#### Question

1. [10.01] Simplify 12 times f to the sixth power times g all over 9 times f cubed..

A. 3f^2g

B. 4 times f squared times g all over 3.

C. 3f^3g

D. 4 times f cubed times g all over 3.

2. [10.01] Which factor can you cancel from the numerator and denominator to simplify 4 times x minus 16 all over 12 minus 3 times x.? [Hint: (a?x) = ? (x ? a)]

A. x ? 4

B. 4 over 3.

C. 3 over 4.

D. x + 4

3. [10.01] Simplify x squared minus 3 times x minus 18 all over x squared minus 36..

A. x minus 6 all over x minus 3.

B. x plus 6 all over x minus 6.

C. x minus 3 all over x plus 3.

D. x plus 3 all over x plus 6.

4. [10.02] Which pair of ratios forms a proportion?

A. 10 over 15. and 5 over 30.

B. 8 over 40. and 16 over 20.

C. 18 over 13. and 9 over 26.

D. 18 over 12. and 36 over 24.

5. [10.02] A map has a scale of 3 km to 2 inches. Which ratio of measures forms a proportion with the map's scale of km to inches?

A. 7 over 8.

B. 8 over 12.

C . 6 over 5.

D. 15 over 10.

6. [10.02] Solve the proportion 35 over 28 equals x over 4.. What is the value of x?

A. 3

B. 5

C. 7

D. 11

7. [10.02] Solve the proportion x over x plus 1 equals 4 over x plus 4.. What is the value(s) of x?

A. x = ?2

B. x = ?2 and x = 2

C. x = ?1 and x = ?4

D. x = 4

8. [10.03] Which number equals the square root of 1, 875.?

A. 5 the square root of 15.

B. 5 the square root of 3.

C. 25 the square root of 3.

D. 15 the square root of 15.

9. [10.03] Which expression is the simplified form of the square root r to the forty-ninth power.?

A. r^7 the square root of r.

B. r^24

C. r^24 the square root of r.

D. r^7

10. [10.03] Which expression is the simplified form of the square root 338 times w to the eighteenth power.?

A. 13w^3 the square root 2 times w.

B. 2w^9 the square root 13 times w.

C. 2w^3 the square root 13 times w.

D. 13w^9 the square root of 2.

11. [10.04] What is the exact value of the expression the square root of 7. + 2 the square root of 6. + 3 the square root of 7.?

A. the square root of 20.

B. 6 the square root of 20.

C. 3 the square root of 7. + 2 the square root of 6.

D. 4 the square root of 7. + 2 the square root of 6.

12. [10.04] What is the exact value of the expression the square root of 294. ? the square root of 24. + the square root 54.? Simplify if possible.

A. 8 the square root of 2.

B. 8 the square root of 6.

C. 12 the square root of 2.

D. 12 the square root of 6.

13. [10.04] What is the exact value of the expression the square root of 16 times y to the sixth power. + 9 the square root of y to the eighth power. ? 3the square root of y to the sixth power. ? the square root of y to the eighth power.? Simplify if possible.

A. y^3 + 8y^4

B. 9y^2

C. 13y^3 + 2y^4

D. 9y^7

14. [10.06] What is the product of 2 the square root of 9 times d. ? 3d the square root of 5.? Simplify if possible.

A. 9d the square root of 5.

B. 18d the square root of 5 times d.

C. 6d the square root of 3 times d.

D. 3d the square root of 15 times d.

15. [10.06] What is the product of 3the square root of u. (the square root of 448. + 4the square root of 7.)? Simplify if possible.

A. 24 the square root of 7 times u. + 4the square root of 7.

B. 204 the square root of 7 times u.

C. 24u the square root of 7.

D. 36 the square root of 7 times u.

16. [10.06] The area of a rectangle is the product of width and length. If a rectangle has length 12mthe square root of 21 times m. and width the square root of 16 times m., which of the following is the area of the rectangle?

A. 192m the square root of 21 times m.

B. 192m^2 the square root of 21.

C. 24m the square root of 21 times m.

D. 48m^2 the square root of 21.

17. [10.07] What is the exact value of the square root of the quantity 75 over 36.?

A. 5 the square root of 3 all over 6.

B. 25 the square root of 3 all over 9.

C. 5 the square root 3 all over 9.

D. 9 the square root of 3 all over 4.

18. [10.07] What is the exact value of the square root of 38 over 2 the square root of 6.?

A. 19 the square root of 57 all over 6.

B. 2 the square root of 57 all over 3.

C. the square root of 57 over 3.

D. the square root of 57 over 6.

19. [10.07] What is the exact value of 5 times z all over the square root of z to the fifth power.?

A. 5 the square root of z all over z cubed.

B. 5 the square root of z all over z squared.

C. 5 the square root of z all over z to the fourth power.

D. 5 the square root of z all over z.

1)

12 times f to the sixth power times g all over 9 times f cubed..

12 * f^6 * g / (9 * f^3)

4 * f^6 * g / (3 * f^3)

4 * f^3 * g / (3) <====== D

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2)

(4x - 16) / (12 - 3x)

4(x - 4) / 3(4 - x)

4(x - 4) / -3(x - 4)

(-4/3) <====== well, it is suppose to be negative.

anwer is either -4/3 or the factor (x - 4)

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3)

(x^2 - 3x - 18) / (x^2 - 36)

(x - 6)(x + 3) / (x - 6)(x + 6)

(x + 3) /(x + 6) <===== D

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4)

A. 10 over 15. and 5 over 30.

10/15 = 5/30 ====> 2/3 = 1/6 ====> 6*2 = 3*1 ====> NO

B. 8 over 40. and 16 over 20.

8/40 = 16/20 ====> 1/5 = 4/5 ====> 5*1 = 5*4 ====> NO

C. 18 over 13. and 9 over 26.

18/13 = 9/26 ====> 18 * 26 = 13 * 9 ====> 468 = 117 ===> NO

D. 18 over 12. and 36 over 24.

18/12 = 36/24 ====> 3/2 = 3/2 ====> YES

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