ALLIED MAT110 MODULE 8 CHECK YOUR UNDERSTANDINGS

Question Points

1. One technique of controlling cancer is to use radiation therapy. After such a treatment, the total number of cancerous cells N, in thousands, can be estimated by the equation N = –3t2 + 6t + 220 where t is the number of days of treatment. How many days of treatment are required to kill all the cancer cells?

a. 8

b. 10

c. 12

d. 14

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2. Solve. (x – 1)2 = 5

a.

b.

c. -

d.

1

3. Solve for x. 5(x – 2)2 = 3

a.

b.

c.

d.

1

4. Solve by completing the square. x2 = 5x + 2

a.

b.

c.

d.

5. Solve the equation for x. (2x + 5)2 – 49 = 0

a.

b. 6, 1

c. -6, 1

d.

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6. Solve by completing the square. x2 – 12x + 20 = 0

a. –10, –2

b. 10, –2

c. –10, 2

d. 10, 2

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7. Determine whether the following trinomial is a perfect square. x2 + 10x + 25

a. Yes

b. No

8. Use the quadratic formula to solve the following equation. x2 = 7x – 7

a.

b.

c.

d.

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9. A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30 ft by 40 ft. The total area, garden plus walkway, is to be 1800 ft2. What must be the width of the walkway to the nearest thousandth?

a. 7.720 ft

b. 5.430 ft

c. 3.860 ft

d. 2.610 ft

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10.

Find the constant term that should be added to make the following expression a perfect-square trinomial.

x2 + 11x

a.

b. 121

c.

d.

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11. Solve. 2x2 + 5x – 1 = 0

a.

b.

c.

d. -

12. Find two consecutive positive integers such that the sum of their squares is 113.

a. 5, 6

b. 6, 7

c. 7, 8

d. 8, 9

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13. The base of a 17-ft ladder is 7 feet away from the wall. How far above the floor is the top of the ladder? Give your answer to the nearest thousandth.

a. 13.360 feet

b. 15.492 feet

c. 17.793 feet

d. 14.471 feet

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14. Solve for x.

a.

b.

c.

d.

15. Solve for x. x2 + 4 = 20

a.

b.

c.

d.