Finish the questions on the pictures below. Show your work.
1. List the range of the relation { (2,16), (3,9), (4,4) }. 2. State the domain and range in set notation {not interval notation) of the following: 3. Water is draining out of a tub at a constant rate. After 4 min the water level is 62 cm and after 9 minutes the water level is 15 cm. a) Is this relationship a function or not? Explain. b) Is this relationship discrete or not? Explain. c) Plot the ordered pairs (time, water level) to represent this information. Be sure to include a main title, axes titles and units. d) Calculate the slope of the line segment algebraically. e) Explain what the slope of the graph represents. 4. Find the slope of the line passing through the points (no decimals, complete algebraically). a) (7, 5) and (7, 4) b) ( 1/3, 3/2) and (2, 7/2) 5. Algebraically determine the x and y intercepts for the linear equation 3x + 6y 7 = 0. 6. Determine the equation ofthe line passing through the following points in slopepoint form: (3, 4) and (11, 25) 7. Consider the lines 3x 5y 15 = 0 and ax + 2y 6 = 0. If the lines have the same slope determine the value of a. 8. Find the equation of a line in slope-intercept form that is perpendicular to 6x 2y + 5 = O and has the same x-intercept as 2x y + 8 = 0 9. Solve the systems using any algebraic method. You must choose elimination for one and substitution for the other: 4x+2y=13 3x=1y a b )Sx3y=19 ) 2x+5y=22 10. Solve the system by graphing using the grid to the right: x+2y=5 2x+y=1 -6-5-4-3-2-1_l 1 2 3 4 5 6 x -2 11. How can you tell if a system of linear equations will have no solution, one solution or infinitely many solutions? 12. Candy costing $6 per kg is mixed with candy costing $4.50 per kg to produce 112kg of candy worth $612. How many kg of each type of candy was used? Write a system to model this situation, define variables, solve, and verify your solution. 13. Use prime factorization to determine the greatest common factor and least common multiple of the following three numbers: 630, 945, and 4914. 14. Expand (3x 5)(4x + 7) 15. Expand (71" + 4s)(7r 4s) 15. Expand (11a + 9)2 17. Factor each of the following polynomials completely. a) 5x2 +6x8 b) 4x2 +20x+25 c) 4r2 2552 d) 12a22a4 18. List all the number systems (N, W, 2, Q, (I, R) the following numbers belong to: a) 431/5 b) 221/17 6) 4.6796796... 19. Convert each of the following to a simplified mixed radical. a. b. {/567 20. Express S as an entire radical. 21. Evaluate the following without using a calculator: a) [ g] b) 27'3 c) (33; 22. Simplify the following expressions: 2 E a) [a4] 23. Use the diagram to answer the following questions. x2 2x+1 a) Write, expand and simplify an expression that represents the surface area of this prism. b) Write, expand and simplify an expression that represents the volume of the prism. c) If x = 5 cm, what is the surface area in cmz? d) What is the volume in cm3 if x = 4 cm? 24. Find the measure of y in the diagram below. 25. The angle of elevation to the top of a tree from point A is 52. From the point B, on the other side of the tree, the angle of elevation is 73. If the tree is 11.8 m tall, then find how far apart are the points A and B? Draw a diagram
