# Algebra

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.

Â© BrainMass Inc. brainmass.com March 4, 2021, 7:50 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/various-algebra-questions-126657

#### 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).

âˆš50 = âˆš25 * 2

= 5 âˆš2

âˆš18 = âˆš9 * 2

= 3 âˆš2

Then

5 âˆš2 + 3 âˆš2 - 7 âˆš2 = âˆš2

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

#### Solution Summary

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