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Questions in mathematics

[Answered] Which expression can be used to determine the average rate of change in [tex]f(x)[/tex] over the interval [tex]$[2,9]$[/tex]?

[Answered] Evaluate $f(3)$ for the piecewise function: $f(x)=\left[\begin{array}{l} \frac{3 x}{2}+8, x<-6 \\ -3 x-2,-4 \leq x \leq 3 \\ 4 x+4, x>3 \end{array}\right.$ Which value represents $f(3)$? A. -11 B. 9 C. 12.5 D. 18

[Answered] Which of the following describes the transformation of $g(x)=3(2)^{-x}+2$ from the parent function $f(x)=2^x$? A. reflect across the $x$-axis, stretch the graph vertically by a factor of 3, shift 2 units up B. reflect across the $y$-axis, stretch the graph vertically by a factor of 2, shift 3 units up C. reflect across the $x$-axis, stretch the graph vertically by a factor of 2, shift 3 units up D. reflect across the $y$-axis, stretch the graph vertically by a factor of 3, shift 2 units up

[Answered] What is the simplest form of [tex]$\sqrt{1,764}$[/tex]? A. 21 B. 42 C. [tex]$3^2\left(7^2\right)$[/tex] D. [tex]$2^2\left(3^2\right)\left(7^2\right)$[/tex]

[Answered] Which expression is equivalent to $\sum_{n=1}^{60}(2 n-1)^2 $? Check all that apply. $\sum_{n=1}^{60} 4 n^2-4 n-1$ $4 \sum_{n=1}^{\infty} n^2-4 \sum_{n=1}^{\infty} n+\sum_{n=1}^{\infty} 1$ $4 \sum_{n=1}^{\infty} n^2-4 \sum_{n=1}^{\infty} n-\sum_{n=1}^{\infty} 1$ $4 \sum_{n=1}^{\infty} n^2-4 \sum_{n=1}^{\infty} n+60$

[Answered] Select the correct answer. Which statement is true about this radical function? [tex]$f(x)=-\sqrt{x+6}$[/tex] A. As [tex]$x$[/tex] approaches positive infinity, [tex]$f(x)$[/tex] approaches positive infinity. B. As [tex]$x$[/tex] approaches negative infinity, [tex]$f(x)$[/tex] approaches positive infinity. C. As [tex]$x$[/tex] approaches positive infinity, [tex]$f(x)$[/tex] approaches negative infinity. D. As [tex]$x$[/tex] approaches negative infinity, [tex]$f(x)$[/tex] approaches negative infinity.

[Answered] A rectangular prism has side lengths of $2 \sqrt{6} cm, \sqrt{2} cm$, and $2 \sqrt{3} cm$. Without using a calculator, put these side lengths in order from greatest to least. (Hint: consider the value of each radicand and what taking the square root does to each value.) Drag each tile to the correct box. Tiles $2 \sqrt{6} cm$ $\sqrt{2} cm$ $2 \sqrt{3} cm$ Sequence $\square$ $\square > \square$

[Answered] Solve for $x$ in the equation $x^2-12 x+36=90$. A. $x=6 \pm 3 \sqrt{10}$ B. $x=6 \pm 2 \sqrt{7}$ C. $x=12 \pm 3 \sqrt{22}$ D. $x=12 \pm 3 \sqrt{10}$

[Answered] $\lim _{x \rightarrow 0}\left(\frac{\cot x}{\cot 2 x}\right)=2$

[Answered] There are 128 seats in a movie theater and $[3 / 4]$ of them are occupied by moviegoers. How many moviegoers are in the theater?