ASSIGNMENT 01



ASSIGNMENT 6

MA240 College Algebra

Directions: Be sure to make an electronic copy of your answer before submitting it to Ashworth College for grading. Unless otherwise stated, answer in complete sentences, and be sure to use correct English spelling and grammar. Sources must be cited in APA format. Your response should be a minimum of one (1) single-spaced page to a maximum of two (2) pages in length; refer to the "Assignment Format" page for specific format requirements.

NOTE: Show your work on the problems.

1. Determine whether the equation defines a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y.

x|y| = x + 9

2. Use the graph of the function to estimate:

a. f(2)

b. f(–4)

c. All x such that f(x) = 0

3. For the following graph:

a. Find the domain of f.

b. Find the range of f.

c. Find the x-intercepts.

d. Find the y-intercept.

e. Find the intervals over which f is increasing.

f. Find the intervals over which f is decreasing.

g. Find the intervals over which f is constant.

h. Find any points of discontinuity.

4. Use the following to answer questions a-d:

f(x) = x2 + x and g(x) = x – 5

a. Find h(x) = (f ◦ g)(x).

b. State the domain of h(x) = (f ◦ g)(x).

c. Find h(x) = (g ◦ f)(x).

d. State the domain of h(x) = (g ◦ f)(x).

5. The graph of the polynomial function P(x) is shown.

a. List the real zeros of P(x).

b. List the turning points of P(x).

c. State the left and right behavior of P(x).

6. $2,350 is invested in account paying 9% compounded semiannually. How much will the account be worth after 8 years? Show your work.

7. Change each exponential form to an equivalent logarithmic form:

a. 32 = 25

b. [pic] = 25–3/2

c. 12 = 1441/2

8. Change each logarithmic form to an equivalent exponential form:

a. log 3 81 = 4

b. log 10 0.0001 = –4

c. [pic]

This is the end of Assignment 6.

|MULTIPLE CHOICE QUESTIONS |

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|Part 1 of 1 - |

|Question 1 of 20 |

|5.0 Points |

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|[pic]Which property of the real numbers is illustrated by the following statement? |

|w + bn = w + nb |

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|[pic] |

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|A. Commutative property of multiplication |

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|[pic] |

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|B. Associative property of addition |

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|[pic] |

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|C. Associative property of multiplication |

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|[pic] |

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|D. Distributive property |

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|Question 2 of 20 |

|5.0 Points |

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|[pic]Which property of the real numbers is illustrated by the following statement? |

|4(3x) = (4 ∙ 3)x |

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|[pic] |

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|A. Commutative property of multiplication |

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|[pic] |

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|B. Associative property of addition |

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|[pic] |

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|C. Associative property of multiplication |

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|[pic] |

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|D. Distributive property |

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|Reset Selection |

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|Question 3 of 20 |

|5.0 Points |

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|[pic]Which property of the real numbers is illustrated by the following statement? |

|8(c + ax) + 0 = 8(c + ax) |

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|[pic] |

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|A. Additive identity property |

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|[pic] |

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|B. Associative property of addition |

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|[pic] |

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|C. Associative property of multiplication |

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|[pic] |

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|D. Distributive property |

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|Question 4 of 20 |

|5.0 Points |

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|[pic]Simplify: |

|[(0 + 6) ÷ 12]–1 |

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|[pic] |

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|A. 0 |

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|[pic] |

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|B. 1 |

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|[pic] |

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|C. 2 |

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|[pic] |

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|D. -1 |

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|Question 5 of 20 |

|5.0 Points |

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|[pic]Add: |

|3/4 + 1/8 |

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|[pic] |

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|A. 9/8 |

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|[pic] |

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|B. 3/4 |

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|[pic] |

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|C. 1/2 |

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|[pic] |

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|D. 7/8 |

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|Question 6 of 20 |

|5.0 Points |

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|[pic]Multiply: |

|2/9 x 4/5 |

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|[pic] |

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|A. 8/45 |

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|[pic] |

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|B. 4/7 |

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|[pic] |

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|C. 360/45 |

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|[pic] |

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|D. 5/18 |

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|Question 7 of 20 |

|5.0 Points |

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|[pic]Simplify: |

|(5/9)-1 + 3-1 |

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|[pic] |

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|A. -32/9 |

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|[pic] |

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|B. -5/3 |

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|[pic] |

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|C. 32/15 |

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|[pic] |

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|D. 2/3 |

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|Question 8 of 20 |

|5.0 Points |

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|[pic]Write the set using the listing method. |

|{x | x is an odd integer between –6 and 0} |

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|[pic] |

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|A. {–5, –4, –3, –2, –1} |

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|[pic] |

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|B. {–6, –4, –2, 0} |

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|[pic] |

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|C. {–5, –3, –1} |

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|[pic] |

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|D. {–6, –5, –4, –3, –2, –1, 0} |

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|Question 9 of 20 |

|5.0 Points |

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|[pic]Evaluate:(–8)2 |

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|[pic] |

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|A. 64 |

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|[pic] |

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|B. -64 |

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|[pic] |

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|C. 16 |

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|[pic] |

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|D. -16 |

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|Question 10 of 20 |

|5.0 Points |

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|[pic]Evaluate:(-3)3 |

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|[pic] |

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|A. 9 |

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|[pic] |

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|B. -9 |

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|[pic] |

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|C. -27 |

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|[pic] |

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|D. 27 |

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|Question 11 of 20 |

|5.0 Points |

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|[pic]Evaluate:64-2/3 |

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|[pic] |

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|A. -1/16 |

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|[pic] |

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|B. 1/16 |

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|[pic] |

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|C. -128/3 |

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|[pic] |

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|D. Irrational |

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|Question 12 of 20 |

|5.0 Points |

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|[pic]Evaluate:1–4 + 5–1 |

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|[pic] |

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|A. -6/5 |

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|[pic] |

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|B. 6/5 |

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|[pic] |

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|C. -6 |

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|[pic] |

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|D. -9 |

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|Question 13 of 20 |

|5.0 Points |

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|[pic]Simplify and express your answer using positive exponents only. |

|m8m–14 |

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|[pic] |

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|A. m6 |

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|[pic] |

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|B. -m112 |

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|C. 1/m112 |

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|[pic] |

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|D. 1/m6 |

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|Question 14 of 20 |

|5.0 Points |

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|[pic]Write 75,200,000 in scientific notation. |

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|[pic] |

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|A. 7.52 x 107 |

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|[pic] |

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|B. 7.52 x 106 |

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|[pic] |

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|C. 75.2 x 107 |

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|[pic] |

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|D. 75.2 x 106 |

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|Question 15 of 20 |

|5.0 Points |

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|[pic]Write 3.88 x 105 in decimal notation. |

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|A. 38,800 |

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|B. 388,000 |

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|C. 3,880,000 |

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|[pic] |

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|D. 38,800,000 |

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|Question 16 of 20 |

|5.0 Points |

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|[pic]The distance from a star to a planet is 9.1 X 1018 m. How long does it take light, traveling at 1016 m/year, to travel from |

|the star to the planet? |

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|[pic] |

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|A. 9144 years |

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|[pic] |

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|B. 9 years |

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|[pic] |

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|C. 910 years |

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|[pic] |

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|D. 9264 years |

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|Question 17 of 20 |

|5.0 Points |

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|[pic]Evaluate to four significant digits using a calculator. |

|67–3/5 |

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|[pic] |

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|A. 12.4636 |

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|[pic] |

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|B. –12.4636 |

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|[pic] |

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|C. 0.0802 |

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|[pic] |

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|D. –0.0802 |

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|Question 18 of 20 |

|5.0 Points |

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|[pic]Write in rational exponent form. Do not simplify. |

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|[pic] |

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|[pic] |

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|A. (–175)1/2 |

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|[pic] |

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|B. –1751/2 |

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|[pic] |

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|C. 175–1/2 |

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|[pic] |

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|D. –175–1/2 |

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|Question 19 of 20 |

|5.0 Points |

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|[pic]Simplify: |

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|[pic] |

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|[pic] |

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|A. 18x2y4 |

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|[pic] |

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|B. 6x2y8 |

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|[pic] |

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|C. 18x2y8 |

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|[pic] |

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|D. 6x2y4 |

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|Question 20 of 20 |

|5.0 Points |

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|[pic]Simplify: |

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|[pic] |

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|[pic] |

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|A. 15a5b2 |

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|[pic] |

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|B. 5a5b |

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|[pic] |

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|C. 3a5b |

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|[pic] |

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|D. 2ab5 |

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|Part 1 of 1 - |

|Question 1 of 20 |

|5.0 Points |

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|[pic]The width of a rectangle is 9 inches less than 2 times the length. If x represents the length, write an algebraic expression|

|in terms of x that represents the area of the rectangle. Simplify the expression. |

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|[pic] |

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|A. 9x2 – 2x |

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|B. 9x2 + 2x |

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|[pic] |

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|C. 2x2 – 9x |

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|[pic] |

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|D. 2x2 + 9x |

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|Question 2 of 20 |

|5.0 Points |

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|[pic]Add: |

|3p2 – 5p – 4 and 9p2 + 10p – 2 |

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|[pic] |

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|A. 12p2 + 15p – 6 |

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|[pic] |

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|B. 12p2 + 5p – 2 |

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|[pic] |

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|C. 12p2 + 5p – 6 |

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|[pic] |

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|D. 12p2 + 15p – 2 |

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|Question 3 of 20 |

|5.0 Points |

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|[pic]Is the algebraic expression a polynomial? If so, give its degree. |

|9x3 + 6x6 + 8 |

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|[pic] |

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|A. Yes; degree = 9 |

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|[pic] |

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|B. Yes; degree = 8 |

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|C. Yes; degree = 6 |

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|[pic] |

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|D. This algebraic expression is not a polynomial. |

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|Question 4 of 20 |

|5.0 Points |

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|[pic]Perform the indicated operations and simplify. |

|5x – 4x[8 – 3(x – 2)] |

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|[pic] |

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|A. 6x2 – 3x |

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|[pic] |

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|B. 12x2 – 51x |

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|[pic] |

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|C. 12x2 + 5x + 6 |

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|[pic] |

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|D. 12x2 + 5x – 6 |

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|Question 5 of 20 |

|5.0 Points |

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|[pic]Multiply and simplify. |

|(3x – 1)(2x + 5) |

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|[pic] |

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|A. 6x2 – 13x – 5 |

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|[pic] |

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|B. 6x2 – 17x – 5 |

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|[pic] |

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|C. 6x2 + 13x – 5 |

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|[pic] |

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|D. 6x2 + 17x – 5 |

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|Question 6 of 20 |

|5.0 Points |

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|[pic]Multiply and simplify: |

|(5x – 3y)2 |

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|[pic] |

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|A. 25x2 – 30xy + 9y2 |

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|[pic] |

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|B. 25x2 – 9y2 |

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|[pic] |

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|C. 25x2 – 30xy – 9y2 |

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|[pic] |

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|D. 25x2 + 9y2 |

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|Question 7 of 20 |

|5.0 Points |

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|[pic]Multiply and simplify: |

|(3x2 – 2x – 1)(x2 + x + 5) |

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|[pic] |

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|A. 3x4 + 2x3 + 12x2 – 11x – 5 |

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|[pic] |

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|B. 3x4 + x3 + 12x2 – 10x – 5 |

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|[pic] |

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|C. 3x4 + x3 + 12x2 – 11x – 5 |

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|[pic] |

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|D. 3x4 + x3 + 14x2 – 11x – 5 |

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|Question 8 of 20 |

|5.0 Points |

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|[pic]Subtract 4x2 – 5x from the sum of 9x2 – 2 and 6x – 1. |

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|[pic] |

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|A. –5x2 – x + 1 |

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|[pic] |

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|B. –5x2 + 11x – 1 |

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|[pic] |

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|C. 5x2 + x – 3 |

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|[pic] |

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|D. 5x2 + 11x – 3 |

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|Question 9 of 20 |

|5.0 Points |

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|[pic]Factor completely relative to the integers. |

|x2 – 8x + x – 8 |

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|[pic] |

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|A. (x + 8)(x – 1) |

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|[pic] |

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|B. (x – 8)(x – 1) |

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|[pic] |

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|C. (x + 1)(x + 8) |

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|[pic] |

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|D. (x – 8)(x + 1) |

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|Question 10 of 20 |

|5.0 Points |

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|[pic]Factor completely relative to the integers. |

|25x2 – 5x – 2 |

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|[pic] |

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|A. (5x – 2)(5x + 1) |

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|[pic] |

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|B. (5x + 2)(5x – 1) |

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|[pic] |

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|C. (25x – 2)(x + 1) |

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|[pic] |

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|D. (5x + 1)(5x – 2) |

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|Question 11 of 20 |

|5.0 Points |

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|[pic]Factor completely relative to the integers. |

|49a2b – b3 |

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|[pic] |

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|A. (7a + b2)(7a – b) |

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|[pic] |

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|B. b(7a – b)2 |

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|[pic] |

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|C. b(7a + b)(7a – b) |

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|[pic] |

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|D. Prime, doesn't factor |

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|Question 12 of 20 |

|5.0 Points |

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|[pic]Factor completely relative to the integers. |

|8a3 + 27 |

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|[pic] |

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|A. (2a – 3)(4a2 + 9) |

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|[pic] |

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|B. (2a – 3)(4a2 + 6a + 9) |

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|[pic] |

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|C. (2a + 3)(4a2 – 6a + 9) |

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|[pic] |

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|D. (2a – 3)(4a2 – 6a + 9) |

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|Question 13 of 20 |

|5.0 Points |

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|[pic]Reduce to lowest terms. |

|[pic] |

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|[pic] |

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|A. -x - 8 |

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|B. x – 8 |

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|[pic] |

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|C. x + 8 |

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|[pic] |

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|D. -x + 8 |

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|Question 14 of 20 |

|5.0 Points |

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|[pic]Subtract and reduce to the lowest terms: |

|2/4 - 1/6 |

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|[pic] |

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|A. 1/3 |

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|[pic] |

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|B. 1/2 |

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|[pic] |

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|C. 4/12 |

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|[pic] |

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|D. 2/6 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 15 of 20 |

|5.0 Points |

| |

|[pic]Perform the indicated operations and reduce to lowest terms. |

|[pic] |

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|[pic] |

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|A. a3/12 |

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|[pic] |

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|B. b2/12a3 |

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|[pic] |

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|C. b2/12 |

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|[pic] |

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|D. 4b2/3 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 16 of 20 |

|5.0 Points |

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|[pic]Divide and reduce to lowest terms. |

|[pic] |

| |

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|[pic] |

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|A. (x + 5)(x + 3) |

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|[pic] |

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|B. (x + 5)(x – 3) |

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|[pic] |

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|C. (x - 5)(x - 3) |

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|[pic] |

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|D. (x - 5)(x + 3) |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 17 of 20 |

|5.0 Points |

| |

|[pic]Factor completely relative to the integers. |

|x2 + 36 |

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|[pic] |

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|A. (x + 6)(x – 6) |

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|[pic] |

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|B. (x + 1)(x + 36) |

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|[pic] |

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|C. (x + 6)2 |

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|[pic] |

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|D. Prime |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 18 of 20 |

|5.0 Points |

| |

|[pic]Reduce to lowest terms: |

|18/54 |

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|[pic] |

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|A. 9/27 |

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|[pic] |

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|B. 1/4 |

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|[pic] |

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|C. 1/3 |

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|[pic] |

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|D. 2/3 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 19 of 20 |

|5.0 Points |

| |

|[pic]Factor completely relative to the integers: |

|16x2 + 40x + 25 |

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|[pic] |

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|A. (4x + 5)2 |

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|[pic] |

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|B. (4x – 5)(4x + 5) |

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|[pic] |

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|C. (16x + 5)(x + 5) |

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|[pic] |

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|D. (4x + 1 )(4x + 25) |

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|Reset Selection |

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|Question 20 of 20 |

|5.0 Points |

| |

|[pic]Factor out, relative to the integers, all factors common to all terms. |

|49x4 – 70x3 + 21x2 |

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|[pic] |

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|A. 7x2(7x2 – 70x + 21) |

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|[pic] |

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|B. 7x2(7x2 – 10x + 3) |

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|[pic] |

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|C. 49x2(x2 – 10x + 3) |

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|[pic] |

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|D. 49x(x3 – 70x2 + 21x) |

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|Reset Selection |

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|Part 1 of 1 - |

| |

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|Question 1 of 20 |

|5.0 Points |

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|[pic]Solve: |

|9x + 8 = 2x + 8 |

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|[pic] |

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|A. -1 |

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|[pic] |

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|B. 0 |

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|[pic] |

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|C. 1 |

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|[pic] |

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|D. 2 |

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|Reset Selection |

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|Question 2 of 20 |

|5.0 Points |

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|[pic]Solve: |

|[pic] |

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|[pic] |

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|A. 16 |

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|[pic] |

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|B. -16 |

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|[pic] |

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|C. 2 |

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|[pic] |

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|D. –2 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 3 of 20 |

|5.0 Points |

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|[pic]Find a number such that 54 more than one-half the number is twice the number. |

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|[pic] |

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|A. 36 |

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|[pic] |

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|B. 27 |

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|[pic] |

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|C. 15 |

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|[pic] |

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|D. 32 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 4 of 20 |

|5.0 Points |

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|[pic]The length of a rectangle is 2 cm more than twice its width. If the perimeter of the rectangle is 40 cm, find the length of |

|the rectangle. |

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|[pic] |

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|A. 6 cm |

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|[pic] |

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|B. 9 cm |

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|[pic] |

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|C. 11 cm |

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|[pic] |

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|D. 14 cm |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 5 of 20 |

|5.0 Points |

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|[pic]The sale price of an item after a 15% discount is $102. What was the price before the discount? |

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|[pic] |

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|A. $117 |

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|[pic] |

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|B. $125 |

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|[pic] |

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|C. $120 |

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|[pic] |

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|D. $110 |

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|Reset Selection |

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|Question 6 of 20 |

|5.0 Points |

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|[pic]How much pure antifreeze must be added to 12 gallons of 20% antifreeze to make a 40% antifreeze solution? |

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|[pic] |

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|A. 2 gallons |

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|[pic] |

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|B. 4 gallons |

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|[pic] |

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|C. 6 gallons |

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|[pic] |

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|D. 8 gallons |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 7 of 20 |

|5.0 Points |

| |

|[pic]One computer printer can print a company's mailing labels in 40 minutes. A second printer would take 60 minutes to print the|

|labels. How long would it take the two printers, operating together, to print the labels? |

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|[pic] |

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|A. 30 minutes |

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|[pic] |

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|B. 24 minutes |

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|[pic] |

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|C. 50 minutes |

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|[pic] |

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|D. 32 minutes |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 8 of 20 |

|5.0 Points |

| |

|[pic]Rewrite the interval in inequality notation. |

| |

|(-3, [pic]) |

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|[pic] |

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|A. x > -3 |

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|[pic] |

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|B. x < -3 |

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|[pic] |

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|C. x [pic]-3 |

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|[pic] |

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|D. x [pic]-3 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 9 of 20 |

|5.0 Points |

| |

|[pic]Choose the graph of the inequality on a real number line. |

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|-4 [pic]x < 1 |

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|[pic] |

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|A. [pic] |

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|[pic] |

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|B. [pic] |

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|[pic] |

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|C. [pic] |

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|[pic] |

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|D. [pic] |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 10 of 20 |

|5.0 Points |

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|[pic]Fill in the blanks with > or < to make the resulting statement true. |

|-4 _____ -6 and -4 - 5 _____ -6 - 5 |

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|[pic] |

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|A. , > |

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|[pic] |

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|C. |

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|[pic] |

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|D. >, < |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 11 of 20 |

|5.0 Points |

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|[pic]Write as a single interval, if possible. (–2, 4] [pic][0, 5) |

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|[pic] |

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|A. (–2, 5) |

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|[pic] |

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|B. [0, 4] |

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|[pic] |

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|C. (–2, 4] |

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|[pic] |

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|D. [0, 5) |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 12 of 20 |

|5.0 Points |

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|[pic]A musician is planning to market a CD. The fixed costs are $330 and the variable costs are $5 per CD. The wholesale price of|

|the CD will be $8. For the artist to make a profit, revenues must be greater than costs. How many CDs, x, must be sold for the |

|musician to make a profit? |

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|[pic] |

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|A. x > 100 |

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|[pic] |

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|B. x > 110 |

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|[pic] |

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|C. x > 120 |

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|[pic] |

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|D. x > 130 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 13 of 20 |

|5.0 Points |

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|[pic]Evaluate: |

||-5 - (-3)| |

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|[pic] |

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|A. 3 |

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|[pic] |

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|B. 5 |

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|[pic] |

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|C. 1 |

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|[pic] |

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|D. 2 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 14 of 20 |

|5.0 Points |

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|[pic]Find the distance between –1 and 1. |

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|[pic] |

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|A. 1 |

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|[pic] |

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|B. 0 |

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|[pic] |

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|C. 2 |

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|[pic] |

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|D. 3 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 15 of 20 |

|5.0 Points |

| |

|[pic]Solve: |

||x - 4| = 2 |

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|[pic] |

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|A. 6, -2 |

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|[pic] |

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|B. 6, 2 |

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|[pic] |

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|C. -6, 2 |

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|[pic] |

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|D. -6, -2 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 16 of 20 |

|5.0 Points |

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|[pic]Solve. Write the solution in interval notation. |

||x + 4| 6 |

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|[pic] |

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|A. (-[pic], –10) [pic](2, [pic]) |

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|[pic] |

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|B. (-[pic], –10] [pic][2, [pic]) |

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|[pic] |

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|C. (-10, 2) |

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|[pic] |

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|D. [-10, 2] |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 17 of 20 |

|5.0 Points |

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|[pic]Write as an absolute value inequality. |

|x is more than 7 units from 3 |

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|[pic] |

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|A. |x - 3| > 7 |

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|[pic] |

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|B. |x - 3| > 7 |

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|[pic] |

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|C. |x + 3| > 7 |

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|[pic] |

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|D. |x + 3| > 7 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 18 of 20 |

|5.0 Points |

| |

|[pic]Solve: |

||2x – 7| = 3 |

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|[pic] |

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|A. 5, 2 |

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|[pic] |

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|B. 5, –2 |

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|[pic] |

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|C. –5, 2 |

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|[pic] |

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|D. –5, –2 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 19 of 20 |

|5.0 Points |

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|[pic]Solve: |

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|[pic] |

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|[pic] |

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|A. x < –3 |

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|[pic] |

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|B. x < –6 or x > –3 |

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|[pic] |

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|C. 3 < x < 6 |

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|[pic] |

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|D. x < 3 or x > 6 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

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|Question 20 of 20 |

|5.0 Points |

| |

|[pic]Solve: |

||x + 3| = 2x + 1 |

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|[pic] |

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|A. 2 |

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|[pic] |

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|B. -4/3 |

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|[pic] |

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|C. 2, -4/3 |

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|[pic] |

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|D. 2, 4/3 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

| |

|Part 1 of 1 - |

|Question 1 of 20 |

|5.0 Points |

| |

|[pic]Multiply. Write the result in standard form. |

|(5 - i)(4 + 3i) |

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|[pic] |

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|A. 11 + 23i |

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|[pic] |

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|B. 23 + 11i |

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|[pic] |

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|C. 20 - 3i |

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|[pic] |

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|D. 9i |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 2 of 20 |

|5.0 Points |

| |

|[pic]Subtract. Write the results in standard form. |

|(-8 - 4i) - (-5 - 3i) |

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|[pic] |

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|A. -3 - i |

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|[pic] |

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|B. -3 - 7i |

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|[pic] |

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|C. -10i |

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|[pic] |

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|D. -4i |

| |

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|Reset Selection |

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|Question 3 of 20 |

|5.0 Points |

| |

|[pic]Multiply. Write the result in standard form. |

|4i(–10 + 5i) |

| |

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|[pic] |

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|A. –35i |

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|[pic] |

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|B. –60i |

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|[pic] |

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|C. –20 – 40i |

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|[pic] |

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|D. 20 – 40i |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 4 of 20 |

|5.0 Points |

| |

|[pic]Convert imaginary numbers to standard form, perform the indicated operation, and express the answer in standard form. |

|[pic] |

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| |

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|[pic] |

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|A. 1 + i |

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|[pic] |

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|B. 1 - i |

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|[pic] |

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|C. 1 + 49i |

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|[pic] |

| |

| |

|D. 1 - 49i |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 5 of 20 |

|5.0 Points |

| |

|[pic]Convert imaginary numbers to standard form, perform the indicated operation, and express the answer in standard form. |

| |

|[pic] |

| |

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|[pic] |

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|A. 3 – 2i |

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|[pic] |

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|B. 3 + 2i |

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|[pic] |

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|C. -3 - 2i |

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|[pic] |

| |

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|D. -3 + 2i |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 6 of 20 |

|5.0 Points |

| |

|[pic]Divide and write your answer in standard form. |

| |

|[pic] |

| |

| |

| |

|[pic] |

| |

| |

|A. -3 - 2i |

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|[pic] |

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|B. 3 - 2i |

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|[pic] |

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|C. -3 + 2i |

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|[pic] |

| |

| |

|D. 3 + 2i |

| |

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|Reset Selection |

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|Question 7 of 20 |

|5.0 Points |

| |

|[pic]Solve for x and y. |

|(3x + 4) + (5y -1) = 10 - 16i |

| |

| |

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|[pic] |

| |

| |

|A. x = 2, y = -3 |

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|[pic] |

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|B. x = 1, y = -2 |

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|[pic] |

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| |

|C. x = 3, y = 2 |

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|[pic] |

| |

| |

|D. x = -3, y = 1 |

| |

| |

|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 8 of 20 |

|5.0 Points |

| |

|[pic]Solve for x and y. |

| |

|[pic] |

| |

| |

| |

|[pic] |

| |

| |

|A. x = 2, y = -4 |

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|[pic] |

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| |

|B. x = 1, y = -2 |

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|[pic] |

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|C. x = 3, y = -4 |

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|[pic] |

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| |

|D. x = 1, y = -4 |

| |

| |

|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 9 of 20 |

|5.0 Points |

| |

|[pic]Solve by factoring. |

|3x2 = -18x |

| |

| |

| |

|[pic] |

| |

| |

|A. 0, -6 |

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|[pic] |

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|B. 0, 6 |

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|[pic] |

| |

| |

|C. 6, -6 |

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|[pic] |

| |

| |

|D. 2, 6 |

| |

| |

|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 10 of 20 |

|5.0 Points |

| |

|[pic]Use the discriminant to determine the number of real roots the equation has. |

|3x2 – 5x + 1 =0 |

| |

| |

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|[pic] |

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|A. One real root (a double root) |

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|[pic] |

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|B. Two distinct real roots |

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|[pic] |

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|C. Three real roots |

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|[pic] |

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| |

|D. None (two imaginary roots) |

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| |

|Reset Selection |

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|Question 11 of 20 |

|5.0 Points |

| |

|[pic]Use the discriminant to determine the number of real roots the equation has. |

|7x2 + 3x + 1 =0 |

| |

| |

| |

|[pic] |

| |

| |

|A. One real root (a double root) |

| |

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|[pic] |

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| |

|B. Two distinct real roots |

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|[pic] |

| |

| |

|C. Three real roots |

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|[pic] |

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|D. None (two imaginary roots) |

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|Question 12 of 20 |

|5.0 Points |

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|[pic]The product of two consecutive positive even integers is 360. Find the integers. |

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|[pic] |

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|A. 18 and 20 |

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|[pic] |

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|B. 10 and 12 |

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|[pic] |

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|C. 14 and 16 |

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|[pic] |

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|D. 16 and 18 |

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|Question 13 of 20 |

|5.0 Points |

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|[pic]Two trains travel at right angles to each other after leaving the same train station at the same time. One hour later they |

|are 100 miles apart. If one travels 20 miles per hour faster than the other, what is the rate of the faster train? |

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|[pic] |

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|A. 60 mph |

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|[pic] |

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|B. 70 mph |

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|[pic] |

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|C. 80 mph |

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|[pic] |

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|D. 90 mph |

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|Question 14 of 20 |

|5.0 Points |

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|[pic]A boater travels 12 miles upstream against a 2 mi/h current, then returns downstream to the starting point. If the entire |

|trip took 8 hours, what is the rate of the boat in still water? |

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|[pic] |

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|A. 3 mi/h |

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|[pic] |

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|B. 4 mi/h |

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|[pic] |

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|C. 5 mi/h |

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|[pic] |

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|D. 6 mi/h |

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|Question 15 of 20 |

|5.0 Points |

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|[pic]Solve: |

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|[pic] |

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|[pic] |

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|A. 2 |

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|[pic] |

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|B. 0 |

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|[pic] |

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|C. -2 |

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|[pic] |

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|D. No solution |

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|Question 16 of 20 |

|5.0 Points |

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|[pic]Solve: |

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|[pic] |

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|[pic] |

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|A. 0, -1/9 |

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|[pic] |

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|B. 0, 1/9 |

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|[pic] |

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|C. 0 |

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|[pic] |

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|D. No solution |

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|Question 17 of 20 |

|5.0 Points |

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|[pic]Solve. |

||x + 5| = 1 - 3x |

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|[pic] |

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|A. 3 |

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|[pic] |

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|B. -1 |

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|[pic] |

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|C. -1, 3 |

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|[pic] |

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|D. No solution |

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|Question 18 of 20 |

|5.0 Points |

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|[pic]Solve. |

||10x - 1| = x - 10 |

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|[pic] |

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|A. -1, 1 |

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|[pic] |

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|B. 1 |

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|[pic] |

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|C. -1 |

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|[pic] |

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|D. No solution |

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|Question 19 of 20 |

|5.0 Points |

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|[pic]Solve. |

|5x2/3 - 13x1/3 - 6 = 0 |

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|[pic] |

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|A. -14/122, 25 |

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|[pic] |

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|B. -8/125, 27 |

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|[pic] |

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|C. 15/123, 26 |

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|[pic] |

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|D. -8/12, 20 |

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|Question 20 of 20 |

|5.0 Points |

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|[pic]Solve. |

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|(x2 – x)2 – 14(x2 – x) + 24 = 0 |

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|[pic] |

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|A. 3, 1, -2, -4 |

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|[pic] |

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|B. 1, -3, -4, 2 |

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|[pic] |

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|C. -3, -1, 2, 4 |

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|[pic] |

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|D. -2, 3, -4, 1 |

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|Part 1 of 1 - |

|Question 1 of 20 |

|5.0 Points |

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|[pic]Plot the point (–4, 3) in a rectangular coordinate system. |

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|[pic] |

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|A. [pic] |

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|[pic] |

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|B. [pic] |

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|[pic] |

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|C. [pic] |

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|[pic] |

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|D. [pic] |

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|Question 2 of 20 |

|5.0 Points |

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|[pic]Graph the line 3x + 2y = 6. |

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|[pic] |

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|A. [pic] |

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|[pic] |

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|B. [pic] |

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|[pic] |

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|C. [pic] |

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|[pic] |

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|D. [pic] |

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|Question 3 of 20 |

|5.0 Points |

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|[pic]Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. |

|x2 + y2 + x2y2 = 4 |

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|[pic] |

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|A. Symmetric with respect to the x-axis |

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|[pic] |

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|B. Symmetric with respect to the y-axis |

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|[pic] |

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|C. Symmetric with respect to the origin |

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|[pic] |

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|D. Symmetric with respect to the x-axis, the y-axis, and the origin |

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|Question 4 of 20 |

|5.0 Points |

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|[pic]Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. |

|x2 + xy2 + x = 2 |

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|[pic] |

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|A. Symmetric with respect to the x-axis |

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|[pic] |

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|B. Symmetric with respect to the y-axis |

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|[pic] |

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|C. Symmetric with respect to the origin |

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|[pic] |

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|D. Symmetric with respect to the x-axis, the y-axis, and the origin |

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|Question 5 of 20 |

|5.0 Points |

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|[pic]Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. |

|x2 + xy2 + 2y = 1 |

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|[pic] |

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|A. Symmetric with respect to the x-axis |

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|[pic] |

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|B. Symmetric with respect to the y-axis |

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|[pic] |

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|C. Symmetric with respect to the origin |

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|[pic] |

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|D. Not symmetric with respect to the x-axis, the y-axis, or the origin |

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|Question 6 of 20 |

|5.0 Points |

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|[pic]Find the distance between (–6, 4) and (0, –4). |

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|[pic] |

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|A. 6 |

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|[pic] |

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|B. 2 |

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|[pic] |

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|C. 10 |

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|[pic] |

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|D. 4 |

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|Question 7 of 20 |

|5.0 Points |

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|[pic]Find the midpoint of the line segment with endpoints (-5, -5) and (7, 9). |

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|[pic] |

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|A. (2, 4) |

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|[pic] |

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|B. (-12, -14) |

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|[pic] |

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|C. (1, 2) |

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|[pic] |

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|D. (-6, -7) |

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|Question 8 of 20 |

|5.0 Points |

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|[pic]Find the center and radius of the circle.(x + 5)2 + (y – 3)2 = 49. |

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|[pic] |

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|A. Center (5, –3) and radius 7 |

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|[pic] |

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|B. Center (–5, 3) and radius 7 |

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|[pic] |

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|C. Center (5, –3) and radius 49 |

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|[pic] |

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|D. Center (–5, 3) and radius 49 |

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|Question 9 of 20 |

|5.0 Points |

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|[pic]Find the center and radius of the circle. |

|3x2 + 3y2 – 18x + 6y – 162 = 0 |

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|[pic] |

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|A. Center (3, –1) and radius 8 |

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|[pic] |

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|B. Center (–3, 1) and radius 8 |

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|[pic] |

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|C. Center (3, –1) and radius 64 |

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|[pic] |

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|D. Center (–3, 1) and radius 64 |

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|Question 10 of 20 |

|5.0 Points |

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|[pic]Find the equation of a circle with center (2, –3) and the graph of which contains the point (3, 4). |

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|[pic] |

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|A. (x – 2)2 + (y + 3)2 = 50 |

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|[pic] |

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|B. (x + 2)2 + (y – 3)2 = 50 |

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|[pic] |

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|C. (x – 2)2 + (y + 3)2 = -50 |

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|[pic] |

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|D. (x + 2)2 + (y – 3)2 = -50 |

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|Question 11 of 20 |

|5.0 Points |

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|[pic]Indicate the slope. |

|3x + 4y = 12 |

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|[pic] |

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|A. -4/3 |

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|[pic] |

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|B. 4/3 |

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|[pic] |

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|C. -3/4 |

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|[pic] |

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|D. 3/4 |

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|Question 12 of 20 |

|5.0 Points |

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|[pic]Find the equation of the line with slope -6 and y-intercept 3. Write the equation in standard form Ax + By = C, A > 0. |

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|[pic] |

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|A. 6x - y = 3 |

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|[pic] |

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|B. 6x - y = -3 |

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|[pic] |

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|C. 6x + y = 3 |

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|[pic] |

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|D. 6x + y = -3 |

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|Question 13 of 20 |

|5.0 Points |

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|[pic]Write the equation of the line with slope 0 and y-intercept -7. Write the equation in standard form Ax + By = C, A > 0. |

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|[pic] |

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|A. -7x - y = 0 |

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|[pic] |

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|B. -7x + y = 0 |

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|[pic] |

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|C. y = -7 |

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|[pic] |

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|D. x = -7 |

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|Question 14 of 20 |

|5.0 Points |

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|[pic]Write the equation of the line passing through (0, –5) and (0, 1). |

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|[pic] |

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|A. x = 0 |

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|[pic] |

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|B. y = 0 |

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|[pic] |

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|C. y = x + 0 |

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|[pic] |

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|D. y = 6x |

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|Question 15 of 20 |

|5.0 Points |

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|[pic]The Number Two Plumbing Co. charges $45 per hour plus a fixed service call charge of $65. Write an equation that will allow |

|you to compute the total bill for any number of hours, x, that it takes to complete a job. |

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|[pic] |

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|A. C = 45x + 65 |

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|[pic] |

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|B. C = 65x + 45 |

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|[pic] |

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|C. 65x + 45C = 0 |

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|[pic] |

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|D. 45x + 65C = 0 |

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|Question 16 of 20 |

|5.0 Points |

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|[pic]A business purchases a copier for $5,500 and anticipates it will be worth $2,500 after 10 years. Use straight-line |

|depreciation to find a linear model for the depreciated value V of the copy machine after t years of use. |

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|[pic] |

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|A. V = -5,500 + 300t |

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|[pic] |

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|B. V = 300 - 5500t |

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|[pic] |

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|C. V = -300 + 5500t |

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|[pic] |

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|D. V = 5,500 - 300t |

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|Question 17 of 20 |

|5.0 Points |

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|[pic]The regression model for the data shown in the table is y = 2.3x + 3.9 |

|x |

|y |

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|4 |

|14 |

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|1 |

|6 |

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|3 |

|9 |

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|2 |

|9 |

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|5 |

|17 |

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|7 |

|20 |

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|6 |

|16 |

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|Use the model to estimate y when x = 3.5. |

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|[pic] |

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|A. 8.5 |

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|[pic] |

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|B. 9 |

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|[pic] |

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|C. -0.17 |

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|[pic] |

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|D. 11.95 |

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|Question 18 of 20 |

|5.0 Points |

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|[pic]The regression model for the data shown in the table is y = -3.0x + 134.6. |

|x |

|y |

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|10 |

|114 |

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|8 |

|108 |

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|15 |

|77 |

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|14 |

|87 |

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|20 |

|75 |

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|17 |

|94 |

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|Use the model to estimate y when x = 45. |

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|[pic] |

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|A. -0.5 |

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|[pic] |

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|B. -0.4 |

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|[pic] |

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|C. -0.3 |

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|[pic] |

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|D. -0.2 |

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|Question 19 of 20 |

|5.0 Points |

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|[pic]Find a linear regression model for the data. Round regression coefficients to two significant digits. |

|x |

|y |

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|2 |

|15 |

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|5 |

|12 |

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|6 |

|16 |

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|11 |

|14 |

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|12 |

|20 |

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|15 |

|35 |

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|20 |

|38 |

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|21 |

|42 |

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|24 |

|47 |

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|[pic] |

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|A. y = 2.7x + 6.1 |

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|[pic] |

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|B. y = 3x + 5 |

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|[pic] |

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|C. y = 1.7x + 5.1 |

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|[pic] |

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|D. y = 1.5 + 4.7 |

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|Question 20 of 20 |

|5.0 Points |

| |

|[pic]The data in the table shows the height x (in inches) compared to the shoe size y worn for a random sample of 12 males. |

|x |

|y |

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|64 |

|9 |

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|66 |

|10 |

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|67 |

|9.5 |

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|76 |

|11.5 |

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|71.5 |

|13 |

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|62 |

|9 |

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|65.5 |

|11 |

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|68 |

|10.5 |

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|73 |

|12 |

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|63 |

|12 |

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|70 |

|11 |

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|65 |

|10 |

| |

|Find a linear regression model for the data. |

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|[pic] |

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|A. y = 0.48x - 1.15 |

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|[pic] |

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|B. y = 0.38x - 1.25 |

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|[pic] |

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|C. y = 0.28x - 1.35 |

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|[pic] |

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|D. y = 0.18x - 1.45 |

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|Part 1 of 1 - |

|Question 1 of 20 |

|5.0 Points |

| |

|[pic]Solve the system by substitution. |

|x + y = 4 |

|x - y = 2 |

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|[pic] |

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|A. (1, 3) |

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|[pic] |

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|B. (-1, 5) |

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|[pic] |

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|C. (3, 1) |

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|[pic] |

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|D. (5, -1) |

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|Question 2 of 20 |

|5.0 Points |

| |

|[pic]Solve the system by substitution. |

|6x - 5y = 11 |

|7x + 5y = 2 |

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|[pic] |

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|A. (1, -2) |

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|[pic] |

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|B. (1, -1) |

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|[pic] |

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|C. (2, -1) |

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|[pic] |

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|D. (2, -2) |

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|Question 3 of 20 |

|5.0 Points |

| |

|[pic]Solve the system by substitution. |

|x - y = -11 |

|x + 3y = 5 |

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|[pic] |

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|A. (-7, 4) |

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|[pic] |

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|B. (-8, 4) |

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|[pic] |

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|C. (-7, 5) |

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|[pic] |

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|D. (-8, 5) |

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|Question 4 of 20 |

|5.0 Points |

| |

|[pic]Solve the system using elimination by addition. |

|x + y + z = 0 |

|-x + y - 2z = 6 |

|2x + y + z = 0 |

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|[pic] |

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|A. (1, 1, -1) |

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|[pic] |

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|B. (0, 2, -1) |

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|[pic] |

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|C. (0, 2, -2) |

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|[pic] |

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|D. No solution |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 5 of 20 |

|5.0 Points |

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|[pic]Solve the system using elimination by addition. |

|2x + 2y + 3z = 23 |

|2x + 2y + 5z = 33 |

|-4x - 4y - 8z = -55 |

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|[pic] |

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|A. (0, 4, 5) |

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|[pic] |

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|B. (0, 3, 6) |

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|[pic] |

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|C. (0, 5, 4) |

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|[pic] |

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|D. No solution |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 6 of 20 |

|5.0 Points |

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|[pic]Solve the system using elimination by addition. |

|4x - 2y + 2z = 2 |

|-x + y - 3z = -4 |

|4x - 3y + 7z = 9 |

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|[pic] |

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|A. (-1, -7, 0) |

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|[pic] |

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|B. (3, 3, 2) |

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|[pic] |

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|C. {(2s – 3, 5s – 7, s) | s is any real number} |

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|[pic] |

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|D. No solution |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 7 of 20 |

|5.0 Points |

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|[pic]Solve the system using Gauss-Jordan elimination. |

|x1 + 2x2 = 6 |

|-3x1 + x2 = 17 |

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|[pic] |

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|A. x1 = –4, x2 = 4 |

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|[pic] |

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|B. x1 = –3, x2 = 5 |

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|[pic] |

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|C. x1 = –4, x2 = 5 |

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|[pic] |

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|D. No solution |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 8 of 20 |

|5.0 Points |

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|[pic]Solve the system using Gauss-Jordan elimination. |

|-12x1 - 4x2 = -20 |

|3x1 + x2 = -5 |

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|[pic] |

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|A. x1 = -4, x2 = 6 |

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|[pic] |

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|B. x1 = -3, x2 = 7 |

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|[pic] |

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|C. x1 = -4, x2 = 7 |

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|[pic] |

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|D. No solution |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 9 of 20 |

|5.0 Points |

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|[pic]Solve the system using Gauss-Jordan elimination. |

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|-x1 + x2 - x3 = 5 |

|x1 + x2 + 4x3 = -1 |

|-3x1 + x2 + x3 = 11 |

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|[pic] |

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|A. x1 = -3, x2 = 2, x3 = 0 |

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|[pic] |

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|B. x1 = -3, x2 = 2, x3 = 1 |

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|[pic] |

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|C. x1 = -2, x2 = 1, x3 = 1 |

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|[pic] |

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|D. No solution |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 10 of 20 |

|5.0 Points |

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|[pic]Write the system as a matrix equation and solve using inverses. |

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|x1 + 2x2 - x3 = -3 |

|-2x1 - x2 + 3x3 = 0 |

|-4x1 + 4x2 - x3 = -12 |

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|[pic] |

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|A. x1 = 2, x2 = -3, x3 = 1 |

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|[pic] |

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|B. x1 = 1, x2 = -2, x3 = 1 |

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|[pic] |

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|C. x1 = 1, x2 = -2, x3 = 0 |

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|[pic] |

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|D. x1 = 1, x2 = -3, x3 = 1 |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 11 of 20 |

|5.0 Points |

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|[pic]Adult tickets for a play cost $19 and child tickets cost $7. If there were 29 people at a performance and the theatre |

|collected $323 from ticket sales, how many adults and how many children attended the play? |

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|[pic] |

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|A. 9 adults and 20 children |

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|B. 10 adults and 19 children |

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|C. 11 adults and 18 children |

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|[pic] |

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|D. 12 adults and 17 children |

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|[pic]Mark for Review What's This? |

|Question 12 of 20 |

|5.0 Points |

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|[pic]Solve the system. |

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|x2 + y2 = 4 |

|y - x = 2 |

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|[pic] |

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|A. (0, 2), (2, 0) |

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|[pic] |

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|B. (0, 2), (-2, 0) |

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|[pic] |

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|C. (0, -2), (2, 0) |

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|[pic] |

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|D. (0, -2), (-2, 0) |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 13 of 20 |

|5.0 Points |

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|[pic]Solve the system. |

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|3x2 - 2y2 = -5 |

|x2 + y2 = 25 |

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|[pic] |

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|A. (3, 4), (3, -4), (-3, 4), (-3, -4) |

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|[pic] |

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|B. (4, 4), (5, 4), (3, -4), (1, –4) |

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|[pic] |

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|C. (-3, 4), (1, 4), (-3, -4), (2, -4) |

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|[pic] |

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|D. (1, 4), (2, –4), (–4, 3), (–3, –3) |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 14 of 20 |

|5.0 Points |

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|[pic]Find the coordinates of the corner points using the following: |

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|x - y = -2 |

|2x + y = -1 |

|x = -2 |

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|[pic] |

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|A. (-2, 0) |

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|[pic] |

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|B. (-2, 0), (-1, 1) |

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|[pic] |

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|C. (-2, 0), (-1, 1), (-2, 3) |

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|[pic] |

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|D. (-1, 1), (-2, 3) |

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|Reset Selection |

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|[pic]Mark for Review What's This? |

|Question 15 of 20 |

|5.0 Points |

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|[pic]Esther wants to spend no more than $60 buying gifts for her friends Barb and Wanda. She wants to spend at least $20 on |

|Wanda's gift. |

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|Let B represent the amount Esther spends on Barb's gift and W represent the amount she spends on Wanda's gift. Write a system of |

|linear inequalities that models the information. |

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|[pic] |

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|A. B + W < 60 |

|B < 20 |

|W > 0 |

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|[pic] |

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|B. B + W > 60 |

|B < 20 |

|W > 20 |

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|[pic] |

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|C. B + W < 60 |

|B > 0 |

|W > 20 |

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|[pic] |

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|D. B + W > 60 |

|B > 0 |

|W > 20 |

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|Reset Selection |

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|Question 16 of 20 |

|5.0 Points |

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|[pic]2x + y < 20 |

|x + 3y < 30 |

|x, y > 0 |

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|Maximize z = 3x + 12y subject to the region. |

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|[pic] |

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|A. Maximum value of 114 at (6, 8) |

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|[pic] |

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|B. Maximum value of 60 at (20, 0) |

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|[pic] |

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|C. Maximum value of 120 at (0, 10) |

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|[pic] |

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|D. Maximum value of 30 at (10, 0) |

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|Reset Selection |

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|Question 17 of 20 |

|5.0 Points |

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|[pic]2x + y > 14 |

|x + 3y < 12 |

|x, y > 0 |

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|Minimize z = 3x + 5y subject to the given region. |

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|[pic] |

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|A. Minimum value of 20 at (0, 4) |

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|[pic] |

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|B. Minimum value of 21 at (7, 0) |

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|[pic] |

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|C. Minimum value of 28 at (6, 2) |

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|[pic] |

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|D. Minimum value of 36 at (12, 0) |

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|Reset Selection |

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|Question 18 of 20 |

|5.0 Points |

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|[pic]x + 2y < 18 |

|x + y < 10 |

|2x + y < 18 |

|x, y > 0 |

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|Maximize z = 3x + 4y subject to the given region. |

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|[pic] |

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|A. Maximum value of 42 at (6, 6) |

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|[pic] |

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|B. Maximum value of 38 at (2, 8) |

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|[pic] |

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|C. Maximum value of 36 at (0, 9) |

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|[pic] |

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|D. Maximum value of 32 at (8, 2) |

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|Reset Selection |

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|Question 19 of 20 |

|5.0 Points |

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|[pic]x + 2y < 18 |

|x + y > 10 |

|2x + y < 18 |

|x, y > 0 |

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|Minimize z = 3x + 5y subject to the given region. |

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|[pic] |

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|A. Minimum value of 27 at (9, 0) |

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|[pic] |

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|B. Minimum value of 45 at (0, 9) |

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|[pic] |

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|C. Minimum value of 34 at (8, 2) |

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|[pic] |

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|D. Minimum value of 0 at (0, 0) |

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|Reset Selection |

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|Question 20 of 20 |

|5.0 Points |

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|[pic]A stationery store sells rolls of standard gift wrap and deluxe gift wrap. They can stock a total of 100 rolls of gift wrap,|

|of which at least 30 must be standard wrap and at least 20 must be deluxe wrap. The profit on a roll of standard wrap is $2 and |

|the profit on a roll of deluxe wrap is $6. How many rolls of each type of gift wrap should the store stock to maximize its |

|profit? |

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|[pic] |

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|A. 29 rolls of standard gift wrap and 71 rolls of deluxe gift wrap |

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|[pic] |

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|B. 30 rolls of standard gift wrap and 70 rolls of deluxe gift wrap |

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|[pic] |

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|C. 31 rolls of standard gift wrap and 69 rolls of deluxe gift wrap |

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|[pic] |

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|D. 32 rolls of standard gift wrap and 68 rolls of deluxe gift wrap |

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|Reset Selection |

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