Chapter 9.2, Problem 1MR

(a)

To determine

To copy the figure from page 545.

Explanation of Solution

Given:

Label the width of rectangular sign $x$ and label the height $y$ .

Calculation:

The following is the required figure-

(b)

To determine

To write the proportion using the similar triangles and solve for $y$ in terms of $x$

Answer to Problem 1MR

  $y=-\frac{2x}{3}+12$

Explanation of Solution

The proportion will be as follows-

  $\begin{array}{l}\frac{x}{18}=\frac{12-y}{12}\\ \frac{x}{3}=\frac{12-y}{2}\\ 12-y=\frac{2x}{3}\\ y=-\frac{2x}{3}+12\end{array}$

(c)

To determine

To find the equation for the function $A\left(x\right)$ that represents the area of rectangular sign.

Answer to Problem 1MR

  $-\frac{2x^2}{3}+12x$

Explanation of Solution

The following equation shows the function $A\left(x\right)$ that represents the area of rectangular sign

  $\begin{array}{l}A(x)=x\times y\\ A(x)=x\times \left(-\frac{2x}{3}+12\right)\\ A(x)=-\frac{2x^2}{3}+12x\end{array}$

(d)

To determine

To find the out the kind of function you found in part (c).

Answer to Problem 1MR

Quadratic function.

Explanation of Solution

Given:

The function obtained in part (c) is-

  $-\frac{2x^2}{3}+12x$

Calculation:

Since the degree of the function $-\frac{2x^2}{3}+12x$ is $2$ therefore, the function $-\frac{2x^2}{3}+12x$ is quadratic function.