Extra Math Practice #186-190

$\begin{align*}y&>\dfrac{1}{3}x-3\\y&>2x+1\end{align*}$

If the system of inequalities above is graphed in the $xy$ -plane and the ordered pair $(a,b)$ is in the solution set, then which of the following statements cannot be disproven?

A)If $a>0$ , then $b>0$ .

B)If $a<0$ , then $b<0$ .

C)If $a<0$ , then $b>0$ .

D)If $a>0$ , then $b<0$ .

Which of the following statements CANNOT be true about a set of 10 numbers?

The median of the 10 numbers is one of the 10 numbers
The sum of the 10 numbers is equal to the average (arithmetic mean) of the 10 numbers
The set of 10 numbers has 6 modes.

A)I and II

B)II and III

C)I, II, and III

D)III only

$\begin{align*}y&\leq (x-3)^2\\y&\geq -x+9\end{align*}$

In the $xy$ -plane, a point with coordinates $(a, b)$ lies in the solution set of the system of inequalities above. If $a$ and $b$ are greater than zero, what is the least possible value of $a$ ?

$\begin{align*}3x+4y&=8\\2x+8y&=4\\10x-ay&=a\end{align*}$

If the three equations above are graphed in the $xy$ -plane, they form three lines that intersect at one point. What is the value of the constant $a$ ?

$\begin{align*}y=6x-\dfrac{a}{2}\\[8pt]y-ax=2a\end{align*}$

In the system of equations above, $a$ is a constant. When the equations are graphed in the $xy$ -plane, they form parallel lines. What is the positive difference between the $y$ -intercepts of the two lines?

A)6

B)9

C)12

D)15