: ; number of pears: = a. { + = 1 b. Multipl the second equation b 79. Subtract the new equation from the first one and solve the resulting equation for. c. Solve the second equation for. Substitute the epression for in the first equation and solve the resulting equation for. d. 9 polester-fill, down-fill 1. 1 pies, 1 jars of applesauce 1. a. Multipl the first equation b 1. and subtract. This would be less than ideal because ou would introduce decimals into the solution process. b. Yes; multipl the first equation b and the infinitel man solutions 11. one solution 1. one solution 1. one solution 17. No; although the lines do not intersect on the graph, the intersect at a point that is not on the graph. To prove that a sstem has no solution, ou must do so algebraicall. 19. No; both Juan and Tor run at the same rate, so the lines representing the distances each has run are parallel. There is no solution to the sstem. 1.,, and must all be the same multiple of,, and, respectivel. The two equations represent a single line, so the coefficients and constants of one equation must be a multiple of the other. S11

12 UNIT MULE 9 LESSN transformation. preimage; image. The orientation will be the same.. The are congruent.. W X b. The translation moved the triangle units to the left and units down. c. The are congruent P S Q - P R S R 11. The hot air balloon was translated units to the right and units up. 1a. c. Y Q LESSN 9.. E line of reflection a. E - Z W Y X - X X Y Z Z Y - Z - 7a. - E - E Y F F X - d. The original triangle was translated units up and units to the left. Z - b. The are congruent. c. The orientation would be reversed horizontall: the figure from left to right in the preimage would match the figure from right to left in the image.. and 7. Sample answer: Since each triangle is either a reflection or translation of triangle, the are all congruent. 9. Yes; if the point lies on the line of reflection, then the image and the preimage will be the same point. Houghton Mifflin Harcourt Publishing ompan S1

13 11a. c. E F - - E" - - " E F X'(, -), Y'(, 0), and Z'(7, -) - Y Y X X 7 Houghton Mifflin Harcourt Publishing ompan F" d. Sample answer: Translate triangle EF 7 units down and units to the left. Then reflect the image across the -ais. LESSN (, -) - 1. point. Each leg in the preimage is perpendicular to its corresponding leg in the image.. Yes, the figures are congruent.. - E F E G F 7a. was rotated 90 counterclockwise about the origin. b. ' (, 1); ' (, ); ' (-1, ) rotation about the origin clockwise clockwise times; 1 time; times 19. Sample answer: If is at the origin, then so is ' for an rotation about the origin. therwise, ' is on the -ais for 90 and 70 rotations and on the -ais for a 10 rotation. LESSN (-, -), (-, 0), (-, -), and (-, 0); the rectangle is translated units to the left and units down.. '(-, -), '(0, -), and '(, 1). J'(, -), K'(-, 1), and L'(-, ) -7 Z Z. The -coordinate remains the same, while the -coordinate changes sign.. The triangle is rotated 90 clockwise about the origin (, ) ( -, - ); translation of units to the left and units down 7. (, ) ( -., + 1); Y'(., ), Z (., ) 9. The rectangle is translated units to the left and units down. - - G 11. (, ) ( + 0., - 0.) 1a. (-, -); and are equal, so switching and has no effect on the coordinates. b. = c. The triangle is reflected across the line =. S1

14 UNIT (cont d) - - 1a. "(1, 0), "(0, ), and "(, ) b. (, ) ( +, + ) LESSN 9.. Rotation 90 clockwise about the origin, translation units down; (, ) (, -), (, ) (, ) ifferent orientation No; the ratios of the lengths of the corresponding sides are not equal. 9. Yes; a dilation produces an image similar to the original figure. 11. Yes; each coordinate of triangle U'V'W' is _ times the corresponding coordinate of triangle UVW. 1. changed; same; same 1. same; changed; same Locate the corresponding vertices of the triangles and draw lines connecting each pair. The lines will intersect at the center of dilation. LESSN 10.. (, ) ( 1_, 1_ ) Z Y E - -. reflection across the -ais. translation units right and units down. (, ) (-, ), (, ) ( +, - ). The figures have the same size and the same shape. ifferent orientation 11. Sample answer: translation units right and units down, reflection across -ais; size: no; orientation: es 1. No; the point (1, ) translated units to the right becomes (, ), rotated 90 clockwise about the origin, it becomes (, -). The point (1, ) rotated 90 clockwise around the origin becomes (, -1), translated units to the right, it becomes (, -1), which is not the same. MULE 10 LESSN The scale factor is 0.. Z' X Y' X' 1. - PreImage Image (, 0) (, 0) (0, ) (0, ) (-, 0) (-, 0) (0, -) (0, -) Houghton Mifflin Harcourt Publishing ompan 1. ;. equal; equal.. congruent. - S1

15 . I F I' F' H G H' G' (, ) (1., 1.). (, ) ( 1_, 1_ ). Green square: (, ) (, ); Purple square (, ) ( 1_, 1_ ) 7. (, ) ( _, _ ) 9a. The scale factor is. b. inches or feet c. (, ) (, ) d. Q (.,.), R (.7,.), S (.7,.), and T (.,.) e. imensions on blueprint:. in. b.7 in. imensions in house: ft b 1 ft 11. The crewmember s calculation is incorrect. The scale factor is 1 0, not The figure is dilated b 1 a factor of, but the orientation of the figure is rotated 10. LESSN 10.. Sample answer: (, ) ( + 7, - 1); rotation 90 clockwise about the origin; (, ) ( +, + ); (, ) (, ) (, ) (, -); (, ) ( +, - ). (, ) (, + ); rotate 90 counterclockwise. (, ) (1., 1.); (, ) ( +, + ) 7. ilate the image b a scale factor of 1_ and reflect it back across the -ais; (, ) ( 1_, 1_ ), (, ) (, -). 9. Rotate the image 90 counterclockwise and dilate it b a factor of 1_ ; (, ) (-, ), (, ) ( 1_, 1_ ). 11. There must be an even number of dilations and for each dilation applied to the figure, a dilation that has the opposite effect must be applied as well. Houghton Mifflin Harcourt Publishing ompan S1

16 UNIT 11 MULE LESSN VWZ. alternate interior same-side interior 7. 1 and, and, and 7, and 9. alternate interior angles ; the angle is supplementar to the larger angle because the two angles are same-side interior angles. 19. and are corr., so m = 1. and are alt. int., so m = 1. and 7 are corr., so m 7 = 1. and are same-side int., so m = 10-1, or. and are corr., so m =. and are alt. int., so m =. 1 and are corr., so m 1 =. 1. angles; angles; no LESSN ; ; 9 ;. 90 ; ;. 0 ; 7 ;. 19 ; ; ; ; ; ; 90 ; 0 ; No; the measure of an obtuse angle is greater than 90. If a triangle had two obtuse angles, the sum of their measures would be greater than 10, the sum of the angle measures of a triangle. 17a. 0 b. The sum of the angle measures of a quadrilateral is 0. Sample answer: n quadrilateral can be divided into two triangles, so the sum of its angle measures is 10 = 0. LESSN 11.. The triangles are not similar, because onl one angle is congruent. The angle measures of the triangles are 70,, and and 70, 1, and 9.. inches. 1 ft 1. 1, 109, and 0 ; 1, 109, and 0 ; two angles; two angles; similar. 7.;.; 17.. congruent; alternate interior angles; congruent; alternate interior angles; Similarit; similar. m =, m F = 9, m H =, m K = 7. J, L, and K 9. feet 11. In the first line, Ran should have added 19. and. to get a denominator of for the epression on the right side to get the correct value of 1. cm for h. MULE 1 LESSN ft. 9 in.. r = _, so the greatest length is 1 in , 7, a b.. in.; es. 11. in in feet 11.. ft; = c, so = c, 1 = c, and 0. c. dding this to the height of the bottom of the tree: =. ft. 1. _ + (or _ or _ ); if a = and b =, then + = c. Thus, c = _ +. LESSN 1.. not a right triangle. right triangle. right triangle. not a right triangle. Yes; = 0,000; 0 0 = 0,000; 0,000 = 0, No; =, =,. No; there are no pairs of whole numbers whose squares add to 1 = 1. 1a. ;, 10 b.,, 10;,, 100; 100, 100; is. 9, 1, 1; 9, 1, 1; 1, 1, ;, ; is not. Yes;. + =.,. =.,. =.. right triangle 7. not a right triangle 9. not a right triangle 11. right triangle 1. not a right triangle 1. No; =, 1 =, and. 17. No; = 1, 1 = 1, and Yes; since = 1., the triangles are right triangles. djoining them at their hpotenuses will form a rectangle with sides 1 m and 0.7 m. 1. Yes LESSN units. approimatel 1.7 meters 1.. units. 1 units. 10. miles Houghton Mifflin Harcourt Publishing ompan S1

17 Houghton Mifflin Harcourt Publishing ompan 7a. ET = _ 11 units b. Let ( 1, 1 ) = (-, ) and (, ) = (, -). Substitute the coordinates into the istance Formula and then simplif. 9. (, 0), (, ), (, ), (0, ), (-, ), (-, ), (-, 0), (-, -), (-, -), (0, -), (, -), (, -); The points would form a circle. 11. Let ( 1, 1 ) = (, ), and (, ) = (1, 1). Use the istance Formula to show that hpotenuse = _ MULE 1 LESSN in. 0.9 ft.. in 1. two congruent circles that lie in parallel planes. Sample answer: 7 in ; there are 1 cubes on the bottom of the clinder. The height is 7 cubes. V = 1 7 = 7 in. ; 1; ; 1; 19.; ; in 9. 9 in m 1..9 in 1. 9,10 m in 19. ivide the diameter b to find the radius. Substitute the volume and radius in V = π r h and solve for h. LESSN cm. 1. ft. 19,,9. m 1. ; 10; 0; 0; 10; 10. m ; the volume of a clinder is times the volume of a cone with a congruent base and height...9 ft. 11,9 in. 11. in. 1,0. m 9..1 in m in 1. in 17. cm 19a. either the diameter or the radius of the base b. No; the cone is tapered from top to bottom. n equal volume of sand has a smaller radius and a greater height as the sand rises. 1. Since the radius and height of the cones and clinder are the same, it will take cones to equal the volume of the clinder. LESSN c m. 0. m. 90. in 1. the same distance. radius.. in.,1.7 c m. 1.1 f t.. d in. i n 9a. 1_ ; the ball takes up _ of the space, so 1_ is empt. b. (r) = r c. lmost 1_ ; the empt space is r - _ πr, or about.1 r, and m i n cm cm cm 1. ivide V = _ πr b to find the volume of the hemisphere: V = _ πr. dd the volume of the clinder, V = πr h = πr : V = _ πr + πr = _ πr.. 1. i n. The clindrical glass; the clinder has a volume of πr, the hemisphere s volume is _ πr, and the cone s volume is 1_ πr. 7. bout 1 feet; 1 is times 17, so the volume must be times as big. ecause =, this means the radius, and thus the diameter, must be twice as big. S17

18 UNIT LESSN 1.1. Positive and basicall linear: older students would be taller and read at a higher level Height (in.) MULE MULE ge (r). Positive and basicall linear; the plot shows ob s height increasing as he gets older.. There is a cluster for 0- shots attempted and a lesser one for 7-1 shots attempted; (, 1) is an outlier.. generall positive linear association: as the ear increases, so does the winning distance. 7. Nonlinear; the points generall rise up to 19 and then fall from 19 to 01, so there is no overall linear pattern. 1. Yes; for eample, the points ma appear to lie along a rising or falling curve, or ma generall rise or fall, but not in a wa that suggests a linear association. LESSN 1.. Sample answer: = 9 10 nswers for 1 ma var slightl. 1. Price ($) Weight (ounces). Most data points are close to the trend line, with about the same number of points above and below the line.. = $0.; $.0 nswers for 1 ma var slightl. 7. negative; basicall linear 9a. about - F b. about - F 11. pparent Temperature at a Room Temperature of 7 F pparent temperature ( F) Humidit (%) 1. about 7 F 17a. No; two data points are not enough to create a scatter plot or trend line. random sample of man counties should be used. b. Sample answer: Marlene s conjecture is incorrect. Harris and allas counties are countereamples to Marlene s original conclusion. 1 LESSN 1.1. Yes; the relative frequenc of visiting a park = = 0. =.%; relative frequenc of a high school student visiting a park = =.7%; 10.7% >.%, so being in high school improves the likelihood that a student has visited a national park. 1. og No og TTL at No at 1 0 TTL 1 0. No; the relative frequenc of being left-handed (10%) is the same as the relative frequenc of being a left-handed bo (10%)..a. Prefer Science Seventh Grade Eighth Grade Prefer Math TTL TTL b. No; the relative frequenc of being an eighth-grader who prefers math ( = 0% 0 ) is less than the relative frequenc of preferring math ( % ). Houghton Mifflin Harcourt Publishing ompan S1

19 7.a. ges 1 1 ges 1 1 Prefer Surfing Prefer Snorkeling TTL 0%; 0% 7 0%; 7% % %; 0% %; % 0 100% TTL 10 0%; 100% 10 0%; 100% % b. It is the relative frequenc of teenagers who are 1 to 1 ears old and who prefer snorkeling to all 1- to 1-ear-olds who were surveed. c. No; the total numbers in the last column (ages) are not the same as the total numbers in the last row (preferences), so the relative frequencies are different. d. It is the relative frequenc of teenagers who are 1 to 1 ears old and who prefer snorkeling to all of those surveed who prefer snorkeling. LESSN , or 0.9% Step1: % becomes %; Step : % becomes %, 0% becomes 0%, and % becomes 77%; Step : conclusions would not change. 1. a-c. TTL row: 1,,, ; TTL column: 1, 1, d. Preferred Pet Seashore Mountains ther TTL Gender Girl o TTL e. 0.0, or % f. 0., or % g. 0., or %; 1 in girls surveed prefer the mountains; girls are more likel than bos to prefer the mountains.. a. first row: 10, 0; second row:,, ; third row: 0, 1 b. Sample answer: I worked backward from the given data, using the fact that the sum of the entries in each row and each column must equal the total for that row or column.. a. 1% b. % c. about 0% 7. No; each data value should have been divided b the grand total, 00, not b the row total.. Yes, the data in the Total row, the marginal relative frequencies of each column, are correct. The joint relative frequencies and their marginal relative frequencies in the Total column are incorrect. Houghton Mifflin Harcourt Publishing ompan S19