finite math

mat210- Review for the final GHA

The final GHA does contain concepts introduced in Weeks 3, 6, 9, and 10.

1. Determine if 4 is a solution to the equation -3x - 5 = 7.

2. Solve for c in the equation 15 = 12 - 4c.

3. Solve for x in the equation 5x - 4 = 3x - 10.

4. Evaluate the expression: 18 - 5[ 8 - 2(3)] ÷ 10.

5. Determine if (2, 1) is a solution to the linear equation y = 2x - 3.

6. Simplify the expression -7(7b + 3) + 7b.

7. Solve the system of equations: 2x - 3y = 6 and 3x + 6y = 16.

8. Find the slope of a line passing thru points (5, 2) and (3, -1).

9. What is the slope of a line that is perpendicular to a line with slope 2?

10. What is the slope of a line that passes through points (5, -3) and (5, 1)?

11. Write the equation y = 3x - 2 in the Standard Form.

12. A company that makes bird feeders sells feeders for $6,00 per feeder. Fixed costs are $37,500 and the variable cost is $2.00 per feeder. How many feeder must be sold to realize a profit?

13. Write the intercept-form of the line given the slope = 1 and y-intercept = -3.

14. Write the standard form of a line given point (-5, 4) and slope = -1/5.

15. Write the slope-intercept form of the equation given point (-4, 2) parallel to the equation y = 4.

16. Find the midpoint of a line segment that have endpoints P(5, 6) and Q(3, -2).

17. Find the distance of the line segment between points (9, 5) and (3, 8).

18. Solve the system of equations x - y = -2 and 4x + 5y = 1.

19. Find the solution to the system of equations 2x + 3y = 8 and 5x - 3y = -1.

20. Evaluate the determinant:

4	-3
2	1

21. Evaluate the determinant:

	1	2	-1
	2	0	3
	-2	1	4

22. The school that Natalie attends is selling tickets to a play. On the first day of the ticket sales, the school sold 6 adult and 2 children tickets for a total of $88. The school took in $60 on the second day by selling 3 adult and 3 children tickets. Find the price of each adult and each children's ticket.

23. The cost to rent gowns from a rental place is $20 plus $88 per gown. Write the function of x, the number of gowns rented. Use your function to find out how much it would cost to rent 100 gowns.

24. Add [ 2 -4 5] + [-5 -3 6]

25. If A = [3 2 -1] , find 2A

26. In the figure to the left, the line crosses the x axis at point (3,0)

and the y axis at point (0, 2).

What is the equation of this line?

27. What is the solution of the system 5x - 2y = 2 and 5x - 2y = -4?

28. Given a profit equation of P = 4x + 3y with constraints x + y < 8, 2x + y < 10, x > 0 , y > 0, find the corner point which would give the greatest profit.

29. Suppose $1,000 is invested at 8% interest compounded annually for 3 years. Find the total value in the account after 3 years.

30. Find the simple interest on $400 at 5.2% for 6 months.

31. You have to payback a loan of $20,000 during 4 years with monthly payments. How much will be your monthly payment if the annual interest rate on this loan is 6%?

Answers

1. No 18. (-1, 1)

2. c = -3/4 19. (1, 2)

3. x = -3 20. 10

4. 17 21. -33

5. true 22. $12-adult, $8-child

6. -42b - 21 23. $8,820

7. (4, 2/3) 24. [-3 -7 11]

8. 3/2 25. [6 4 -2]

9. -1/2 26. 2x + 3y = 6

10. undefined 27. no solution

11. 3x - y = 2 28. (2, 6)

12. must sell 9376 to get a profit 29. $12,59.71

13. y = x - 3 30. $10.40

14. x + 5y = 15 31. $469.70

15. y = 2

16. (4, 2)

17. 3√ 5