Extra Math Practice #136-140

$\begin{align*}y&=3x+4\\ax-by&=11\end{align*}$

In the system of equations above, $a$ and $b$ are constants. If the system has no solutions, what is the value of $\dfrac{b}{a}$ ?

A) $-\dfrac{1}{3}$

B) $\dfrac{1}{3}$

C) $\dfrac{11}{3}$

D) $3$

In the $xy$ -plane, a triangle is formed with vertices at $(5,3)$ , $(-2,-2)$ , and $(0,-2)$ . What is the area of the triangle?

A square is formed in the $xy$ -plane by connecting four points: $(1,-2)$ , $(2,3)$ , $(7,2)$ , and $(a,b)$ , where $a$ and $b$ are constants. What is the value of $a-b$ ?

Which of the following equations, when graphed in the $xy$ -plane, does not contain any points in Quadrant IV?

A) $y=|3-x|-1$

B) $y=|x-1|-3$

C) $y=1-|3-x|$

D) $y=|3+x|-1$

5 A certain parabola has the equation $y=(x+a)(x+b)$ , where $a$ and $b$ are constants. In terms of $a$ and $b$ , what is the $x$ -value of the parabola's vertex?

A) $-\dfrac{a+b}{2}$

B) $\dfrac{a-b}{2}$

C) $\dfrac{a+b}{2}$

D) $-\dfrac{ab}{2}$