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 $1,000
i = 0.03 x $1,000

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

1

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 12 meters so the equation becomes: 2w + 2h = 12.

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

2w + 2h = 12
w + h = \( \frac{12}{2} \)
w + h = 6
w = 6 - h

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

w = 6 - 2w
3w = 6
w = \( \frac{6}{3} \)
w = 2

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

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

\( \frac{3}{6} \) x \( \frac{3}{6} \) = \( \frac{3 x 3}{6 x 6} \) = \( \frac{9}{36} \) = \(\frac{1}{4}\)

First, solve for \( \left|c - 6\right| \):

\( \left|c - 6\right| \) - 4 = -5
\( \left|c - 6\right| \) = -5 + 4
\( \left|c - 6\right| \) = -1

The value inside the absolute value brackets can be either positive or negative so (c - 6) must equal - 1 or --1 for \( \left|c - 6\right| \) to equal -1:

So, c = 7 or c = 5.