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$$57x^{2}+\big{(}57b+a\big{)}x+ab=0$$ 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 $k$?

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\[q-29r=s\] The given equation relates the positive numbers $q$, $r$, and $s$. Which equation correctly expresses $q$ in terms of $r$ and $s$?

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

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

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The function $f$ is defined by $f(x)=\frac{1}{6x}$. What is the value of $f(x)$ when $x=37$

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An oceanographer uses the equation $\boldsymbol{S=\frac{3}{2}P}$ 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?

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

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

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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 $r$?

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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\)?

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**Abstract** We study the

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$\frac{x^{2}-c}{x-b}$ 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 $c$ ? B. 6 C. 8 D. 10

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$(x-4)(x+2)(x-1)=0$ What is the product of the solutions to the given equation?

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Which of the following is equivalent to $3\times$

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

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Which expression is equivalent to $20w-(4w+3w)$?

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Which expression is equivalent to $50x^{2}+5x^{2}$?

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Which expression is equivalent to $11x^{3}-5x^{3}$?

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$f(x)=4x^{2}+64x+262$ The function $g$ is defined by $g(x)=f(x+5)$. For what value of $x$ does $g(x)$ reach its minimum?

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\[f(x)=ax^{2}+4x+c\] In the given quadratic function, $a$ and $c$ are constants. The graph of $y=f(x)$ in the $xy$-plane is a parabola that opens upward and has a vertex at the point $(h,k)$, where $h$ and $k$ are constants. If $k<0$ and $f(-9)=f(3)$, which of the following must be true? I. $c<0$ II. $a\geq 1$

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2x$({}^{2}-2)=2x+3$ Which of the following is a solution to the equation above?

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\[7m=5(n+p)\] The given equation relates the positive numbers $m$, $n$, and $p$. Which equation correctly gives $n$ in terms of $m$ and $p$?

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$y=76$ $y=x^{2}-5$ The graphs of the given equations in the $xy$-plane intersect at the point $x,y$. What is a possible value of $x\)?

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The equation above estimates the global data traffic $D$, in terabytes, for the year that is $t$ years after 2010. What is the best interpretation of the number 5,640 in this context?

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$\begin{tabular}{|c|c|} \hline Day & Number of bacteria per milliliter at end of day \\ \hline 1 & 2.5\times10^{5} \\ \hline 2 & 5.0\times10^{5} \\ \hline 3 & 1.0\times10^{6} \\ \hline \end{tabular}$ A culture of bacteria is growing at an exponential rate, as shown in the table above. At this rate, on which day would the number of bacteria per milliliter reach $5.12\times 10^{5}$?

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