**MATH 209 FINAL EXAM_20 Questions_A+_Perfect Answer **

**MATH 209 FINAL EXAM_20 Questions_A+_Perfect Answer **

MATH 209 FINAL EXAM_20 Questions_A+_Perfect Answer

MATH 209 — FINAL EXAM

There are 20 questions.

For questions 1 through 5, perform the indicated operations. If possible, simplify the answer.

1. [2 – 5(6 – 2)²] ÷ (8 – 4•3)

2.

Expand:

27x^6 * 2x^-3 / 6x^3

3.

Common denominators:

3x/x + 3/x

————-

4x/x + 4/x

4.

Factor:

(y-3)(y-1) / (y-3)(y+3)

—————————

(y+6)(y+1) / (y+6)(y-3)

5.

= 1 / 16^3/4

6. Solve the equation: T = (3a + b)/2 for a.

7. Factor completely: x³ + 1

For problems 8 – 11, solve each equation, inequality or system of equations. Choose whatever method you like, but remember to show your methodology along with your answer.

8. (x + 2)/3 = (x – 1)/4

9.

Square both sides:

x-1 = x^2-2x+1

10. (7x –6)² = 48

11. a) 170 is what percent of 20?

b) 20 is what percent of 170?

12. Select the graph that best satisfies the equation: y = x² – 2x – 3

U shape, through (-1, 0) and (3, 0)

13. Select the equation that best fits the following graph:

14. Write a quadratic equation for which the following are solutions for x: 7 and – 3,

15. Write a quadratic equation for which the following are solutions for x: ± 3i.

Questions 16 through 20 are word problems. Take your time to make sure that your equations fit the words before you start solving them.

16. Hector can shovel show off the sidewalks in three hours (He doesn’t live in Southern California, of course). Oliver can shovel snow off the same sidewalks in 2 hours. How long will it take them to shovel the snow off

the sidewalks if they work together?

17. Park rangers catch, tag and then release 140 elk back into a National Park. One month later, they’re able to round up 130 elk, and find that 91 of them have been tagged. Assuming the ratio of tagged elk to the total in the sample that was rounded up is the same as the ratio of all tagged elk to the total elk population in the park, how many elk are in the park? By the way, they’re beautiful animals. I’ve seen them at the Grand Canyon.

18. Staying on the animal theme, a tourist visits the zoo, and is interested in knowing how many birds and lions are on display. The Zookeeper tells him that between birds and lions there are 30 heads and 100 feet. From this information, can you tell how many birds and lions there are? If so, how many birds and lions are in this zoo?

19. In a triangle, the measure of the second angle is 40º less than the measure of the first angle. The measure of the third angle is twice the first. What are the measures of each of the angles in the triangle?

20. A school with 125 teachers and 4650 students wants to maintain a student-to-teacher ratio of 30:1. How many teachers do they need to hire in order to meet that ratio?

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