Why would you eliminate the factor pair $(5)\left(9 z^2\right)$ in determining the binomial factors of $x^2+18 x z+45 z^2$?

Verify that $3 g h \sqrt{275 g^7 h^9}$ can be simplified to $15 g^4 h^5 \sqrt{11 g h}$.

The speed of a pitched ball is represented by the expression $9 x^2-36 x-13$. Factor the expression completely.

Maria has a white gold ring with a mass of 10.3 grams and a volume of 0.7 cubic centimeters. White gold is made of nickel and gold. Nickel's mass is 9 grams per cubic centimeter and gold's mass is 19 grams per cubic centimeter. What is the volume of each metal in the ring?

The equation y = 4 describes a horizontal line with zero slope. The equation x = 4 describes a vertical line with infinite slope. Classify the system formed by these two equations.

In an antique shop, a painting is inclined on a display easel at an angle of 65 degrees. The angle of inclination can be increased or decreased by a maximum of 8 degrees from the present setting by an adjustment screw. Write and solve an absolute-value equation for the maximum and minimum angles of inclination for the easel.

Solve the inequality $\frac{n}{5} \leq-3$. Then select several values of $n$ to substitute into the inequality to verify the answer.

Write an equation for a direct variation that includes the point (13,13).

True or False: The lines represented by $y=\frac{x}{4}-2$ and 4y = x + 8 are parallel. Explain.

The heat index displays apparent air temperatures in relation to the actual air temperature. The table shows the apparent air temperature for different humidity levels given that the actual air temperature is 85 degrees.

Do the data values show a positive correlation, a negative correlation, or no correlation?

Use the table to determine if there is a positive correlation, a negative correlation, or no correlation between the data sets.

Lou is building a square sandbox. The sandbox has a side length of $6 \sqrt{36}$ inches. What is the area of the sandbox?

A company designs web sites and charges a fee of y = $250 +$50w. The charge includes a base fee of $250, plus a weekly fee based on the number of weeks the client requires full support. If the equation y = 800 represents the amount a company pays, for how many weeks do they receive full support?

Use the Distributive Property to find the product of $\sqrt{4}(3+\sqrt{6})$.