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Questions in mathematics

[Done] $5-(4)^2 \div(-5-3) \cdot 2

[Done] Point S is on line segment $\overline{R T}$. Given $S T=3 x-8, R T=4 x$, and $R S=4 x-7$, determine the numerical length of $\overline{R T}$.

[Done] \begin{tabular}{|l|l|} \hline Expression 1 & Expression 2 \\ \hline & \\ \hline \end{tabular} 2. The value of $27^{\frac{2}{3}}$ is 9 32 54 72 For questions $3-5$, write an equivalent radical expression and then find the value of expression. 3. $(-125)^{\frac{2}{3}}=$ $\qquad$ = $\qquad$

[Done] Match each term with its appropriate variable, [tex]$x$[/tex] or [tex]$y$[/tex]. | | [tex]$x$[/tex] | [tex]$y$[/tex] | | :-------------------- | :-------------: | :-------------: | | dependent variable | 0 | 0 | | domain | 0 | 0 | | independent variable | 0 | 0 | | input | 0 | 0 | | output | 0 | 0 | | range | 0 | 0 |

[Done] Evaluate the left hand side to find the value of $a$ in the equation in simplest form. [tex]\frac{x^{\frac{3}{2}}}{x^{\frac{2}{3}}}=x^a[/tex]

[Done] $\int \sec ^2(\theta) \tan ^6(\theta) d \theta$

[Done] A researcher wants to study the effects of sleep deprivation on motor skills. Nine people volunteer for the experiment: Amanda, Brian, Christine, David, Emily, Fred, George, Heather, and Ivan. Use the third row of digits in the random number table below to select a simple random sample of three subjects (ignore zeros). The other six subjects will go into the control group. If the subjects are numbered 1 through 9 alphabetically, what are the numbers of the three subjects selected? List the subjects that will go in the treatment group. \begin{tabular}{|l|l|l|l|l|}\hline Line/Column & (1) & (2) & (3) & (4) \\ \hline 1 & 37330 & 87385 & 32323 & 71009 \\ \hline 2 & 46254 & 15935 & 65321 & 89215 \\ \hline 3 & 65216 & 32341 & 68693 & 55931 \\ \hline \end{tabular} What are the numbers of the three subjects selected? The three subjects, in the order selected, are Brian, Emily, and Fred.

[Done] The graph of the even function [tex]f(x)[/tex] has five [tex]x[/tex]-intercepts. If [tex](6,0)[/tex] is one of the intercepts, which set of points can be the other [tex]x[/tex]-intercepts of the graph of [tex]f(x)[/tex]? A. [tex](-6,0),(-2,0)[/tex], and [tex](0,0)[/tex] B. [tex](-6,0),(-2,0)[/tex], and [tex](4,0)[/tex] C. [tex](-4,0),(0,0)[/tex], and [tex](2,0)[/tex] D. [tex](-4,0),(-2,0)[/tex], and [tex](0,0)[/tex]

[Done] It is asking to factor out the following equation: x^(3)+x^(2)-x-10. I know I need to get the possible rational roots, but I don’t know how to get it.

[Done] 16. $4+2 g+5 g=-66$ 17. $5 h+3 \geq 3 h+11$ 18. $5 i+4=14+4 i$ 19. $4 j+26=50+6 j$ 20. $2 k+36=6 k-12$ 21. $L+21=-L+87$