First, solve for \( \left|c + 0\right| \):

\( \left|c + 0\right| \) + 9 = -9
\( \left|c + 0\right| \) = -9 - 9
\( \left|c + 0\right| \) = -18

The value inside the absolute value brackets can be either positive or negative so (c + 0) must equal - 18 or --18 for \( \left|c + 0\right| \) to equal -18:

So, c = 18 or c = -18.

Monica scored 78% on the test meaning she earned 78% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.78 = 94 points. Each question is worth 2 points so she got \( \frac{94}{2} \) = 47 questions right.

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 54 meters so the equation becomes: 2w + 2h = 54.

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

2w + 2h = 54
w + h = \( \frac{54}{2} \)
w + h = 27
w = 27 - h

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

w = 27 - 2w
3w = 27
w = \( \frac{27}{3} \)
w = 9

Since h = 2w that makes h = (2 x 9) = 18 and the area = h x w = 9 x 18 = 162 m²

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-5y⁶ x 9y⁷
(-5 x 9)y^{(6 + 7)}
-45y¹³

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 $300
i = 0.03 x $300
i = $9