sat-dog

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

If and , which of the following is equal to ?

Which of the following is a solution to the equation ?

$q-29r=s$

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

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

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 $k$?

$-x^2+bx-676=0$

In the given equation, $b$ is a positive integer. The equation has no real solution. What is the greatest possible value of $b$?

Function $f$ is defined by $f\left(x\right)=-a^x+b$, where $a$ and $b$ are constants. In the xy-plane, the graph of $y=f\left(x\right)-15$ has a y-intercept at $\left(0,-\frac{99}{7}\right)$. The product of $a$ and $b$ is $\frac{65}{7}$. What is the value of $a$?

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

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

If , which of the following expressions is equivalent to ?

$g\left(x\right)=x^2+55$

What is the minimum value of the given function?

$f\left(x\right)=\left(x-14\right)\left(x+19\right)$

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

If $3x^2-18x-15=0$, what is the value of $x^2-6x$?

In the xy-plane, what is the y-coordinate of the point of intersection of the graphs of and  ?

What is the y-intercept of the graph shown?

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 ?

What is the x-intercept of the graph shown?

$14j+5k=m$

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

$f\left(x\right)=\left(x+6\right)\left(x-4\right)$

If the given function $f$ is graphed in the xy-plane, where $y=f\left(x\right)$, what is the x-coordinate of an x-intercept of the graph?

$x\left(kx-56\right)=-16$

In the given equation, $k$ is an integer constant. If the equation has no real solution, what is the least possible value of $k$?

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

What is the positive solution to the given equation?

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

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 $t\le 5$?

$0.36x^2+0.63x+1.17$

The given expression can be rewritten as $a\left(4x^2+7x+13\right)$, where $a$ is a constant. What is the value of $a$?

$f\left(x\right)=\left(59-2x\right)$

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

$\frac{14x}{7y}=2\sqrt{w+19}$

The given equation relates the distinct positive real numbers $w$, $x$, and $y$. Which equation correctly expresses $w$ in terms of $x$ and $y$?