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:

8a⁶ - 3a⁶
(8 - 3)a⁶
5a⁶

First, solve for \( \left|c - 4\right| \):

\( \left|c - 4\right| \) - 7 = -1
\( \left|c - 4\right| \) = -1 + 7
\( \left|c - 4\right| \) = 6

The value inside the absolute value brackets can be either positive or negative so (c - 4) must equal + 6 or -6 for \( \left|c - 4\right| \) to equal 6:

So, c = -2 or c = 10.

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.

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

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 18 meters so the equation becomes: 2w + 2h = 18.

Putting these two equations together and solving for width (w):

2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3

Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m²