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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?

MathAdvanced Math

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\)?

MathAdvanced Math

**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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