6w 2 = 13w 6. x 2 = 2 ( x + 180) x 2 3x 10 = 0. x 2 = 5 8 x 1 16

Transcription

1 . Solve the equation: 2 x 5 = 3 x Solve the equation: 6w + 48 = 4w z 3. Solve the equation 4 = 4 20 z Solve the equation: 4(x + 0) + 2 = 5(x + 7) Solve the equation by factoring 6w 2 = 3w 6 6. Solve the equation by factoring x 2 = 2 ( x + 80) 7. Solve the equation by completing the square x 2 3x 0 = 0 8. Solve the equation by completing the square x 2 = 5 8 x 6 PAGE

2 9. Solve the equation by completing the square x 2 + 4x + 48 = 0 0. Find all real solutions of the quadratic equation. Use any method. x 2 + 4x 24 = 0. Find all real solutions of the equation = 0 2. Find all real solutions of the equation 5 x 8 x = 0 3. Find all real solutions of the equation x 2 x + 6 = 4. Find all real solutions of the equation x 7 7 x 2 = 0 5. Find all real solutions of the equation x + + x = 3 PAGE 2

3 6. Find all real solutions of the equation x 29x + 00 = 0 7. Find all real solutions of the equation x 7 4 x + 2 = 0 8. Find all real solutions of the equation x 3 x + 2 = 0 9. A small appliance manufacturer finds that the profit P ( in dollars ) generated by producing x microwave ovens per week is given by the formula P = x ( 280 x ) provided that 0 x 200. How many ovens must be manufactured in a given 0 week to generate a profit of $320? 20. Express the concentration (in oz/gal) of salt in a mixture of gallons of brine containing 27 ounces of salt, to which has been added some pure water, where x = volume of pure water added (in gallons). 2. Find three consecutive integers whose sum is Find two numbers whose sum is 35 and whose product is 294. PAGE 3

4 23. Find the length x if the shaded area is 5220 cm 2 and y = 3 cm. 24. A farmer has a rectangular garden plot surrounded by 260 feet of fence. Find the length and width of the garden if its area is 4000 feet A merchant blends tea that sells for $3.05 a pound with tea that sells for $2.80 a pound to produce 80 lb of a mixture that sells for $2.95 a pound. How many pounds of each type of tea does the merchant use in the blend? PAGE 4

5 26. The figure shows a lever system, similar to a seesaw that you might find in a children s playground. For the system to balance, the product of the weight and its distance from the fulcrum must be the same on each side; that is x w = x 2 w 2 This equation is called the law of the lever, and was first discovered by Archimedes. A woman and her son are playing on a seesaw. The boy is at one end, 2 feet from the fulcrum. If the son weighs 90 lb and the mother weighs 35 lb, where should the woman sit so that the seesaw is balanced? 27. A pilot flew a jet from Montreal to Los Angeles, a distance of 200 miles. On the return trip the average speed was 20% faster than the outbound speed. The round trip took 0 hours 30 minutes. What was the speed from Montreal to Los Angeles? 28. A storage bin for corn consists of a cylindrical section made of wire mesh, surmounted by a conical tin roof, as shown in the figure. The height of the roof is one third the entire height of the structure. If the total volume of the structure is 200 feet 3 and its radius is r = 0 feet, what is its height? Hint: use the formulas for the volume of the solid. Volume of cone = Volume of cylinder = 3 R 2 h R 2 h PAGE 5

6 29. A wire 390 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire to the nearest tenth of an inch? 30. Let S = { 5, 0, 7, 7, 7.} Use substitution to determine which elements of S satisfy the inequality 2x + 2 > Let S = { 2, 0, 5, 5, 5.} Use substitution to determine which elements of S satisfy the inequality x Let S = {, 0, 5, 5, 5.} Use substitution to determine which elements of S satisfy the inequality x < Solve the inequality. Express the solution using interval notation. 5x + 9 < 4. PAGE 6

7 34. Solve the inequality. Express the solution using interval notation. 7 4x Solve the inequality. Express the solution using interval notation. 0 < 4x. 36. Solve the inequality. Express the solution using interval notation. 4 x 3x Solve the inequality. Express the solution using interval notation. 8 9 x + < 9 8x. 38. Solve the inequality. Express the solution using interval notation. 7 x + 9 < Solve the inequality. Express the solution using interval notation. 2 < 4x Solve the inequality. Express the solution in interval form. (x )(x 6) > 0 PAGE 7

8 4. Solve the inequality. Express the solution in interval form. x 2 2x Solve the inequality. Express the solution in interval form. 5 x 2 3 x < 4 x Solve the inequality. Express the solution in interval form. x Solve the inequality. Express the solution in interval form. (x + 4)(x )(x 4) Solve the inequality. Express the solution in interval form. 2x + 0 x 2 < Solve the inequality. Express the solution in interval form. 2x + 2 x Solve the nonlinear inequality. Express the solution using interval notation. 3 x 4 x PAGE 8

9 48. Solve the inequality. Express the solution in interval form. x x Solve the inequality. Express the solution in interval form. x 5 > x Solve the inequality. Express the answer using interval notation. x < 6 5. Solve the inequality. Express the answer using interval notation. x 8 > Solve the inequality. Express the answer using interval notation. x Solve the inequality. Express the answer using interval notation. 7 x 4 < Solve the inequality. Express the answer using interval notation. x PAGE 9

10 55. Solve the inequality. Express the answer using interval notation. 5 2x The relationship between degrees Celsius ( C ) and degrees Fahrenheit ( F ) is given by the equation C = 5 ( F 32 ). Use 9 this relationship between C and F to find the interval on the Fahrenheit scale corresponding to the temperature range 20 C Using calculus it can be shown that if a ball is thrown upward with an initial velocity of 6 ft/s from the top of a building 64 ft high, then its height h above the ground t seconds later will be h = t 6t 2 During what time interval will the ball be at least 32 ft above the ground? PAGE 0

11 58. For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the following formula: d = v + v 2 0 where d is measured in feet. Kerry wants her stopping distance not to exceed x = 300 ft. At what range of speeds can she travel? 59. A car rental company offers two plans for renting a car. Plan A: Plan B: $35 per day and $0.25 per mile. $45 per day with free unlimited mileage. For what range of miles will plan B save you money? 60. A gardener has 40 ft of deer resistant fence. She wants to enclose a rectangular vegetable garden in her backyard, and she wants the area enclosed to be at least 000 ft 2. What range of values is possible for the length of her garden? 6. Solve the inequality for x, assuming that p, q, and h are positive constants. p( qx h ) qh. 62. Determine the values of the variable for which the expression is defined as a real number. Express the solution in interval form. 25 4x 2 PAGE

12 63. Determine the values of the variable for which the expression is defined as a real number. Express the solution in interval form. 4 2 x 2 + x 64. Find the midpoint of the segment joining points (7, 8) and (5, 6). 65. A pair of points is given: (6, 0), (0, 0). Find the midpoint of the segment that joins them. 66. Find the area of the triangle shown in the figure. 67. Find a point on the y axis that is equidistant from the points (3, 6) and (5, 2). 68. Find the point that is one fourth of the distance from the point P( 3, 5) to the point Q(, 9) along the segment PQ. PAGE 2

13 69. Plot the points P( 7, 4), Q( 2,0), and R(5,2) on a coordinate plane. Where should the point S be located so that the figure PQRS is a parallelogram? 70. If M(6, 9) is the midpoint of the line segment AB, and if A has coordinates (2, 5), find the coordinates of B. 7. Sketch the parallelogram with vertices A ( 4, 4), B (2, ), C (7, 8), and D (, 3). Find the midpoints of the diagonals of this parallelogram. PAGE 3

14 ANSWER KEY , , 8 5, 2 8, 2 8, , 3 6 4,5 3, 2 8,56 5 8,25, 8, 25 8,256, ( +x) 2. 3,4, , , , , { 0, }, , , } 32. { ,0, 33. (, 3) 34. 6, ) , 4 (, 2, 0 2, ) (,5 (,) ( 6, ) 2,4 ( 2,5) (, 2 2, ) (, 4,4 ( 5,2) (,4) 4, ) 2,0) (,2 PAGE

15 ANSWER KEY x (, 4) 3, 2) (, ) ( 6,6) (,0) ( 6, ) (, 6 2, ) 2 7, 6 7 (, 22 8, ) (, 8 5, ) 68,40 0,2 0,50 m>40 20,50 h ( p+q) ( p q) 5 2, 5 2 ( 2,2 (, 7) ( 8,5) 8 ( 0, ) ( 2,6) ( 0, 2) ( 0,3) (.5,2), (.5,2) PAGE 2