A circle has a radius of x. Another circle has a radius of 3x.

Write equations for the areas of both circles.

If a 9% decrease from the original price resulted in a new price of $227,500, what was the original price?

The width of a rectangle is represented by the expression (4x - 6) and the length (8x + 7). Would the area of the rectangle be correctly expressed as $32 x^2+20 x-42$? If not, what is the correct area?

The volume of a sphere is $V=\frac{4}{3} \pi r^3$. Describe in words the relationship between the volume of a sphere and its radius. Identify the constant of variation.

(x + 10)(x - 2) the correct factorization for $x^2-8 x-20$? Explain.

Given the following table, find the value of the constant of variation and complete the missing values in the table given that y varies directly with x and inversely with z.

Write an equation where j is inversely proportional to m and n and directly proportional to p and q.

Evaluate the following expression for the given values.

$-x^2-3 x y+y$ for x = 3 and y = -1

Explain why some absolute-value equations have no solutions.

Solve the following.

-3(r - 2) > -2(-6)

Using the path of a ball thrown into the air as an example, describe in mathematical terms each part of the graph the path of the ball creates.

Evaluate for the given value.

$y=-x^2+5 x-6$ for x = -2

Simplify the following.

$$\frac{16 g^4}{2 g+3}-\frac{81}{2 g+3}$$

Solve the equation $\frac{10|x|}{3}+18=4$ and graph the solution.