A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0009781 in scientific notation is 9.781 x 10^-4

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

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

First, solve for \( \left|b + 3\right| \):

\( \left|b + 3\right| \) + 2 = 0
\( \left|b + 3\right| \) = 0 - 2
\( \left|b + 3\right| \) = -2

The value inside the absolute value brackets can be either positive or negative so (b + 3) must equal - 2 or --2 for \( \left|b + 3\right| \) to equal -2:

So, b = -1 or b = -5.

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

\( \frac{4}{7} \) ÷ \( \frac{2}{7} \) = \( \frac{4}{7} \) x \( \frac{7}{2} \)

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

\( \frac{4}{7} \) x \( \frac{7}{2} \) = \( \frac{4 x 7}{7 x 2} \) = \( \frac{28}{14} \) = 2