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 24 meters so the equation becomes: 2w + 2h = 24.

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

2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h

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

w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4

Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m²

Latoya scored 96% on the test meaning she earned 96% of the possible points on the test. There were 400 possible points on the test so she earned 400 x 0.96 = 384 points. Each question is worth 4 points so she got \( \frac{384}{4} \) = 96 questions right.

The greatest common factor (GCF) is the greatest factor that divides two integers.

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 $400
i = 0.07 x $400

No payments were made so the total amount due is the original amount + the accumulated interest:

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