Gateway exam practice - Math Insight

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Section:
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Total points: 10

Time limit: 50 minutes

Find the equation for the line through the points $(8,-9)$ and $(-9,7)$.
$y = $
Let the variable $x$ be in the range \begin{align*} -2< x <8. \end{align*} If $y= 7 x + 2$, what is the range of the variable $y$?

$\lt y \lt$
Solve the equation $- 10 z \left(z^{2} + 2 z - 24\right) =0$ by factoring.
The solutions are $z = $

If there are more than one solution, separate answers by commas
Rewrite the exponential function \[ z(t) = \frac{ 29 }{ 3^{ t - 4 } } \] in the form $z(t)=ab^t$, where we call $a$ the “initial value” (the value when $t=0$) and $b$ the “growth factor.” In this form:
$a = $

$b = $
Compute the value of $f(f(\frac{1}{ 5 }))$ for the function $f(x)=2x(1-x)$.
$f(f(\frac{1}{ 5 })) =$
Solve the equation $x^{2} + 3 x + 2 =0$ by factoring.
The solutions are $x = $

If there are more than one solution, separate answers by commas
Solve for $v$. \begin{align*} 3 Z - 6 = - Z + 6 v - 8 \end{align*} $v = $
Consider the function $f(t)=14(1.35)^t. \;\;$ Find the doubling time, i.e. find $t$ such that $f(t)= 2f(0).$
Doubling time =

(If you round your answer, include at least 4 significant digits.)
Let $w(x) = - 9 x^{2} - 4$ and $g(x) = \sqrt{ 7 x}$. What is $w(g(x))$?
$w(g(x)) = $
Simplify the inequality below: \begin{align*} -4<\frac{8 x}{5} + 2<-2 \end{align*}

$\lt x \lt$