Solve each absolute value equation x 7 = x 9 = (3x 12) = - 12

Transcription

1 Solve each absolute value equation x 7 = x 9 = (3x 12) = Explain why there can be one, two or no solutions to an absolute value equation. 5. Solve each equation for the specified variable.! 20.!"!! = h, for x 21. h + g = d, for h!! x = Write and solve an equation to find three 23. Two is subtracted from a number, and consecutive odd integers whose sum is 3. Then the difference is multiplied by 5. The result is 30. Find the number.

2 Solve each absolute value equation x 7 = x 9 = (3x 12) = Explain why there can be one, two or no solutions to an absolute value equation. Solve each equation for the specified variable.! 22. Write and solve an equation to find three 23. Two is subtracted from a number. consecutive odd integers whose sum is 3. Then the difference is multiplied by 5. The result is 30. Find the number. 24. Two trains leave Raleigh at the same time, one traveling north, and the other south. The first train travels at 50 miles per hour and the second at 60 miles per hour. In how many hours will the trains be 275 miles apart? 25. A pineapple drink contains 15% pineapple juice. How much pure pineapple juice should be added to 8 quarts of the pineapple drink to obtain a mixture containing 50% pineapple juice?

3 Ch 2 Proportions & Percents 26. Mary can read 22 pages in 30 minutes. How long would it take her to read a 100- page book? Write your answer in hours and minutes and round to the nearest minute, if needed. 27. Use the table to the right about pumpkins at Niederman farm. a. Do the Niderman s use a consistent unit rate to determine the price of their pumpkins? If so, what is it? Pumpkins! 6 oz. 12 oz. 30 oz. $1.50 $3.00 $7.50 b. What is another unit rate that could be used to represent the price of the pumpkins? Solve each percentage problem. 28. During a Black Friday sale at Best Buy, Jeremy plans to buy a new HDTV. The TV is going to be 40% off on Friday and if he arrives before 9 a.m., he will receive an additional 20% off at the register. Jeremy thinks he will get the TV for 60% off. a) Explain why Jeremy s thinking is incorrect. b) If the original price of the TV was $435, what will the discounted price be? 29. The population of a small town increased from 4,198 people to 5,350 people over the span of 5 years. What was the percent increase in the town s population during that time? 30. Andy Dalton completed only 15% of his passes thrown last Sunday. If he completed 3 passes, how many passes did he throw? Unit 3: Relations & Functions 31. The graph to the right represents the price of stock over time. Identify the independent and dependent variable for the relation. Then describe what happens in the graph.

4 Determine whether the following relations are functions. Justify your reasoning 32. X Y x = If f(x) = 2x 6 and g(x) = x 2x 2, find each value. 36. g(- 2) 37. f(7) f(- ½) 39. g(3y) 40. Many cell phones have a text messaging option in addition to regular cell phone service. The function for the monthly cost of text messaging service from Noline Wireless Company is f(x) = 0.10x + 2, where x is the number of text messages that are sent. Find f(10) and f(30), and explain what each value represents. 41. You receive a gift card for trading cards from a local store. The function d = c represents the remaining dollars d on the gift card after obtaining c packages of cards. Find the x- intercept of this function. Describe what this value means in this context. Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, and the x- coordinate of any relative extrema

5 Unit 4: Linear Functions x y 44. Determine whether the function in the table is linear. Justify your reasoning Determine the slope of the line that passes through each pair of points. 45. (4, 3.5), (- 4, 3.5) 46. (14, - 8), (7, - 6) 47. (- 4, - 1), (- 4, - 5) Use the two points to answer questions 48-52: (3, - 4), (7, - 6). 48. Write the equation of the line in point- slope form. 49. Write the equation in slope- intercept form. 50. Write the equation in standard form. 51. Write the equation of the line that passes through (1,2) that is perpendicular to the line. 52. Write the equation of the line that passes through (1, 2) that is parallel to the given line. 53. There is a daily fee for renting a moving truck, plus a charge of $0.50 per mile driven. It costs $64 to rent the truck on a day when it is driven 48 miles. a. Write the equation in slope- intercept form to find the b. What is the daily fee? total charge y for a one- day rental with x miles driven. 54. Yvonne and her friends held a bake sale to benefit a shelter for homeless people. The friends sold 22 cakes on the first day and 15 cakes on the second day of the bake sale. They collected $88 on the first day and $60 on the second day. Let x represent the number of cakes sold and y represent the amount of money made. Write an equation in slope intercept form to represent this situation.

6 Ch. 5 Linear Inequalities Solve and graph each inequality r + 2(4r + 2) 2(6r + 1) 56. d 3 < 6d + 12 < 2d a or 10 < 6a (x 1) x x + 1 > Naomi practices the violin at least 12 hours per week. She practices for three fourths of an hour each session. If Naomi has already practiced 3 hours in one week, how many sessions remain to meet or exceed her weekly practice goal? 62. The ideal diameter of a piston for one particular car engine is 90 mm. The diameter can vary from the ideal by at most.008 mm. Write an absolute value inequality to represent the situation. 63. The menu at Jeanne s favorite restaurant states that the roasted chicken with vegetables entree typically contains 480 Calories. Based on the size of the chicken, the actual number of Calories in the entree can vary by as many as 40 Calories from this amount. a. Write an inequality to represent the situation. b. What is the range of the number of Calories in the chicken entree?

7 Graph each linear inequality y x < x 2y 8 Systems of Linear Equations Solve each of the following systems using substitution x 2y = ½x + 2y = 12 x ½y = 4 x 2y = 6 Solve each of the following systems using elimination x 4y = x ¾y = -7 4x + 2y = -3 x + ½y = Two planes are in flight near a local airport. One plane is at an altitude of 1000 meters and is ascending at a rate of 400 meters per minute. The second plane is at an altitude of 5900 meters and is descending at a rate of 300 meters per minute. a. Write a system of equations that represents b. Find the solution and explain its significance. the progress of each plane

8 71. Ramiro earns $20/hr during the week and $30/hr for overtime on the weekends. One week Ramiro earned a total of $650. He worked 5 times as many hours during the week as he did on the weekend. Write and solve a system of equations to determine how many hours of overtime Ramiro worked on the weekend. 72. Anya makes 14 baskets during her game. Some of these baskets were worth 2-pts and others were worth 3-pts. In total, she scored 30 points. Write and solve a system of equations to find how 2-pt baskets she made. 73. Graph the system. Write the system of inequalities represented by each graph. x > y -3x + 2