(MATH 114 Week 8 Practice Final)
1. Question: Solve the following system of equations by graphing. If the system is inconsistent or the equations are dependent, say so.
24x–4y=48
6x = y + 12
2. Question: A motel clerk counts his $1and $10 bills at the end of the day. He finds that he has a total of 60 bills having a combined monetary value of $195. Find the number of bills of each denomination he has.
3. Question: Determine whether the graph to the right is a function. Using the vertical line test, is this the graph of a function?
4. Question: Factor the trinomial.
s2–17s +70
5. Question: Use the quadratic formula to solve the equation.
5×2–7x–3 = 0
6. Question: Complete thefactoring.
7. Question:Given the function f(x) = x2 – x + 6, find each of the following.
f(5), f(- 8), f(0)
8. Question:Factor completely.
9. Question: Find
– √(9/4)
10. Question: Use the square root property to solve the equation.
(x – 1)2 = 16
11. Question: Factor by grouping.
3s2 + 16s + 5
12. Question:Simplify
13. Question:Solve the following system by the substitution method. Check the solution(s).
7y – 6x = – 15
x – 5y = – 9
14. Question: Solve the following system by the elimination method. Check the solution.
2.6x + 1.6y = 11.2
1.3x – 0.3y = 12.2
15. Question: Graph the quadratic function by plotting points. Give the coordinates of the vertex.
y = -2×2 + 4
16. Question: Find the domain and the range of the relation, and determine whether it is a function.
{(10, 1),(- 1, – 4),(2, -2),(5, – 9)}
17. Question: Factor the trinomial.
c2 – c – 6
18. Question: Find all the square roots of 100.
19. Question: Simplify byfactoring.
20. Question: Use the quadratic formula to solve the equation.
x2-= 1
21. Question: Factor the trinomial completely.
2r2+9r + 9
22. Question: Sketch the graph of the parabola. Find the coordinates of the vertex.
y = – x2 + 4x – 9
23. Question: Assume that all variables represent nonnegative real numbers.
24. Question: Factor the trinomial.
5n3 – 15n2 – 2300n
25. Question: Solve the following problem using a system of equations.
How many pounds of nuts selling for $6 lb and raisins selling for $3 per lb should a person combine to obtain 90 lb of a trail mix selling for $4 per lb?
26. Question: Solve the equation by using the square root property. Simplify all radicals.
x2 = 100
27. Question: The product of two consecutive positive integers is 1 more than their sum. Find the integers.
28. Question: Solve the following system by the elimination method.
5x – y = 25
x + 3y =21
29. Question:Solve the following system by the substitution method. Check the solution (s).
15x – 10y = 5
15y = – 4 + 5x