An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

You have 4 out of the total of 200 raffle tickets sold so you have a (\( \frac{4}{200} \)) x 100 = \( \frac{4 \times 100}{200} \) = \( \frac{400}{200} \) = 2% chance to win the raffle.

Christine scored 80% on the test meaning she earned 80% of the possible points on the test. There were 360 possible points on the test so she earned 360 x 0.8 = 288 points. Each question is worth 4 points so she got \( \frac{288}{4} \) = 72 questions right.

First, solve for \( \left|z + 4\right| \):

\( \left|z + 4\right| \) - 3 = 3
\( \left|z + 4\right| \) = 3 + 3
\( \left|z + 4\right| \) = 6

The value inside the absolute value brackets can be either positive or negative so (z + 4) must equal + 6 or -6 for \( \left|z + 4\right| \) to equal 6:

So, z = -10 or z = 2.

To add these radicals together their radicands must be the same:

8\( \sqrt{20} \) + 6\( \sqrt{5} \)
8\( \sqrt{4 \times 5} \) + 6\( \sqrt{5} \)
8\( \sqrt{2^2 \times 5} \) + 6\( \sqrt{5} \)
(8)(2)\( \sqrt{5} \) + 6\( \sqrt{5} \)
16\( \sqrt{5} \) + 6\( \sqrt{5} \)

Now that the radicands are identical, you can add them together: