MATH 115 SPRING 2019 REVIEW SHEET TEST 2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Decide whether or not the ordered pair is a solution to the equation. 1) 4x - 4y = 28; (4, 3) 1) Graph the equation. 2) y = - x - 4 2) 3) y = x + 4 3) Graph. 4) y = -x2-3 4) 1
Determine whether the ordered pair is a solution of the system of equations. Remember to use alphabetical order of variables. 5) (-4, 2); x + 4y = 4 5) 3x + 4y = -4 Graph the line. 6) y - 3 = - 1 (x - 3) 6) 2 Graph the specified line. 7) The line with slope 5 4 that passes through the point (4, 2) 7) Find an equation of the line containing the given pair of points. Write your final answer in slope-intercept form. 8) (-5, -3) and (-1, 4) 8) 9) (5.5, -8) and (7.5, 4) 9) Find an equation of the line meeting the specified conditions. Write your final answer in slope-intercept form. 10) Containing the point (3, -5) and perpendicular to y = 1 8 x + 3 10) Identify the system as consistent or inconsistent, and dependent or independent. 11) x + 6y = 38 4x - 3y = -10 11) 2
Solve by the substitution method. 12) 0.7x + 0.2y = 6.6-0.4x + 0.1y = -2.7 12) 13) 1 3 x + 1 3 y = -3 13) 1 2 x - 1 2 y = 1 2 Solve the system using the substitution method. If there is no solution or an infinite number of solutions, state this. 14) 2x + 3y = 5 14) 6x = 10 + 9y Solve the problem. 15) The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width by 7 inches, the perimeter would be 160 inches. What is the width? 15) 16) The difference of two numbers is nine more than the smaller number, and the sum of the two numbers is 54. Find the smaller number. 16) Solve the system graphically. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. 17) 3x + y = 8 17) 6x + 2y = 16 Solve the problem. 18) Andy has 24 coins made up of quarters and half dollars, and their total value is $10.75. How many quarters does he have? 18) 19) A merchant has coffee worth $6 a pound that she wishes to mix with 2 pounds of coffee worth $9 a pound to get a mixture that can be sold for $7 a pound. How many pounds of the $6 coffee should be used? 19) 20) A plane flies 420 miles with the wind and 300 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plane in still air? 20) 3
Graph the system of inequalities. Find the coordinates of any vertices. 21) 3y - x 9, y + 2x 10, y 0 21) 22) y - x 1 y - x 3-6 x -1 22) 23) x + 3y 12 3x + y 12 x 0 y 0 23) 4
Graph the system of linear inequalities. 24) y -x + 2 y 2 24) Graph the system of inequalities. Find the coordinates of any vertices. 25) 3y - x 9, y + 2x 10, y 0 25) Graph on a plane. 26) 5x - 3 7x + y 26) 5
27) x 4 27) 28) -4 < y < 6 28) Determine whether the ordered pair is a solution of the given inequality. 29) (3, -1); 2x - 4y < 6 29) Graph on a plane. 30) y < -2x + 1 30) Solve the problem. 31) Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 220 miles in the same time that Dana travels 190 miles. If Chuck's rate of travel is 6 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel? 31) 6
32) The speed of a stream is 6 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream, what is the speed of the boat in still water? 32) 33) The owner of Nuts2U Snack Shack mixes cashews worth $5.50 a pound with peanuts worth $2.30 a pound to get a half-pound mixed nut bag worth $1.80. How much of each kind of nut is included in the mixed bag? 33) Solve the system of equations using the substitution method. 34) 4x - 3 = y y - 4x = 3 34) Solve the problem. 35) A garage owner wants to fill a 55-gallon drum with a 20% winter mixture of antifreeze for his customers. How many gallons of 100% antifreeze should he mix with some 10% antifreeze mixture in order to fill the drum? 35) 36) How many liters of a 10% alcohol solution must be mixed with 30 liters of a 60% solution to get a 40% solution? 36) 37) Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 33 pounds of feed worth 0.50 per pound by mixing one kind worth $0.30 per pound with another worth $0.80 per pound. How many pounds of the cheaper kind should they use in the mix? Round your answer to the nearest pound, if necessary. 37) 38) Mardi received an inheritance of $50,000. She invested part at 11% and deposited the remainder in tax-free bonds at 8%. Her total annual income from the investments was $4900. Find the amount invested at 11%. 38) 39) Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $2.00 each and Kathy selling adult tickets for $4.50 each. If their total income for 364 tickets was $1175.50, how many did Ron sell? 39) Identify the system as consistent or inconsistent, and dependent or independent. 40) x - 5 = y y + 6 = x 40) 7
Solve the system graphically. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. 41) y = -9-5x 41) x + 3y = -13 Find an equation of the line meeting the specified conditions. Write your final answer in slope-intercept form. 42) Containing the point (2, 6) and parallel to y = -4x - 1 42) Find an equation of the line having the specified slope and containing the indicated point. Write your answer in slope-intercept form. 43) m = - 4 ; (12, -1) 43) 5 For the point-slope equation given, state the slope and the point on the graph used in creating the equation. 44) y - 6 = - 1 (x + 7) 44) 4 Write a slope-intercept equation of the line whose graph is described. 45) Parallel to the graph of y = 8x - 4; y-intercept (0, -6) 45) 46) Perpendicular to the graph of 7x + y = 8; y-intercept (0, 9) 46) Determine whether the pair of equations represents perpendicular lines. 47) 12x + 4y = 16 18x + 6y = 25 47) Determine whether the pair of equations represents parallel lines. 48) 3x - 6y = 12 12x + 8y = 12 48) 8
Graph the linear equation. 49) y = - 1 2 x + 5 49) Find the slope-intercept equation for the line with the indicated slope and y-intercept. 50) Slope 3; y-intercept (0, 0) 50) 51) Slope - 2 25 ; y-intercept 0, 3 3 51) Find the slope and the y-intercept of the line. 52) 2x + 7y = 38 52) Find the slope of the line. If the slope is undefined, state so. 53) x = -4 53) 54) y = 1 54) Find the slope of the line containing the given pair of points. If the slope is undefined, state so. 55) (1, 3) and (7, 12) 55) Find the slope of the line, or state that the slope is undefined if appropriate. 56) 56) 9
Use the graph to solve the problem. 57) Find the rate of change of Simone's salary. 57) Year Find the x- and y-intercepts for the equation. Then graph the equation. 58) -5x - 10y = 10 58) Find the coordinates of the y-intercept and the coordinates of all x-intercepts. 59) 59) Determine whether the equation is linear. 60) -30y + 29 x = 0 60) 10
Graph. 61) y = x2 + 4 61) Find the equation for the graph. 62) 62) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide whether or not the ordered pair is a solution to the equation. 63) 4x + 3y = 29; (5, 3) 63) A) Yes B) No 11
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph. 64) y = 1 2 x - 4 64) Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine another solution. Answers may vary. 65) x + 2y = 8; (6, 1), (-4, 6) 65) 12
Answer Key Testname: MATH115REVIEWSHEETTEST2 1) No 2) 3) 4) 5) Yes 13
Answer Key Testname: MATH115REVIEWSHEETTEST2 6) 7) 8) y = 7 4 x + 23 4 9) y = 6x - 41 10) y = - 8x + 19 11) Consistent and independent 12) (8, 5) 13) (-4, -5) 25 14) 12, 5 18 15) 23 in. 16) 15 17) {(x, y) 3x + y = 8} 18) 5 quarters 19) 4 lb 20) 138 mph 14
Answer Key Testname: MATH115REVIEWSHEETTEST2 21) (-9, 0), (3, 4), (5, 0) 22) (-6, -5), (-6, -3), (-1, 0), (-1, 2) 23) (3, 3), (0, 0), (0, 4), (4, 0) 15
Answer Key Testname: MATH115REVIEWSHEETTEST2 24) 25) (-9, 0), (3, 4), (5, 0) 26) 16
Answer Key Testname: MATH115REVIEWSHEETTEST2 27) 28) 29) No 30) 31) 44 mph 32) 18 mph 33) 0.20 lb of cashews and 0.30 lb of peanuts 34) No solution 35) 6 1 9 gal 36) 20 L 37) 20 lb 38) $30,000 39) 185 tickets 17
Answer Key Testname: MATH115REVIEWSHEETTEST2 40) Inconsistent and independent 41) (-1, -4) 42) y = -4x + 14 43) y = - 4 5 x + 43 5 44) m = - 1 ; (-7, 6) 4 45) y = 8x - 6 46) y = 1 7 x + 9 47) No 48) No 49) 50) y = 3x 51) y = - 2 3 x + 25 3 52) - 2 38 ; (0, 7 7 ) 53) Undefined 54) 0 55) 3 2 56) 2 57) $3000 per year 18
Answer Key Testname: MATH115REVIEWSHEETTEST2 58) (0, -1), (-2, 0) 59) (0, 8), (-4, 0), (-2, 0), (1, 0) 60) Not Linear 61) 62) y = 1 2 x - 2 63) A 64) 19
Answer Key Testname: MATH115REVIEWSHEETTEST2 65) Show that (6, 1) is a solution: x + 2y = 8 6 + 2(1) =? 8 6 + 2 =? 8 8 =? 8 TRUE Show that (-4, 6) is a solution: x + 2y = 8-4 + 2(6) =? 8-4 + 12 =? 8 8 =? 8 TRUE Coordinates of the additional solution may vary but should satisfy x + 2y = 8. 20