The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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

4\( \sqrt{28} \) + 3\( \sqrt{7} \)
4\( \sqrt{4 \times 7} \) + 3\( \sqrt{7} \)
4\( \sqrt{2^2 \times 7} \) + 3\( \sqrt{7} \)
(4)(2)\( \sqrt{7} \) + 3\( \sqrt{7} \)
8\( \sqrt{7} \) + 3\( \sqrt{7} \)

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

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

2 + (4 + 5) ÷ 2 x 2 - 4²
P: 2 + (9) ÷ 2 x 2 - 4²
E: 2 + 9 ÷ 2 x 2 - 16
MD: 2 + \( \frac{9}{2} \) x 2 - 16
MD: 2 + \( \frac{18}{2} \) - 16
AS: \( \frac{4}{2} \) + \( \frac{18}{2} \) - 16
AS: \( \frac{22}{2} \) - 16
AS: \( \frac{22 - 32}{2} \)
\( \frac{-10}{2} \)
-5

47% of the water consumption is industrial use and 27% is personal use so (47% - 27%) = 20% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{20}{100} \) x 30,000 gallons = 6,000 gallons.

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