First, solve for \( \left|y + 2\right| \):

\( \left|y + 2\right| \) + 8 = 0
\( \left|y + 2\right| \) = 0 - 8
\( \left|y + 2\right| \) = -8

The value inside the absolute value brackets can be either positive or negative so (y + 2) must equal - 8 or --8 for \( \left|y + 2\right| \) to equal -8:

So, y = 6 or y = -10.

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 7 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 7 x 3 = 21 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 21 - 6 = 15 new staff for the busy season.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

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

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 25mph \times 2h \)
50 miles