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 36 meters so the equation becomes: 2w + 2h = 36.

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

2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h

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

w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6

Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m²

First, solve for \( \left|b + 4\right| \):

\( \left|b + 4\right| \) + 8 = 6
\( \left|b + 4\right| \) = 6 - 8
\( \left|b + 4\right| \) = -2

The value inside the absolute value brackets can be either positive or negative so (b + 4) must equal - 2 or --2 for \( \left|b + 4\right| \) to equal -2:

So, b = -2 or b = -6.

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

There are 3 5-passenger taxis available so that's 3 x 5 = 15 total seats. There are 20 people needing transportation leaving 20 - 15 = 5 who will have to find other transportation.