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Diverse algebra quetions

Could I please get step-by-step solutions to these problems to help me understand? I have attached a pdf file and a word file, they have the same questions. Thank you very much

(rewrite using only positive exponents, calculate equations, simplify, Pythagorean Theorem,Graph the inequality,Rationalize the denominator, Solve by factoring,Solve by using the square root property, Solve by completing the square, etc)

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Solution Preview

See attachment.

1. Find:
Solution:

2. Rewrite using only positive exponents:
Solution:

3. Find:
Solution:

4. Simplify:
Solution:

5. Darlene and Harriet are going to paint their apartment. If Darlene could paint the apartment by herself in three days and Harriet could paint it in five days by herself, how long would it take Darlene and Harriet to paint the apartment working together?
Solution: The speed of Darlene is 1/3 (apartment / day), and the speed of Harriet is 1/5 (apartment /day), then the time (day) for both of them to paint the apartment is (day)

6. Solve for x:
Solution: The equation is equivalent to

by moving to the right hand side. i.e.,
, so
x=1+3/2=2.5

7. The ratio of jellybeans to gummy bears in a bag of candy is seven to two. If there are 459 pieces of candy in the ...

Solution Summary

The problems covered in this solution include the following topics:
rewrite using only positive exponents, calculate equations, simplify, Pythagorean Theorem,Graph the inequality,Rationalize the denominator, Solve by factoring,Solve by using the square root property, Solve by completing the square

$2.19