$f(x)=(x+4)(x-1)(2x-3)$

The function $f$ is defined above. Which of the following is NOT an $x$-intercept of the graph of the function in the $xy$-plane?

Kao measured the temperature of a cup of hot chocolate placed in a room with a constant temperature of 70 degrees Fahrenheit (${}^{\circ}$F). The temperature of the hot chocolate was 185${}^{\circ}$F at 6:00 p.m. when it started cooling. The temperature of the hot chocolate was 156${}^{\circ}$F at 6:05 p.m. and 135${}^{\circ}$F at 6:10 p.m. The hot chocolate's temperature continued to decrease. Of the following functions, which best models the temperature $T(m)$, in degrees Fahrenheit, of Kao's hot chocolate $m$ minutes after it started cooling?

The function $f$ is defined by $f(x)=x^{3}+15$. What is the value of $f(2)$?

The total revenue from sales of a product can be calculated using the formula $T=PQ$, where $T$ is the total revenue, $P$ is the price of the product, and $Q$ is the quantity of the product sold. Which of the following equations gives the quantity of product sold in terms of $P$ and $T$?

If a and c are positive numbers, which of the following is equivalent to $\sqrt{(a+c)^{3}}\cdot\sqrt{a+c}$?

$$f(x)=9(4)^{x}$$

The function $f$ is defined by the given equation. If $g(x)=f(x+2)$, which of the following equations defines the function $g$?

$$64x^{2}+bx+25=0$$

In the given equation, $b$ is a constant. For which of the following values of $b$ will the equation have more than one real solution?

Which of the following is equivalent to $\sqrt[4]{x^{2}+8x+16}$, where $x>0$?

The function $f$ is defined by $f(x)=8\sqrt{x}$. For what value of $x$ does $f(x)=48$?

$x^{2}= 64$

Which of the following values of $x$ satisfies the given equation?

$(4x^{3}-5x^{2}+3)-(6x^{3}+2x^{2}-x)$

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

$\frac{4x^{2}}{x^{2}-9}-\frac{2x}{x+3}=\frac{1}{x-3}$

What value of $x$ satisfies the equation above?

$\left(\frac{1}{2}x+3\right)-\left(\frac{2}{3}x-5\right)$

Which of the following is equivalent to the expression above?

The equation $E(t)=5{(1.8)}^{t}$ gives the estimated number of employees at a restaurant, where $t$ is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context?

$6x^{2}+5x-7=0$

What are the solutions to the given equation?

The function $p$ is defined by $p(n)=7n^{3}$. What is the value of $n$ when $p(n)$ is equal to 56?

$(2x+3)-(x-7)$

Which of the following is equivalent to the given expression?

$y=x^{2}+3x-f$

$y-5x+8=0$

How many solutions are there to the system of equations above?

Which of the following is equivalent to

$(1-p)(1+p+p^{2}+p^{3}+p^{4}+p^{5}+p^{6})$?

$(2x^{3}+3x)(x^{3}-2x)$

Which of the following is equivalent to the expression above?

$x=8$

$y=x^{2}+8$

The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is the value of $y$?

$$x^{2}-40x-10=0$$

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

If $a=c+d$, which of the following is equivalent to the expression $x^{2}-c^{2}-2cd-d^{2}$?

Function $f$ is defined by $f(x)=(x+6)(x+5)(x+1)$. Function $g$ is defined by $g(x)=f(x-1)$. The graph of $y=g(x)$ in the $xy$-plane has x-intercepts at $(a,0)$, $(b,0)$, and $(c,0)$, where $a$, $b$, and $c$ are distinct constants. What is the value of $a+b+c$?

$y=x^{2}$

$2y+6=2(x+3)$

If $\{x,y\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?