A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

50,000 fans x \( \frac{4}{5} \) = \( \frac{200000}{5} \) = 40,000 fans.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-5z³ + 2z³
(-5 + 2)z³
-3z³

First, solve for \( \left|a - 7\right| \):

\( \left|a - 7\right| \) + 1 = 5
\( \left|a - 7\right| \) = 5 - 1
\( \left|a - 7\right| \) = 4

The value inside the absolute value brackets can be either positive or negative so (a - 7) must equal + 4 or -4 for \( \left|a - 7\right| \) to equal 4:

So, a = 3 or a = 11.

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

5\( \sqrt{125} \) + 8\( \sqrt{5} \)
5\( \sqrt{25 \times 5} \) + 8\( \sqrt{5} \)
5\( \sqrt{5^2 \times 5} \) + 8\( \sqrt{5} \)
(5)(5)\( \sqrt{5} \) + 8\( \sqrt{5} \)
25\( \sqrt{5} \) + 8\( \sqrt{5} \)

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

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.