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

First, solve for \( \left|b + 6\right| \):

\( \left|b + 6\right| \) + 3 = -2
\( \left|b + 6\right| \) = -2 - 3
\( \left|b + 6\right| \) = -5

The value inside the absolute value brackets can be either positive or negative so (b + 6) must equal - 5 or --5 for \( \left|b + 6\right| \) to equal -5:

So, b = -1 or b = -11.

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

To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{5} \) ÷ \( \frac{1}{7} \) = \( \frac{4}{5} \) x \( \frac{7}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{5} \) x \( \frac{7}{1} \) = \( \frac{4 x 7}{5 x 1} \) = \( \frac{28}{5} \) = 5\(\frac{3}{5}\)

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