Answers to Algebra 1 Unit 3 Practice

Transcription

1 1. C(t) 5 13t $13/da; each etra da the canoe is rented increases the total cost b $ B. Disagree; the average rate of change between ears 1,1,1 and is , while the average rate of change between ears and 5 is 1, The rate of change is 5 minutes/pound. For each etra pound that a chicken weighs, the cooking time increases b 5 minutes. 6. C(w) 5.35w, where C is the cost in dollars and w is the weight in pounds; domain: {w, w, 7}; range: {C(w), C(w),.5} 7. C(w) w, where C is the cost in dollars and w is the weight in pounds; domain: {w w $ 7}; range: {C(w) C(w) $.5} 8. B 9. C(w) 5 1. M(a) 5.35w, when, w, w, when w $ a, when # a # (a 1), when 1, a # 8, or equivalent; the mass of the bab panda increased b grams 11. A(8) 5 11; After 8 weeks, Teresa has saved $ D 13. Answers to Algebra 1 Unit 3 Practice f () 1. Alan used the wrong piece of the function rule to find the value of f(). Alan used the first piece, which onl applies to value of less than. He should have used the second piece, which applies to values of greater than or equal to. The correct answer is f() Answers ma var. Both are piecewise-defined functions with two pieces. The functions are identical for, t # with a rate of change of $1/hour. For values of t., the rate of change for Valdez Bikes drops to $5/hour. For Adam s Biccles, the rate of change does not drop to $5/hour until t C 17. f() 5 1 5, when, , or equivalent, when $ Answers ma var. Both are piecewise-defined functions with two pieces. The domains of the pieces are the same, and the graphs of both functions change direction at the point (1, 3). For, 1, the rates of change for the functions are both negative, but the graph of f() is steeper. For $ 1, the rates of change for the functions have opposite signs. 19. Students should represent both functions as equations or as graphs. The equation for g() is 1 5, when 1 # # g() 5 1. The graph of 1, when, # 6 f() is shown below. Students should note that the functions are identical ecept for their domains. The domain of f() is all real numbers, and the domain of g() is { 1 # # 6}. 6 6 f () 1 College Board. All rights reserved. A1

2 . d 5 1.t 1. a..; Shari s speed is. km/min. b. The graph shows Shari s remaining distance to the finish, and this quantit is decreasing over time.. 5 min; eplanations ma var. The graph shows that Shari had kilometers of distance remaining after 5 minutes. 3. B. 1 min; eplanations ma var. The equation that represents Jod s data is d 5 1.5t, where d is the distance in kilometers remaining and t is the time in minutes. Substituting for d and solving for t gives t 5. So, Jod finished the race in minutes, which is 1 minutes faster than Shari s time ft/r; the rate of change equals the slope of the graph, which is Height (ft) h American Elm Ideal Good 1 3 Time (r) 5 7. h 5 t 1 6; the constant 6 represents the height of the tree in feet when it is planted. The coefficient of t is ; it represents the average increase in the height of the tree in feet per ear. 8. B 9. The tree was planted between and 6 ears ago. I determined this b etending the coordinate plane so I could see the value of of h t where h The height of a tree grown under ideal conditions would reach 18 feet after ears; the height of an elm grown under good conditions would reach 18 feet after 6 ears. 3. A 31. b t 1 8 t 3. In Item 3, the coefficient of t is 1 ; it represents the number of bracelets Carl can make per hour when it takes her hours to make each bracelet. In Item 31, the coefficient of t is 1 ; it represents the 3 number of bracelets Carl can make per hour when it takes her 3 hours to make each bracelet. The constant of 8 in both equations represents the number of bracelets Carl alread has. 33. Total Number of Bracelets b Bracelets for Craft Fair 1 bracelet 16 ever h bracelet ever 3 h Time Worked (hours) 3. If Carl works 18 hours, she will have between 1 and 17 bracelets for the craft fair; 1 # b # D # 3, or equivalent 37. Answers ma var. Five large sandwiches alone would cost 5($6) 5 $3, which is the total amount on the gift card. So, Jesse could not bu regular sandwiches in addition to 5 large sandwiches. 38. If Jesse bus 1 regular sandwich and large sandwiches, he will have spent 1($) 1 ($6) 5 $16 of the gift card, leaving $1 on the gift card. The inequalit is now 1 6 # 1. Jesse should then bu regular sandwiches and 1 large sandwich; this is the onl combination of sandwiches that totals $ t 1 College Board. All rights reserved. A

3 . C 5. B 1. Highwa Distance (miles) Distance on Five Gallons of Gasoline Cit Distance (miles) 6. (8, ); the solution represents the width (8 ards) and length ( ards) of a field that has a 6-ard perimeter, and a length that is three times its width. Length (d) l Wheat Field Dimensions. The -intercept is (1, ), which means that the greatest distance Dale could drive in the cit, with miles driven on the highwa, is 1 miles. The -intercept is (, 15), which means that the greatest distance Dale could drive on the highwa, with miles driven in the cit, is 15 miles. 3. Answers ma var. Solve the inequalit for. Then graph the boundar line. Use a dashed line for, or.. Use a solid line for # or $. Check a test point in the inequalit, such as (, ). If the test point makes the inequalit true, shade the halfplane that includes the test point. If the test point makes the inequalit false, shade the half-plane that does not include the test point.. (3, ) Width (d) 7. Regina is not correct. The ordered pair (, ) is a solution of the first equation in the sstem, but not the second equation in the sstem. An ordered pair must be a solution of both equations in a sstem of two equations in order to be a solution of the sstem. 8. (, 6); tables ma var. = w = Answers ma var. Enter as Y 1 and enter as Y. Net, view a graph of the equations on the same screen. Then use the Intersect feature to verif that the graphs of the equations intersect at the point (, 6). 1 College Board. All rights reserved. A3

4 5. (, 5) 51. A 5. (5, 53.5); the total cost of the web hosting services will be the same if the services are used for 5 months. The total cost for 5 months with both services is $ Answers ma var. Use substitution because both equations in the sstem are alread solved for. Set the two epressions for equal to each other and then solve for. Then use the value of to determine the value of. 5. A 55. Sample answer: Sarah bought a bottle of fruit juice and sandwiches for $9 while Manuel bought bottles of fruit juice and 3 sandwiches for $1. The solution (1, ) represents the prices of these items: a bottle of fruit juice is $1 while a sandwich is $. 56. r 1 g 5 16 and 15r 1 1.5g 5, where r is the number of fluid ounces of orange juice and g is the number of fluid ounces of grapefruit juice 57. (9.6, 6.); each bottle will hold 9.6 fluid ounces of orange juice and 6. fluid ounces of grapefruit juice milliliters of the 1% solution and 375 milliliters of the 3% solution; eplanations ma var. Write the sstem and (5) to represent the situation, where is the number of milliliters of the 1% solution and is the number of milliliters of the 3% solution. Then use elimination to solve the sstem. The solution is (15, 375). 59. A 6. None; the graph of the sstem is a pair of parallel lines. Parallel lines do not intersect, so the sstem has no solution and ; the sstem has infinitel man solutions because the equations of the lines are equivalent. 6. No; eplanations ma var. The sstem c (t 1) and c 5 6t 1 1 represents the situation, where c is the total charge in dollars and t is the length of the job in hours. A graph of the sstem consists of two parallel lines, so the sstem has no solution. In this contet, a sstem with no solution means that there is no job length for which the total charge for Duke Electric is the same as the total charge for Spence Electrical. 63. No; eplanations ma var. The sstem d 5 8t and d (t 15) represents this situation, where d is the distance in feet from Kae s starting point and t is the time in seconds since Kae started jogging. A graph of this sstem consists of a pair of coincident lines, so the sstem has infinitel man solutions. In this contet, a sstem with infinitel man solutions means that once Kae reaches Tanner, the sta together, running at the same speed without either passing the other. 6. Infinitel man; eplanations ma var. The slope-intercept forms of the equations in the sstem are identical. Therefore, the lines are coincident, which means that the sstem has infinitel man solutions. 65. The lines are parallel. Eplanations ma var. The slope-intercept forms of the equations show that the lines both have a slope of 1, but different -intercepts. Therefore, the lines are parallel. 66. Answers and eplanations ma var and ; solving the sstem b elimination shows that it has one solution of, 3. Sstems with one solution are independent (because their graphs consist of two distinct intersecting lines) and consistent (because the have a solution). 67. D 1 College Board. All rights reserved. A

5 68. Answers ma var. If the lines have different slopes, then the sstem is independent and consistent. If the lines have the same slope and different -intercepts, then the sstem is independent and inconsistent. If the lines have the same slope and the same -intercept, then the sstem is dependent and consistent B 71. # No; eplanations ma var. The point (, 3) lies within the solution region of the inequalit # 1, but it lies on the boundar line of 3 the inequalit. 1. Because this second inequalit includes the smbol., points on the boundar line are not included in the solution set. So, (, 3) is not a solution of the sstem because it is not a solution of Sample answers: (, ), (3, 3), and (, ) 7. The solution region lies between the parallel boundar lines. 75. C 76. Let represent the number of regular tickets sold to a performance and represent the number of discounted tickets sold to a performance. Note that students could interchange the meanings of and, in which case the equations will change to reflect that. # $ Ticket Sales Discounted Tickets Regular Tickets 78. Answers ma var. The ordered pair (, 5) is in the solution region and makes sense in this contet because it is possible for the theater to sell regular tickets and 5 discounted tickets and make a profit. The ordered pair (15.5, 9.5) is in the solution region, but does not make sense in this contet because the theater can onl sell whole numbers of tickets. 1 College Board. All rights reserved. A5