Answers To Algebra 1 Unit 3 Practice

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Answers to Algebra 1 Unit 3 Practice14. Alan used the wrong piece of the function rule tofind the value of f(4). Alan used the first piece,which only applies to value of x less than 4. Heshould have used the second piece, which appliesto values of x greater than or equal to 4. Thecorrect answer is f(4) 5 27.1. C(t) 5 13t 1 392. 13/day; each extra day the canoe is rentedincreases the total cost by 13.3. B4. Disagree; the average rate of change between years14,000 210,120 38800 and 2 is55 1940, while2202the average rate of change between years 2 and 5 is10,12026240 388055 1293.3.522315. Answers may vary. Both are piecewise-definedfunctions with two pieces. The functions areidentical for 0 , t # 4 with a rate of change of 10/hour. For values of t . 4, the rate of change forValdez Bikes drops to 5/hour. For Adam’s Bicycles,the rate of change does not drop to 5/hour untilt . 5.5. The rate of change is 25 minutes/pound. For eachextra pound that a chicken weighs, the cookingtime increases by 25 minutes.16. C22x 1 5, when x , 16. C(w) 5 0.035w, where C is the cost in dollars and wis the weight in pounds; domain: {w 0 , w , 700};range: {C(w) 0 , C(w) , 24.5}17. f(x) 57. C(w) 5 2.1 1 0.032w, where C is the cost indollars and w is the weight in pounds; domain:{w w 700}; range: {C(w) C(w) 24.5}18. Answers may vary. Both are piecewise-definedfunctions with two pieces. The domains of thepieces are the same, and the graphs of bothfunctions change direction at the point (1, 3). Forx , 1, the rates of change for the functions areboth negative, but the graph of f(x) is steeper. Forx 1, the rates of change for the functions haveopposite signs.8. B9. C(w) 510. M(a) 50.035w, when 0 , w , 7002.1 1 0.032w, when w 7001 x 1 5 , when x 1 , or equivalent2219. Students should represent both functions asequations or as graphs. The equation for g(x) is100 1 13a, when 0 # a # 14282 1 22(a 2 14), when 14 , a # 28,or equivalent; the mass of the baby panda increasedby 590 2 304 5 286 gramsg(x) 52x 1 5, when 21 # x # 2. The graph of2 1 x 1 4, when 2 , x # 62f(x) is shown below. Students should note that thefunctions are identical except for their domains.The domain of f(x) is all real numbers, and thedomain of g(x) is {x 21 # x # 6}.11. A(8) 5 110; After 8 weeks, Teresa has saved 110.12. D13.yy46f (x)224402224xf (x)22202224246x22 2014 College Board. All rights reserved.A1SpringBoard Algebra 1, Unit 3 Practice

20. d 5 10 2 0.2t1; it represents2the number of bracelets Carly can make per hourwhen it takes her 2 hours to make each bracelet. In1Item 31, the coefficient of t is ; it represents the3number of bracelets Carly can make per hour whenit takes her 3 hours to make each bracelet. Theconstant of 8 in both equations represents thenumber of bracelets Carly already has.32. In Item 30, the coefficient of t is21. a. 20.2; Shari’s speed is 0.2 km/min.b. The graph shows Shari’s remaining distanceto the finish, and this quantity is decreasingover time.22. 50 min; explanations may vary. The graph showsthat Shari had 0 kilometers of distance remainingafter 50 minutes.23. B33.24. 10 min; explanations may vary. The equation thatrepresents Jody’s data is d 5 10 2 0.25t, where d isthe distance in kilometers remaining and t is thetime in minutes. Substituting 0 for d and solvingfor t gives t 5 40. So, Jody finished the race in40 minutes, which is 10 minutes faster thanShari’s time.Total Number of Braceletsb Bracelets for Craft Fair25. 3 ft/yr; the rate of change equals the slope of thegraph, which is 3.26.201 braceletevery 2 h16121 braceletevery 3 h84048121620tTime Worked (hours)hAmerican Elm34. If Carly works 18 hours, she will have between 14and 17 bracelets for the craft fair; 14 # b # 1720Height (ft)16Ideal35. D1236. 4x 1 6y # 30, or equivalentGood837. Answers may vary. Five large sandwiches alonewould cost 5( 6) 5 30, which is the total amounton the gift card. So, Jesse could not buy 2 regularsandwiches in addition to 5 large sandwiches.4012345tTime (yr)38. If Jesse buys 1 regular sandwich and 2 largesandwiches, he will have spent 1( 4) 1 2( 6) 5 16 of the gift card, leaving 14 on the gift card.The inequality is now 4x 1 6y # 14. Jesse shouldthen buy 2 regular sandwiches and 1 largesandwich; this is the only combination ofsandwiches that totals 14.27. h 5 2t 1 6; the constant 6 represents the height ofthe tree in feet when it is planted. The coefficient oft is 2; it represents the average increase in theheight of the tree in feet per year.28. B29. The tree was planted between 4 and 6 years ago. Idetermined this by extending the coordinate planeso I could see the value of of h 5 6 1 2t whereh 5 18. The height of a tree grown under idealconditions would reach 18 feet after 4 years; theheight of an elm grown under good conditionswould reach 18 feet after 6 years.422430. A02224x22131. b 5 t 1 83 2014 College Board. All rights reserved.y39.24A2SpringBoard Algebra 1, Unit 3 Practice

40. C45. B41.46. (80, 240); the solution represents the width(80 yards) and length (240 yards) of a field that hasa 640-yard perimeter, and a length that is threetimes its width.125Wheat FieldDimensions100l7540050320Length (yd)Highway Distance (miles)Distance on Five Gallonsyof Gasoline250255075100 125xCity Distance (miles)0y 3x – 6xy026123423036y –2x 14xy014112210384649. Answers may vary. Enter y 5 3x 2 6 as Y1 andenter y 5 22x 1 14 as Y2. Next, view a graph ofthe equations on the same screen. Then use theIntersect feature to verify that the graphs of theequations intersect at the point (4, 6).424w48. (4, 6); tables may vary.y2160 240 320 40047. Regina is not correct. The ordered pair (4, 4) is asolution of the first equation in the system, but notthe second equation in the system. An ordered pairmust be a solution of both equations in a system oftwo equations in order to be a solution of the system.44. (3, 22)080Width (yd)43. Answers may vary. Solve the inequality for y.Then graph the boundary line. Use a dashed linefor , or . Use a solid line for # or . Check atest point in the inequality, such as (0, 0). If the testpoint makes the inequality true, shade the halfplane that includes the test point. If the test pointmakes the inequality false, shade the half-planethat does not include the test point.221608042. The x-intercept is (100, 0), which means that thegreatest distance Dale could drive in the city, with0 miles driven on the highway, is 100 miles. They-intercept is (0, 125), which means that thegreatest distance Dale could drive on the highway,with 0 miles driven in the city, is 125 miles.24240x2224 2014 College Board. All rights reserved.A3SpringBoard Algebra 1, Unit 3 Practice

50. (22, 5)11x 1 3 and y 5 x 1 3; the system has22infinitely many solutions because the equations ofthe lines are equivalent.61. y 551. A52. (5, 53.45); the total cost of the web hosting serviceswill be the same if the services are used for5 months. The total cost for 5 months with bothservices is 53.45.62. No; explanations may vary. The systemc 5 65 1 60(t 2 1) and c 5 60t 1 12 representsthe situation, where c is the total charge in dollarsand t is the length of the job in hours. A graph ofthe system consists of two parallel lines, so thesystem has no solution. In this context, a systemwith no solution means that there is no job lengthfor which the total charge for Duke Electric is thesame as the total charge for Spence Electrical.53. Answers may vary. Use substitution because bothequations in the system are already solved for y. Setthe two expressions for y equal to each other andthen solve for x. Then use the value of x todetermine the value of y.54. A55. Sample answer: Sarah bought a bottle of fruit juiceand 2 sandwiches for 9 while Manuel bought 2bottles of fruit juice and 3 sandwiches for 14. Thesolution (1, 4) represents the prices of these items:a bottle of fruit juice is 1 while a sandwich is 4.63. No; explanations may vary. The system d 5 8t andd 5 120 1 8(t 2 15) represents this situation,where d is the distance in feet from Kaye’s startingpoint and t is the time in seconds since Kayestarted jogging. A graph of this system consists of apair of coincident lines, so the system has infinitelymany solutions. In this context, a system withinfinitely many solutions means that once Kayereaches Tanner, they stay together, running at thesame speed without either passing the other.56. r 1 g 5 16 and 15r 1 12.5g 5 224, where r is thenumber of fluid ounces of orange juice and g is thenumber of fluid ounces of grapefruit juice57. (9.6, 6.4); each bottle will hold 9.6 fluid ounces oforange juice and 6.4 fluid ounces of grapefruit juice.64. Infinitely many; explanations may vary. Theslope-intercept forms of the equations in thesystem are identical. Therefore, the lines arecoincident, which means that the system hasinfinitely many solutions.58. 125 milliliters of the 10% solution and375 milliliters of the 30% solution; explanationsmay vary. Write the system x 1 y 5 500 and0.1x 1 0.3y 5 0.25(500) to represent the situation,where x is the number of milliliters of the 10%solution and y is the number of milliliters of the 30%solution. Then use elimination to solve the system.The solution is (125, 375).65. The lines are parallel. Explanations may vary. Theslope-intercept forms of the equations show that1the lines both have a slope of , but different2y-intercepts. Therefore, the lines are parallel.59. A60. None; the graph of the system is a pair of parallellines. Parallel lines do not intersect, so the systemhas no solution.66. Answers and explanations may vary. 2x 1 4y 5 3and x 1 8y 5 6; solving the system by elimination 3 shows that it has one solution of 0, . Systems 4 with one solution are independent (because theirgraphs consist of two distinct intersecting lines)and consistent (because they have a solution).y422467. D02224x2224 2014 College Board. All rights reserved.A4SpringBoard Algebra 1, Unit 3 Practice

74. The solution region lies between the parallelboundary lines.68. Answers may vary. If the lines have different slopes,then the system is independent and consistent. Ifthe lines have the same slope and differenty-intercepts, then the system is independent andinconsistent. If the lines have the same slope andthe same y-intercept, then the system is dependentand consistent.y42y69.24402242x222242402224x75. C2276. Let x represent the number of regular ticketssold to a performance and y represent the numberof discounted tickets sold to a performance. Notethat students could interchange the meanings of xand y, in which case the equations will change toreflect that.2470. B171. y # 2 x 2 23y.x21y # 10020x 1 14y 350072. No; explanations may vary. The point (22, 23)lies within the solution region of the inequality1y # 2 x 2 2, but it lies on the boundary line of3the inequality y . x 2 1. Because this secondinequality includes the symbol ., points on theboundary line are not included in the solution set.So, (22, 23) is not a solution of the systembecause it is not a solution of y . x 2 1.77.yTicket SalesDiscounted Tickets50073. Sample answers: (2, 22), (3, 3), and (4, 0)4003002001000100 200 300 400xRegular Tickets78. Answers may vary. The ordered pair (200, 50) is inthe solution region and makes sense in this contextbecause it is possible for the theater to sell 200regular tickets and 50 discounted tickets and makea profit. The ordered pair (150.5, 90.5) is in thesolution region, but does not make sense in thiscontext because the theater can only sell wholenumbers of tickets. 2014 College Board. All rights reserved.A5SpringBoard Algebra 1, Unit 3 Practice

A1 SpringBoard Algebra 1, Unit 3 Practice 1.C(t) 5 13t 1 39 2. 13/day; each extra day the canoe is rented increases the total cost by 13. 3. B 4.Disagree; the average rate of change between years 0 and 2 is 14,000 10,120 20 2 2 5 3880 2 5 1940, while the average rate of change between years 2 and 5 is 2 2 10,120 6240 52 5 3880 3 5 1293.3. 5.

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