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Basic Algebra Review 9. Given ABC where m C 900 , AC 3, and BC 4 . Find the measure of AB . 1. What is the value of x in the equation 2(x − 3) + 1 = 19? 10. Solve. 4x 2 36 0 a) 6 b) 9 c) 10.5 d) 12 11. Christi and Laura start a lawn-mowing 2. What is the solution for the equation business and buy a lawnmower for $225. 5(x + 1) = 5x + 2? They plan to charge $15 to mow one lawn. 1 What is the minimum number of lawns they a) −1 b) c) all real # d) no sol 2 need to mow if they wish to earn a profit of at least $750? 3. When 5 is divided by a number, the result is 3 more than 7 divided by twice the number. What is the number? 12. The formula for converting temperatures in 1 a) 1 b) 2 c) d) 5 degrees Celsius to degrees Fahrenheit is 2 9 F C 32 . If the temperature is 200 C, 5 4. Mr. Linnens has $75 to spend on pizzas and what is the temperature in degrees soda pop. Pizzas cost $9 each and drinks cost Fahrenheit? $0.75 each. Five times as many drinks as a) 68 b) 43.1 c) 33.8 d) 4 pizzas are needed. What is the maximum number of pizzas that Mr. Linnens can buy? 13. The expression x 2 16 is equivalent to a) x 2x 8 b) x 2x 8 5. Give the statements: “t is a multiple of 3” and “t” is even”. What could be a value of t? c) x 4x 4 d) x 8x 8 a) 8 b) 9 c) 15 d) 24 14. The width, w, of a rectangular rug is 4 less 6. The table shows the GPS coordinates of four than its length, l. Which expression cities. represents the area of the rug? Chicago (5985, 3439) a) l 4 l b) l l 4 Denver (7490, 5881) c) 2l 4 2l d) 2w 2l Huston (8936, 3542) Boston (4422, 1241) Find the distance between Boston & Denver. 15. Simplify the expression 6 35x 2 10x . a) 25x b) 8 25x c) 5x 6 d) 12 25x 7. Which equation is equal to 3x 4 y 15? 15 3x 16. Ms. Lucero bought a refrigerator that cost a) y b) y 15 3x 4 $1200, including tax. The cost of electricity to 3x 15 run this refrigerator is estimated at $78 per c) y d) y 3x 15 4 year. Which equation best represents c, the total cost of the refrigerator including electricity over n years of operation? 8. Which equation illustrates the associative a) c = 1200(78n) b) c = 1200(n + 78) property? c) c = 1200 − 78n d) c = 1200 + 78n a) a b b a b) a b c a b c c) ab c ab ac d) a1 a 17. Twenty-two is two less than six times a number. Find the number. 18. The midpoint of TS is the origin and point T is 30. The length of a rectangle is nine and the width located in Quadrant II. What quadrant is (x + 6). Find the value of x if the area of the contains point S? rectangle is 135 cm2. (A = l w) 19. Two cyclists start from the same point and ride 31. Lee, Kelly, Linda, and Madison all took the in opposite directions traveling at the same same math test. Linda earned a lower score speed. In 3 hours they are 72 miles apart. than Kelly, but she did not earn the lowest Find the rate of each cyclist. score. The highest test-scorer’s name does not begin with an L. Madison earned a higher 20. The sum of three consecutive even integers is score than Kelly. Which person earned the forty-two. Find the integers. lowest score on the math test? 21. A coin purse contains 16 coins in nickels and dimes. The coins have a total value of $1. 32. The pattern of dots shown below continues Find the number of each type of coin in the infinitely, with more dots being added at each purse. step. Which expression can be used to determine the number of dots in the nth step? 22. Scientists find that the height of a person, h, in centimeters, is related to the length of the person’s femur bone, f, in centimeters, according to the formula h 69.09 2.24 f What is the height of a person with a femur bone of 48.6 cm in length? a) 2n b) n(n + 2) c) n(n + 1) d) 2(n + 1) 23. One hose can fill a pool in 15 hours. A second hose can fill a pool in 10 hours. How long would it take to fill the pool using both hoses? 33. Which of the following expressions is equal to the area of the shaded region in square units in the diagram shown below? 24. A ship travels from Long Beach to the Jiaozhou Gulf, a distance of 7200 miles. If the ship travels at a rate of 480 miles per day, how long will the trip take? 25. Brycen doubles his favorite number and adds 7 to get 21. What is Brycen’s number? a) 5x2 + 4x - 2 b) 5x2 + 6x - 2 27. Pennie Pinches adds 5 dollars a week to her c) 9x2 + 6x - 2 d) 7x2 + 5x - 2 balance of $144. Write an equation that models this situation. In how many weeks will she have $179? 34. Which algebraic expression best represents the relationship between the terms in the 28. When twice a number is decreased by 3, the following sequence and their position, n, in the result is 253. What is the number? sequence? 0, 6, 16, 30, 48 … 29. The sides of a triangle are (x + 3), a) n – 2 b) 2n2 - 2 (x + 4), and (x + 7). Find the length of the c) 2n - 2 d) n2 - 2 longest side if the perimeter of the triangle is 104 inches.

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