MAT 209 Final Exam Answers Demo content and sample answers Perform the indicated operation: 1. 19×2 - 13x + 31 - 12×2 - 24x - (16×2 - 27x + 25) 2. 7xy2(5×3 – 4x2y2 + 3xy4) 3. (13x + 5)(9x - 13) - - - 4. (25x - 12)2 - - 5. (13a + 15b)(13a - 15b) - - 6. (25×4 - 35×3 + 45×2) / (5×2) - - - 7. (9.63 x 1035)(8.56 x 10-26) answer in scientific notation - - - 8. 2x / (x + 5) – 150 / (x2 - 25) + 3x / (x – 5) - - - - - - - 9. x / (x - y) – y / (x + y) - - - - 10. 5 / [sqrt(5) + sqrt(7)] – 7 / [sqrt(5) – sqrt(7)] - sqrt(7)][ sqrt(5) + sqrt(7)] - - - - Solve the equations for x. 11. (2x – 3)2 - 2x-3- 2x- x- 12. 125×2 - x2- x- x- 13. 8×2 + 6x - 5 - (2x-1)(4x+5)- 2x-1- x- 14. 5×2 – 4x – 3 - X- X- 15. 24×2 + 32x - 96 - 3×2 + 4x – 12- X- X- 16. 4.56×2 + 7.89x – 7.65 - X- - - X- 1

1. MAT 209 Final Exam
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MAT 209 Final Exam Answers
Demo content and sample answers

2. Perform the indicated operation:
1. 19×2 - 13x + 31 - 12×2 - 24x - (16×2 - 27x + 25)
2. 7xy2(5×3 – 4x2y2 + 3xy4)
3. (13x + 5)(9x - 13)
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4. (25x - 12)2
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5. (13a + 15b)(13a - 15b)
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6. (25×4 - 35×3 + 45×2) / (5×2)
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3. 7. (9.63 x 1035)(8.56 x 10-26) answer in scientific notation
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8. 2x / (x + 5) – 150 / (x2 - 25) + 3x / (x – 5)
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9. x / (x - y) – y / (x + y)
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10. 5 / [sqrt(5) + sqrt(7)] – 7 / [sqrt(5) – sqrt(7)]
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sqrt(7)][ sqrt(5) + sqrt(7)]

4. -
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Solve the equations for x.
11. (2x – 3)2 -
2x-3-
2x-
x-
12. 125×2 -
x2-
x-
x-
13. 8×2 + 6x - 5 -
(2x-1)(4x+5)-
2x-1-
x-
14. 5×2 – 4x – 3 -
X-

5. X-
15. 24×2 + 32x - 96 -
3×2 + 4x – 12-
X-
X-
16. 4.56×2 + 7.89x – 7.65 -
X-
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X-
17. x2 -
x2 + 3x -6-
x-
x-
18. x / (x + 7) -
x2 + 6x – 7-
the LCD for the denominators is (x+7)(x-1)
multiply both sides by (x+7)(x-1)
x(x - 1)-
x2-x-

6. x2+11x-12-
(x+12)(x-1)-
x-
when x-
So the solution to the equation is x-
19. Jim made a 350 mile trip in his car at a certain speed. If he had gone 10 mph fa
ster, he could have
made the trip in one hour less time. Find his speed.
Let x represent his speed.
The time he made a 350 mile trip is 350/x hour.
If he had gone 10 mph faster, the speed is (x+10) mph, then the time he made a 35
0 mile trip is
350/(x+10) hour, which is 1 hour less. So we can make an equation:
350/x - 350/(x+10)-
Multiply both sides by x(x+10):
350(x + 10) - 350x-
x2 + 10x - 3500-
x-
x-
Jim’s speed is 54.37 mph

7. 20. The Monahan’s garden is 20 feet by 30 feet.
They wish to lay a uniform border of pine bark
around the garden. How large a strip should they lay if they only have enough bark
to cover 420
square feet? (…and don’t tell me to buy more pine bark…:) )
let x represent the width of the border
the overall dimensions of border and garden is: (2x+20)feet by (2x+30)feet
the area of the garden is 20 * 30 -
The total area of border & garden is (420 + 600) sq ft, which can also express
ed as: (2x+20)(2x+30).
So here is the equation:
(2x+20) * (2x+30) -
4×2 + 100x + 600-
X2 + 25x -105-
(x+26)(x-1)-
X-
So the strip should be 1 foot.
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