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The table above gives the values of the function f for some values of x. Which of the following equations could define f ?

The expression $6\sqrt[5]{3^5{x}^{45}}·\sqrt[8]{2^{8}x}$ is equivalent to $a{x}^b$, where $a$ and $b$ are positive constants and $x>1$. What is the value of $a+b$?

If the given expression is rewritten in the form , where k is a constant, what is the value of k ?

The formula above expresses the square of the speed v of a wave moving along a string in terms of tension T, mass m, and length L of the string. What is T in terms of m, v, and L ?

$64x^2-\left(16a+4b\right)x+ab=0$

In the given equation, $a$ and $b$ are positive constants. The sum of the solutions to the given equation is $k\left(4a+b\right)$, where $k$ is a constant. What is the value of $k$?

$\left(x-2\right)=9$

What is one possible solution to the given equation?

Which expression represents the product of $\left(x^{-6}{y}^3{z}^5\right)$ and $\left(x^4{z}^5+y^8{z}^{-7}\right)$?

If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

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

If , which of the following is equivalent to the expression ?

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

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

$x=8$

$y=x^2+8$

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

Which of the following is equivalent to the expression above?

The exponential function $g$ is defined by $g\left(x\right)=19·a^x$, where $a$ is a positive constant. If $g\left(3\right)=\mathrm{2,375}$, what is the value of $g\left(4\right)$?

$\frac{55}{x+6}=x$

What is the positive solution to the given equation?

The total distance d, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, where t is the time in seconds. At a time of 10.0 seconds, the total distance traveled by the object is 50.0 meters, and at a time of 20.0 seconds, the total distance traveled by the object is 200.0 meters. If the object was at a distance of 0 meters when , then what is the total distance traveled, in meters, by the object after 30.0 seconds?

Which of the following is equivalent to  ?

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

Which of the following is equivalent to the given expression?

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

What are the solutions to the given equation?

The equation $E\left(t\right)=5{\left(1.8\right)}^t$ 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?

Which of the following is equivalent to the expression above?

What value of x satisfies the equation above?

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