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 $700
i = 0.09 x $700

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

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 6 meters so the equation becomes: 2w + 2h = 6.

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

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

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

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

If 42% of the town's 31,000 voters cast ballots the number of votes cast is:

(\( \frac{42}{100} \)) x 31,000 = \( \frac{1,302,000}{100} \) = 13,020

The mayor got 58% of the votes cast which is:

(\( \frac{58}{100} \)) x 13,020 = \( \frac{755,160}{100} \) = 7,552 votes.

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

8\( \sqrt{175} \) + 9\( \sqrt{7} \)
8\( \sqrt{25 \times 7} \) + 9\( \sqrt{7} \)
8\( \sqrt{5^2 \times 7} \) + 9\( \sqrt{7} \)
(8)(5)\( \sqrt{7} \) + 9\( \sqrt{7} \)
40\( \sqrt{7} \) + 9\( \sqrt{7} \)

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