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:

-9x⁴ + 5x⁴
(-9 + 5)x⁴
-4x⁴

If 68% of the town's 10,000 voters cast ballots the number of votes cast is:

(\( \frac{68}{100} \)) x 10,000 = \( \frac{680,000}{100} \) = 6,800

The mayor got 57% of the votes cast which is:

(\( \frac{57}{100} \)) x 6,800 = \( \frac{387,600}{100} \) = 3,876 votes.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

The equation for this sequence is:

a_n = a_n-1 + 3(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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

47,000 fans x \( \frac{3}{4} \) = \( \frac{141000}{4} \) = 35,250 fans.