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Algebra Concepts

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Please see attached file for full problem description. Please show all work when solving the two problems.

1. Why bother factoring a quadratic equation before you solve it?

2. Why are there usually two solutions in a quadratic equation?

3. Under what conditions would one or more solutions of a rational equation be unacceptable?

4. A company specializing in magazine sales over the telephone found that in 2500 phone calls, 360 resulted in sales and were made by male callers, and 480 resulted in sales and were made by female callers. If the company gets twice as many sales per call with a woman's voice then with a man's voice, then how many of the 2500 calls were made by females?

5. Simplify expressions involving rational exponents. Assume all variables represent positive real numbers. Write answer with positive exponents.

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Solution Preview

1. Why bother factoring a quadratic equation before you solve it?

If you factor a quadratic equation before you solve it, the answers are obvious. If you factor an equation, and it looks like this:

(x + 1)(x - 2) = 0

then you know that the answers are x = -1 and x = 2. If you hadn't factored it, you would have had to solve a more complex equation when you used the quadratic formula.

2. Why are there usually two solutions in a quadratic equation?

When you graph a quadratic equation, it looks like a parabola. Draw different parabolas to see that they can ...

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