The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24]. They share 8 factors [1, 2, 3, 4, 6, 8, 12, 24] making 24 the greatest factor 24 and 24 have in common.

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

5\( \sqrt{125} \) + 5\( \sqrt{5} \)
5\( \sqrt{25 \times 5} \) + 5\( \sqrt{5} \)
5\( \sqrt{5^2 \times 5} \) + 5\( \sqrt{5} \)
(5)(5)\( \sqrt{5} \) + 5\( \sqrt{5} \)
25\( \sqrt{5} \) + 5\( \sqrt{5} \)

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

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

31,000 fans x \( \frac{2}{3} \) = \( \frac{62000}{3} \) = 20,667 fans.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (5 + 5) ÷ 4 x 4 - 5²
P: 5 + (10) ÷ 4 x 4 - 5²
E: 5 + 10 ÷ 4 x 4 - 25
MD: 5 + \( \frac{10}{4} \) x 4 - 25
MD: 5 + \( \frac{40}{4} \) - 25
AS: \( \frac{20}{4} \) + \( \frac{40}{4} \) - 25
AS: \( \frac{60}{4} \) - 25
AS: \( \frac{60 - 100}{4} \)
\( \frac{-40}{4} \)
-10

First, solve for \( \left|y + 8\right| \):

\( \left|y + 8\right| \) + 1 = -1
\( \left|y + 8\right| \) = -1 - 1
\( \left|y + 8\right| \) = -2

The value inside the absolute value brackets can be either positive or negative so (y + 8) must equal - 2 or --2 for \( \left|y + 8\right| \) to equal -2:

So, y = -6 or y = -10.