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 48 meters so the equation becomes: 2w + 2h = 48.

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

2w + 2h = 48
w + h = \( \frac{48}{2} \)
w + h = 24
w = 24 - h

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

w = 24 - 2w
3w = 24
w = \( \frac{24}{3} \)
w = 8

Since h = 2w that makes h = (2 x 8) = 16 and the area = h x w = 8 x 16 = 128 m²

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

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.

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

First, solve for \( \left|a - 2\right| \):

\( \left|a - 2\right| \) - 9 = 1
\( \left|a - 2\right| \) = 1 + 9
\( \left|a - 2\right| \) = 10

The value inside the absolute value brackets can be either positive or negative so (a - 2) must equal + 10 or -10 for \( \left|a - 2\right| \) to equal 10:

So, a = -8 or a = 12.