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.

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

4\( \sqrt{28} \) - 2\( \sqrt{7} \)
4\( \sqrt{4 \times 7} \) - 2\( \sqrt{7} \)
4\( \sqrt{2^2 \times 7} \) - 2\( \sqrt{7} \)
(4)(2)\( \sqrt{7} \) - 2\( \sqrt{7} \)
8\( \sqrt{7} \) - 2\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them:

The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

By buying two shirts, Charlie will save $36 x \( \frac{15}{100} \) = \( \frac{$36 x 15}{100} \) = \( \frac{$540}{100} \) = $5.40 on the second shirt.

So, his total cost will be
$36.00 + ($36.00 - $5.40)
$36.00 + $30.60
$66.60

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31