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Which of the following expressions is equivalent to ?

Which of the following expressions is(are) a factor of $3x^2+20x-63$?

1.  $x-9$
2. $3x-7$

If for all positive values of x, what is the value of ?

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 $y=f\left(x\right)-12$ has a y-intercept at $\left(0,-\frac{75}{7}\right)$. The product of $a$ and $b$ is $\frac{320}{7}$. What is the value of $a$?

Scientists recorded data about the ocean water levels at a certain location over a period of $6$ hours. The graph shown models the data, where $y=0$ represents sea level. Which table gives values of $x$ and their corresponding values of $y$ based on the model?

$6r=7s+t$

The given equation relates the variables $r$, $s$, and $t$. Which equation correctly expresses $s$ in terms of $r$ and $t$?

If x is a solution to the given equation, which of the following is a possible value of ?

The function $f$ is defined by $f\left(x\right)=4+\sqrt{x}$. What is the value of $f\left(144\right)$?

A rectangular volleyball court has an area of 162 square meters. If the length of the court is twice the width, what is the width of the court, in meters?

A machine launches a softball from ground level. The softball reaches a maximum height of $51.84$ meters above the ground at $1.8$ seconds and hits the ground at $3.6$ seconds. Which equation represents the height above ground $h$, in meters, of the softball $t$ seconds after it is launched?

The 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 $y=f\left(x\right)$ has an $x$-intercept at $\left(2,0\right)$ and a $y$-intercept at $\left(0,-323\right)$. What is the value of $b$?

The function S above models the annual salary, in dollars, of an employee n years after starting a job, where a is a constant. If the employee’s salary increases by 4% each year, what is the value of a ?

During a 5-second time interval, the average acceleration a, in meters per second squared, of an object with an initial velocity of 12 meters per second is defined by the equation , where v_f is the final velocity of the object in meters per second. If the equation is rewritten in the form v_f = xa + y, where x and y are constants, what is the value of x ?

The expression $90y^5-54y^4$ is equivalent to $r{y}^4\left(15y-9\right)$, where $r$ is a constant. What is the value of $r$?

The revenue , in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of in the xy-plane intersects the x-axis at 0 and a. What does a represent?

The equation above is true for all , where r and t are positive constants. What is the value of rt ?

Which of the following is an equivalent form of ?

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 ?

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?

$y=76$
$y=x^2-5$

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

$7m=5\left(n+p\right)$

The given equation relates the positive numbers $m$, $n$, and $p$. Which equation correctly gives $n$ in terms of $m$ and $p$?

$\sqrt[5]{70n}{\left(\sqrt[6]{70n}\right)}^2$

For what value of $x$ is the given expression equivalent to ${\left(70n\right)}^{30x}$, where $n>1$?

Which of the following is a solution to the equation above?

$f\left(x\right)=a{x}^2+4x+c$

In the given quadratic function, $a$ and $c$ are constants. The graph of $y=f\left(x\right)$ in the xy-plane is a parabola that opens upward and has a vertex at the point $\left(h,k\right)$, where $h$ and $k$ are constants. If $k<0$ and $f\left(-9\right)=f\left(3\right)$, which of the following must be true?

1. $c<0$
2. $a\ge 1$

The x-intercept of the graph shown is $\left(x,0\right)$. What is the value of $x$?