Chapter 3 & Determine whether the pair of equations represents parallel lines. Work must be shown. 2) 3x - 4y = 10 16x + 8y = 10

Transcription

1 Chapter 3 & These are meant for practice. The actual test is different. Determine whether the pair of equations represents parallel lines. 1) = = 39 1) Determine whether the pair of equations represents parallel lines. Work must be shown. 2) 3-4 = = 2) Provide the proper response. 3) Identif whether the slope is positive, negative, zero or undefined. 3) ) Identif whether the slope is positive, negative, zero or undefined. 4) Solve using the substitution method. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. ) + 3 = 80 ) 2 + = 30 6) 3 + = -7 = ) 1

2 7) + 7 = = 34 7) Provide an appropriate response. 8) Does ever straight line have an -intercept? If not, give an eample of an equation whose graph does not have an -intercept. 8) 9) Is it possible for the -intercept and the -intercept of a straight line to be at the same point? Eplain our answer. 9) ) What can ou sa about a line if ever point on the line has the same coordinate? ) 11) Eplain how ou would find the intercept of a line with an equation of the form A + B = C. 11) 12) What can ou sa about the graph of A + B = C if B is equal to zero? 12) 13) What is the -intercept of the line = b? 13) Determine whether the pair of equations represents perpendicular lines. 14) = = 27 14) 1) 3-4 = = -12 1) Find the equation for the graph. 16) 16)

3 17) 17) Solve the sstem graphicall. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. 18) = -3 18) = ) 3-2 = = )

4 Solve the sstem graphicall. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. Label at least two points per line and the solution. 20) = ) = Solve the sstem graphicall. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. 21) = ) 3 = Solve using the elimination method. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. 22) = = 1 22) 4

5 23) 9-6 = = 6 23) 24) 3r - 3s = 2-3r + 3s = 2 24) 2) - 3 = = -39 2) 26) = = ) Answer the question. 27) True or False? In quadrant IV, the -coordinate is alwas positive. 27) 28) True or False? The ordered pair (-6, -9) determines a point in quadrant III with -coordinate -9 and -coordinate ) 29) True or False? The ordered pair (-8, 2) determines a point in quadrant II with -coordinate -8 and -coordinate 2. 29) 30) True or False? In quadrant II, the -coordinate of a point is alwas negative. 30) 31) True or False? The -coordinate is positive in quadrants I and IV. 31) 32) True or False? The ordered pair (0, 0) determines a point in quadrant I with -coordinate 0 and -coordinate 0. 32) Write a slope-intercept equation of the line whose graph is described. 33) Parallel to the graph of = 3-7; -intercept (0, -) 33) 34) Perpendicular to the graph of 2 + = 2; -intercept (0, -) 34) Find the slope and the -intercept of the line. 3) -3 + = - 3)

6 Solve the problem. 36) A sum of mone amounting to $3.0 consists of dimes and quarters. If there are 17 coins in all, how man are quarters? 36) 37) The sum of two numbers is 72, and twice their difference is 24. What is the smaller of the two numbers? 37) 38) Anne and Nanc use a metal allo that is 24.% copper to make jewelr. How man ounces of an allo that is 23% copper must be mied with an allo that is 2% copper to form 88 ounces of the desired allo? 38) 39) The following graph shows data for a recent train ride from New York to Toronto. At what rate did the train travel? 39) Time of Da (PM) 40) And has 3 coins made up of quarters and half-dollars, and their total value is $ How man quarters does he have? 40) 41) A student took out two loans totaling $13,000 to help pa for college epenses. One loan was at 6% simple interest, and the other was at 4%. After one ear, the student owed $720 in interest. Find the amount of the loan at 4%. 41) 42) At :00 AM, Gavin rented a mountain bike. He returned the bike at 3:00 PM. He biked for 27. miles. He paid $4.00 for the rental. Find Gavin's average speed, in miles per hour. 42) 43) There were 620 people at a pla. The admission price was $3.00 for adults and $1.00 for children. The admission receipts were $1320. How man adults and children attended? 43) 44) Two angles are complementar. The sum of the first angle plus twice the second angle is 148. Find the measures of the angles. 44) 4) The perimeter of a rectangle is 6 cm. The length is 12 cm longer than the width. Find the dimensions. 4) 6

7 46) Jill is 13. kilometers awa from Joe. Both begin to walk toward each other at the same time. Jill walks at 2. km/h. The meet in 3 hours. How fast is Joe walking? 46) 47) Two angles are supplementar. One angle is 212 less than three times the other. Find the measures of the angles. 47) 48) In an isosceles triangle, each base angle is less than two times the third angle. Find the measures of all three angles. 48) 49) An orchard operator must dilute 11 quarts of a 60%-insecticide solution b adding water. How man quarts of water should be added to get a miture that is 2% insecticide? 49) 0) John and Ton start from the same place at the same time and head for a town miles awa. John walks twice as fast as Ton and arrives 3 hours before Ton. Find the speed of each. 0) 1) From a point on a river, two boats are driven in opposite directions, one at miles per hour and the other at 6 miles per hour. In how man hours will the be 44 miles apart? 1) 2) In a right triangle, one acute angle is 4 more than twice the other. Find the measure of each acute angle. 2) 3) Mrs. Bod has a desk full of quarters and nickels. If she has a total of 32 coins with a total face value of $4.60, how man of the coins are nickels? 3) 4) A contractor mies concrete from bags of pre-mi for small jobs. How man bags with % cement should he mi with 4 bags of 13.% cement to produce a mi containing 7% cement? 4) ) In a chemistr class, 4 liters of a 4%-saline solution must be mied with a % solution to get a 6% solution. How man liters of the % solution are needed? ) 6) Joe has a collection of nickels and dimes that is worth $4.. If the number of dimes was doubled and the number of nickels was increased b 17, then the value of the coins would be $7.0. How man dimes does he have? 6) 7) A garage owner wants to fill a -gallon drum with a 20% winter miture of antifreeze for his customers. How man gallons of 0% antifreeze should he mi with some % antifreeze miture in order to fill the drum? 7) 8) To the nearest dollar, the average tuition at a public four-ear college was $3068 in 1997 and $3283 in Find, to the nearest dollar per ear, the rate at which tuition was increasing. 8) 9) An epress train and a local train leave a station at the same time (on separate tracks) and head for a town 0 miles awa. The epress travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train. 9) 7

8 60) A woman made a deposit of $187. If her deposit consisted of 63 bills, all $1 bills or $ bills, then how man $1 bills did she deposit? 60) 61) A plane fling the 3922-mile trip from Cit A to Cit B has a 30-mph tailwind. The flight's point of no return is the point at which the flight time required to return to Cit A is the same as the time required to continue to Cit B. If the speed of the plane in still air is 360 mph, how far from Cit A is the point of no return? Round our answer to the nearest mile. 61) 62) To the nearest dollar, the average tuition at a public four-ear college was $302 in 1997 and $3249 in Find, to the nearest dollar per ear, the rate at which tuition was increasing. 62) 63) In a basketball game, Will scored 21 points, consisting onl of three-point shots and two-point shots. He made a total of 9 shots. How man shots of each tpe did he make? 63) Solve b graphing. 64) The population, p, in thousands, of one town can be approimated b p = d, where 64) d is the number of ears since 198. Use a graph to estimate the population of the town in the ear Graph the equation. 6) 4 + = 0 6)

9 66) = ) ) = 0. 67) ) = 1 68)

10 69) = ) ) + = 2 70) ) 2 - = -2 71)

11 72) + = 4 72) Find the - and -intercepts for the equation. Then graph the equation. 73) 6-12 = 0 73) ) = 20 74)

12 7) + = 7) ) 20-4 = -8 76) Find the - and -intercepts for the equation. Then graph the equation. Label the intercepts as ordered pairs.on the graph. 77) = 36 77) Find the slope of the line containing the given pair of points. If the slope is undefined, state so. 78) (-2, -2) and (-2, -4) 78) 12

13 79) (2, 3) and (11, 1) 79) 80) (1, 2) and (7, 11) 80) Find an equation of the line containing the given pair of points. Write our final answer in slope-intercept form. 81) (7, -6) and (3, -1) 81) 82) (8, -8) and (2, -1) 82) 83) (7, ) and (0, 3) 83) 84) (-2, 0) and (-9, -4) 84) 8) (-1, 3) and (-4, -6) 8) 86) (-2, 7) and (, -4) 86) 87) (4, 0) and (-6, 7) 87) Decide whether or not the ordered pair is a solution to the equation. 88) + = 8; (4, 2) 88) 89) + 2 = 0; (-2, 6) 89) Find the coordinates of the -intercept and the coordinates of all -intercepts. Write as ordered pairs. 90) 90)

14 Find the coordinates of the -intercept and the coordinates of all -intercepts. 91) 91) Find the intercepts for the equation. 92) = 7 92) 93) -2 + = -2 93) 94) -4-2 = -4 94) Write an equation of the line containing the specified point and parallel or perpendicular, as indicated, to the given line. Write our final answer in slope-intercept form. 9) (2, 6), parallel to = ) 96) (7, 2), perpendicular to = 4 96) 97) (0, -6), perpendicular to = ) Write the equation of the line on the graph in slope-intercept form. 98) 98)

15 Use the graph to solve the problem. 99) Find the rate of change of Simone's salar. 99) Solve using an appropriate method. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. 0) = 3 0) = 18 Determine whether the ordered pair is a solution of the sstem of equations. Remember to use alphabetical order of variables. 1) (-3, -1); - = -2 1) = Find the slope of the line, or state that the slope is undefined if appropriate. 2) 2) 1

16 3) (3, 3) (3, -3) 3) Find the slope of the line. If the slope is undefined, state so. 4) = -4 4) ) = 1 ) Write an equation for the graph. 6) 6) - - Write an equation in slope-intercept form of the line satisfing the given conditions. 7) Parallel to = and the same -intercept as 9 - = 3. 7) 16

17 Graph the specified line. 8) The line with slope 1 6 that passes through the point (0, 6) 8) Find the slope-intercept equation for the line with the indicated slope and -intercept. 9) Slope 1 ; -intercept (0, 3) 9) 2 17

18 Answer Ke Testname: 11CH3&8P 1) Yes 2) No 3) Negative 4) Positive ) (, ) 6) - 1 7, ) (12, -2) 8) The -intercept is the point where the line crosses the -ais. Lines parallel to the -ais do not intercept the -ais. Thus the graph of an equation of the form = b where b 0 has no -intercept. 9) Yes. If the line passes through the origin, then both the -intercept and the -intercept are at (0, 0). ) The line is vertical. 11) Let = 0 and solve for. 12) The graph is a vertical line. 13) (0, b) 14) No 1) Yes 16) = ) = ) (-3, -7) 19) No solution 20) (6, 1) 21) (6, 9) 22) 9 4, -1 23) (0, 3) 24) No solution 2) (6, -1) 26) (4, 0) 27) False 28) False 29) True 30) True 31) True 32) False 33) = 3-34) = 1 2-3) 3 ; (0, -1) 36) 9 37) 30 38) 22 ounces 39) 60 miles per hour 40) 18 41) $

19 Answer Ke Testname: 11CH3&8P 42). mph 43) Adults: 30; children: ) 32, 8 4) Width: 8 cm; length: 20 cm 46) 2 km/h 47) 98, 82 48) 70, 70, 40 49) 319 quarts 0) Ton: mph; John: 3 3 mph 1) 4 hours 2) 12, 78 3) 17 4) 13 bags ) 2.0 L 6) 21 7) gallons 8) $21 per ear 9) Epress: 0 mph; local: 2 mph 60) 32 61) 1798 miles 62) $66 per ear 63) Two-point shots: 6; three-point shots: 3 64) About 16,000 6)

20 Answer Ke Testname: 11CH3&8P 66) ) )

21 Answer Ke Testname: 11CH3&8P 69) ) )

22 Answer Ke Testname: 11CH3&8P 72) ) (0, 0), (0, 0) )

23 Answer Ke Testname: 11CH3&8P 7) (0, ), (, 0) ) 0, - 2, 2, ) (0, -3), (-6, 0) ) Undefined 79) ) ) =

24 Answer Ke Testname: 11CH3&8P 82) = ) = ) = ) = ) = ) = ) No 89) Yes 90) (0, -8), (-8, 0), (8, 0) 91) (0, 8), (-4, 0), (-2, 0), (1, 0) 92) (7, 0) 93) (1, 0), (0, -2) 94) (1, 0), (0, 2) 9) = ) = ) = ) = ) $3000 per ear 0) No solution 1) Yes 2) ) Undefined 4) Undefined ) 0 6) = 2 7) =

25 Answer Ke Testname: 11CH3&8P 8) ) =