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

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-5b⁷ - 3b⁷
(-5 - 3)b⁷
-8b⁷

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,200
i = 0.07 x $1,200
i = $84

The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.

To add these radicals together their radicands must be the same:

9\( \sqrt{28} \) + 4\( \sqrt{7} \)
9\( \sqrt{4 \times 7} \) + 4\( \sqrt{7} \)
9\( \sqrt{2^2 \times 7} \) + 4\( \sqrt{7} \)
(9)(2)\( \sqrt{7} \) + 4\( \sqrt{7} \)
18\( \sqrt{7} \) + 4\( \sqrt{7} \)

Now that the radicands are identical, you can add them together: