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# Algebra

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Various Algebra Questions. See attached file for full problem description.

1. Simplify: . Show work.

2. Simplify: Show work. Give the exact answer (including a radical).

3. (a) Is the graph of a circle a graph of a function? (Yes or no)

(b) Find the center and the radius of the circle represented by the equation
x2 + y2 + 10x - 4y - 7 = 0

4. Let .

(a) Find g(-1)

(b) Find g(t + 1) and simplify.

(c) Find the domain of the function

5. Acme Electric Company's monthly bill includes a basic customer charge of \$12.00, and a usage charge of \$0.07 for each kilowatt hour of electricity supplied.
(a) Write an equation that can be used to determine the monthly bill, given the number of kilowatt hours h supplied.

(b) Determine the electric bill if 1850 kilowatt hours of electricity are supplied.

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#### Solution Preview

Please see the attached file.

1. Simplify: . Show work.

1 - 2/x = (x - 2)/x

x - 4/x = (x2 - 4) /x
=(x - 2)(x + 2)/x

(1 - 2/x) / (x - 4/x) = ((x - 2)/x)/( (x - 2)(x + 2)/x)
= 1/(x + 2)

2. Simplify: Show work. Give the exact answer (including a radical).

√50 = √25 * 2
= 5 √2

√18 = √9 * 2
= 3 √2

Then

5 √2 + 3 √2 - 7 √2 = √2

3. (a) Is the graph of ...

#### Solution Summary

Various Algebra Questions (simplifying radicals, expressions, graphing etc.) are answered.

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