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Several problems in basic algebra

Please include answer and steps to solve problem and explain if needed.

1) What is 10^-1 + 10^0 + 10^1?

2) 16 is 20% of....

3) If f(x) = x^2 + 1, then 2f(x) = ?

4) If f(x) = x^2 + 1, then f(2x) = ?

5) If f(x) = x^2 + 1, then f(y) = ?

6) If 2x + y = 3, and x - y =3, what is x?

7) If 2x + y = 3, and x - y = 3, what is y?

8) If you walk 3 miles in one hour and then 4 miles in two hours, what is your average speed for the entire trip? (in mph)

a 2.33, b 2.5, c 3.5, d 3.67, e 1.5

9) Jack and Joe leave their homes at the same time and drive toward each other. Jack drives at 60mph while Joe drives at 30mph. They pass each other in 10 minutes. How far apart were Jack and Joe when they started (in miles)?

a 5, b 15, c 30, d 90, e 300

Solution Preview

Please see the attached file.

1
A negative power is the inverse of the base taken by the same power only positive:

So here we have:

2
16 is 20% of what?

Here we use the triangle relations. We want to know what quantity is 100% if 16 is only 20%
If we denote this quantity as x we can write:

Hide the x with your finger. Now x will be equal to the multiplication of the diagonal pair (16 and 100) divided by the unmatched number (20% in this case)

And calculate:

Another ...

Solution Summary

The solution is has a detailed explanations how to solve 9 different problems in algebra.

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