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

-4x² - 7x²
(-4 - 7)x²
-11x²

The equation for this sequence is:

a_n = a_n-1 + 6

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 + 6
a₆ = 25 + 6
a₆ = 31

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{14\sqrt{18}}{7\sqrt{6}} \)
\( \frac{14}{7} \) \( \sqrt{\frac{18}{6}} \)
2 \( \sqrt{3} \)

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

9\( \sqrt{27} \) + 7\( \sqrt{3} \)
9\( \sqrt{9 \times 3} \) + 7\( \sqrt{3} \)
9\( \sqrt{3^2 \times 3} \) + 7\( \sqrt{3} \)
(9)(3)\( \sqrt{3} \) + 7\( \sqrt{3} \)
27\( \sqrt{3} \) + 7\( \sqrt{3} \)

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

52% of the water consumption is industrial use and 24% is personal use so (52% - 24%) = 28% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{28}{100} \) x 35,000 gallons = 9,800 gallons.