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:

-9z⁴ + 4z⁴
(-9 + 4)z⁴
-5z⁴

If 38% of the town's 44,000 voters cast ballots the number of votes cast is:

(\( \frac{38}{100} \)) x 44,000 = \( \frac{1,672,000}{100} \) = 16,720

The mayor got 64% of the votes cast which is:

(\( \frac{64}{100} \)) x 16,720 = \( \frac{1,070,080}{100} \) = 10,701 votes.

The factors of 44 are [1, 2, 4, 11, 22, 44] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 3 factors [1, 2, 4] making 4 the greatest factor 44 and 48 have in common.

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{80} \) = \( \frac{\frac{20}{20}}{\frac{80}{20}} \) = \( \frac{1}{4} \)

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{55}{100} \) = \( \frac{55 x 10}{100} \) = \( \frac{550}{100} \) = 5 shots

The center makes 35% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{5}{\frac{35}{100}} \) = 5 x \( \frac{100}{35} \) = \( \frac{5 x 100}{35} \) = \( \frac{500}{35} \) = 14 shots

to make the same number of shots as the guard and thus score the same number of points.