Extra Math Practice #146-150

Both Louis and Marcy work at jobs where they can collect overtime pay at a rate of 150% of their regular hourly wages for each hour they work beyond 40 hours in a week. Marcy's regular pay rate is $18 per hour, and Louis's regular pay rate is $16 per hour. Last week, Marcy worked for 48 hours and Louis made $64 more than Marcy. How many hours did Louis work last week?

In the equations below, $a$ is a constant.

$\begin{align*}4x+7y&=30\\ax-2y&=5\end{align*}$

If the equations above are graphed in the $xy$ -plane, they form perpendicular lines. What is the value of $a$ ?

In the $xy$ -plane, line $m$ passes through the origin. Which of the following sets of ordered pairs could be on line $m$ ?

A) $(8,5)$ and $(13,10)$

B) $\left(-\dfrac{1}{3},3\right)$ and $\left(\dfrac{1}{9},-1\right)$

C) $\left(2,\dfrac{1}{2}\right)$ and $\left(-\dfrac{1}{2},-2\right)$

D) $(5,4)$ and $(25,16)$

The figure above shows two circles with centers at points $A$ and $B$ . If the length of $\overline{AB}$ is 8 inches, what is the perimeter of the shaded region, in inches?