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:

-4y⁶ - 5y⁶
(-4 - 5)y⁶
-9y⁶

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

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 $800
i = 0.06 x $800

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

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{6 x 5}{2 x 5} \) + \( \frac{8 x 1}{10 x 1} \)

\( \frac{30}{10} \) + \( \frac{8}{10} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{30 + 8}{10} \) = \( \frac{38}{10} \) = 3\(\frac{4}{5}\)

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