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A ball is dropped from an initial height of 22 feet and bounces off the ground repeatedly. The function $h$ estimates that the maximum height reached after each time the ball hits the ground is 85% of the maximum height reached after the previous time the ball hit the ground. Which equation defines $h$, where $h(n)$ is the estimated maximum height of the ball after it has hit the ground $n$ times and $n$ is a whole number greater than $1$ and less than 10?

MathAdvanced Math

$\begin{tabular}{|c|c|} \hline $\chi$ & $\rho(\chi)$ \\ \hline $-2$ & $5$ \\ \hline $-1$ & $0$ \\ \hline $0$ & $-3$ \\ \hline $1$ & $-1$ \\ \hline $2$ & $0$ \\ \hline \end{tabular}$ The table above gives selected values of a polynomial function $\rho$. Based on the values in the table, which of the following must be a factor of $\rho$ ?

MathAdvanced Math

$8x+y=-11$ $2x^{2}=y+341$ The graphs of the equations in the given system of equations intersect at the point $x,y$ in the $xy$-plane. What is a possible value of $x$?

MathAdvanced Math

$8j=k+15m$ The given equation relates the distinct positive numbers $j$, $k$, and $m$. Which equation correctly expresses $j$ in terms of $k$ and $m$?

MathAdvanced Math

In the $xy$-plane, a parabola has vertex $(9,-14)$ and intersects the $x$-axis at two points. If the equation of the parabola is written in the form $\bm{y}=a\bm{x}^{2}+b\bm{x}+\bm{c}$, where $\bm{a}$, $\bm{b}$, and $\bm{c}$ are constants, which of the following could be the value of $\bm{a}+\bm{b}+\bm{c}$?

MathAdvanced Math

An object's kinetic energy, in joules, is equal to the product of one-half the object's mass, in kilograms, and the square of the object's speed, in meters per second. What is the speed, in meters per second, of an object with a mass of 4 kilograms and kinetic energy of 18 joules?

MathAdvanced Math

$f(x)=2(3x)$ For the function $f$ defined above, what is the value of $f(2)$?

MathAdvanced Math

$$\frac{x^{2}}{\sqrt{x^{2}-c^{2}}}=\frac{c^{2}}{\sqrt{x^{2}-c^{2}}}+39$$ In the given equation, $c$ is a positive constant. Which of the following is one of the solutions to the given equation? ### $-c$ B. $-c^{2}-39^{2}$ C. $-\sqrt{39^{2}-c^{2}}$ D. $-\sqrt{c^{2}+39^{2}}$

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$$-9x^{2}+30x+c=0$$ In the given equation, $c$ is a constant. The equation has exactly one solution. What is the value of $c$?

MathAdvanced Math

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MathAdvanced Math

$$f(t)=8,000(0.65)^{t}$$ The given function $f$ models the number of coupons a company sent to their customers at the end of each year, where $t$ represents the number of years since the end of 1998, and $0\leq t\leq 5$. If $y=f(t)$ is graphed in the $ty$-plane, which of the following is the best interpretation of the $y$-intercept of the graph in this context?

MathAdvanced Math

$\begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline $-1$ & $10$ \\ \hline $0$ & $14$ \\ \hline $1$ & $20$ \\ \hline \end{tabular}$ For the quadratic function $f$, the table shows three values of $x$ and their corresponding values of $f(x)$. Which equation defines $f$?

MathAdvanced Math

The expression $2x^{2}+ax$ is equivalent to $x(2x+7)$ for some constant $a$. What is the value of $a$ ?

MathAdvanced Math

The function $$f(w)=6w^{2}$$ gives the area of a rectangle, in square feet $$\left(\text{ft}^{2}\right)$$, if its width is $$w$$ ft and its length is 6 times its width. Which of the following is the best interpretation of $$f(14)=1,176$$?

MathAdvanced Math

$y=x^{2}+2x+1$ $x+y+1=0$ If $x_{1},y_{1}$ and $x_{2},y_{2}$ are the two solutions to the system of equations above, what is the value of $y_{1}+y_{2}$?

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The function $\bm{f}(\bm{x})=\frac{1}{9}(x-7)^{2}+3$ gives a metal ball's height above the ground $\bm{f}(\bm{x})$, in inches, $\bm{x}$ seconds after it started moving on a track, where $0\leq\bm{x}\leq 10$. Which of the following is the best interpretation of the vertex of the graph of $\bm{y}=\bm{f}(\bm{x})$ in the $xy$-plane?

MathAdvanced Math

$\textbf{5}\textbf{x}^{2}+10\textbf{x}+16=0$ How many distinct real solutions does the given equation have?

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MathAdvanced Math

The expression $\frac{1}{3}x^{2}-2$ can be rewritten as $\frac{1}{3}(x-k)(x+k)$, where $$k$ is a positive constant. What is the value of $$k$}?

MathAdvanced Math

$f(x)=x^{3}+3x^{2}-6x-1$ For the function $f$ defined above, what is the value of $f(-1)$?

MathAdvanced Math

$f(x)=x^{3}-9x$ $g(x)=x^{2}-2x-3$ Which of the following expressions is $f(x)$ equivalent to $g(x)$ , for $x>3$ ? $x+1$ $x+3$ B. $x+1$ $x(x-3)$ C. $x+1$ $x(x+3)$ B. $x+1$

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Which expression is a factor of $2x^{2}+38x+107$ B. $5x$ C. $38x$ D. $2x$

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$(x-1)^{2}=-4$ How many distinct real solutions does the given equation have?

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$$y=0.25x^{2}-7.5x+90.25$$ The equation gives the estimated stock price $y_{i}$ in dollars, for a certain company $x$ days after a new product launched, where $0\leq x\leq 20$. Which statement is the best interpretation of $(x,y)=(1,83)$ in this context?

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The expression $4x^{2}+bx-45$, where $b$ is a constant, can be rewritten as $(hx+k)(x+j)$, where $h$, $k$, and $j$ are integer constants. Which of the following must be an integer?

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