$$f(x)=|59-2x|$$

The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?

A model estimates that at the end of each year from 2015 to 2020, the number of squirrels in a population was 150% more than the number of squirrels in the population at the end of the previous year. The model estimates that at the end of 2016, there were 180 squirrels in the population. Which of the following equations represents this model, where $n$ is the estimated number of squirrels in the population $t$ years after the end of 2015 and $t\leq 5$?

Immanuel purchased a certain rare coin on January 1. The function $f(x)=65(1.03)^{x}$, where $0\leq x\leq 10$, gives the predicted value, in dollars, of the rare coin $x$ years after Immanuel purchased it. What is the best interpretation of the statement "$f(8)$ is approximately equal to 82" in this context?

$-4x^{2}-7x=-36$

What is the positive solution to the given equation?

$14j+5k=m$

The given equation relates the numbers $j$, $k$, and $m$. Which equation correctly expresses $k$ in terms of $j$ and $m$?

$2x^{2}-4x=t$

In the equation above, $t$ is a constant. If the equation has no real solutions, which of the following could be the value of $t$ ?

$$f(x)=(x-14)(x+19)$$

The function $f$ is defined by the given equation. For what value of $x$ does $f(x)$ reach its minimum?

$g(x)=x^{2}+55$

What is the minimum value of the given function?

If $x\neq 0$, which of the following expressions is equivalent to $\frac{\sqrt{16x^{4}y^{8}}}{x^{3}}$ ?

$$p=\frac{k}{4j+9}$$

The given equation relates the distinct positive numbers $p$, $k$, and $j$. Which equation correctly expresses $4j+9$ in terms of $p$ and $k$?

$$57x^{2}+(57b+a)x+ab=0$$

In the given equation, $a$ and $b$ are positive constants. The product of the solutions to the given equation is $kab$, where $k$ is a constant. What is the value of $k$?

\[q-29r=s\]

The given equation relates the positive numbers \(q\), \(r\), and \(s\). Which equation correctly expresses \(q\) in terms of \(r\) and \(s\)?

Which of the following is a solution to the equation $2x^{2}-4=x^{2}$?

If $x^{2}=a+b$ and $y^{2}=a+c$ which of the following is equal to $(x^{2}-y^{2})^{2}$?

The function $f$ is defined by $f(x)=\frac{1}{6x}$. What is the value of $f(x)$ when $x=3$?

An oceanographer uses the equation $s=\frac{3}{2}P$ to model the speed $s$, in knots, of an ocean wave, where $p$ represents the period of the wave, in seconds. Which of the following represents the period of the wave in terms of the speed of the wave?

Which expression is equivalent to $(d-6)(8d^{2}-3)$?

$\sqrt[3]{x^{3}y^{6}}$

Which of the following expressions is equivalent to the expression above?

A scientist initially measures 12,000 bacteria in a growth medium. 4 hours later, the scientist measures 24,000 bacteria. Assuming exponential growth, the formula \(P=C(2)^{rt}\) gives the number of bacteria in the growth medium, where \(r\) and \(C\) are constants and \(P\) is the number of bacteria \(t\) hours after the initial measurement. What is the value of \(r\)?

A rectangle has a length of $x$ units and a width of $(x-15)$ units. If the rectangle has an area of 76 square units, what is the value of $x$?

$\dfrac{2(x+1)}{x+5}=1-\dfrac{1}{x+5}$

What is the solution to the equation above?

$\frac{x^{2}-c}{x-b}$

In the expression above, $b$ and $c$ are positive integers. If the expression is equivalent to $x+b$ and $x\neq b$, which of the following could be the value of $c$?

$(x-4)(x+2)(x-1)=0$

What is the product of the solutions to the given equation?

Which of the following is equivalent to $3(x+5)-6$

Which expression is equivalent to $\frac{4}{4x-5} - \frac{1}{x+1}$?