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Questions in mathematics

[Answered] -8(3x - \frac{1}{4}) = 2(9 - 7x)

[Answered] Select all the correct locations on the table. Consider the following expression. [tex]$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$[/tex] Select "equivalent" or "not equivalent" to indicate whether the expression above is equivalent or not equivalent to the values or expressions in the last column. \begin{tabular}{|l|l|l|l|} \hline [tex]$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$[/tex] & Equivalent & Not Equivalent & 343 \\ \hline [tex]$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$[/tex] & Equivalent & Not Equivalent & 49 \\ \hline [tex]$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$[/tex] & Equivalent & Not Equivalent & [tex]$7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}$[/tex] \\ \hline [tex]$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$[/tex] & Equivalent & Not Equivalent & [tex]$49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}$[/tex] \\ \hline \end{tabular}

[Answered] Given [tex]$\sin \theta=\frac{4}{7}$[/tex], what is [tex]$\cos \theta$[/tex]? Report your answer in simplest form.

[Answered] Select the correct descriptions of the function. The table gives the values of a function. [tex]\begin{tabular}{|c|c|}\hline$x$ & $y$ \\ \hline 1 & 5 \\ \hline 2 & 5 \\ \hline 3 & 5 \\ \hline \end{tabular}[/tex] Identify the phrases that correctly describe this function. $\square$ constant rate $\square$ constant function $\square$ linear function $\square$ nonlinear function $\square$ increasing function $\square$ decreasing function

[Answered] Find the derivative of: [tex]f(x)=-5 \sin ^2\left(-2 x^8\right)[/tex]. Hint: [tex]\sin ^2(x)=[\sin (x)]^2[/tex] ... so use the chain rule (twice!).

[Answered] What is the value of $m$ in the equation $\frac{1}{2} m-\frac{3}{4} n=16$, when $n=8$?

[Answered] Simplify $\frac{5^5 \cdot 6^3 \cdot 8^{10}}{5^3 \cdot 6 \cdot 8^9}$

[Answered] Is the expression [tex]x^3 \cdot x^3 \cdot x^3[/tex] equivalent to [tex]x^{3 \cdot 3 \cdot 3}[/tex], or why not? Explain your reasoning. A. Yes, because when multiplying powers with the same exponent, you multiply the bases. B. No, because [tex]x^3 \cdot x^3 \cdot x^3 = x^9[/tex] while [tex]x^{3 \cdot 3 \cdot 3} = x^{27}[/tex], and these are not the same. C. Yes, because the numbers 3 and exponent 3 can be interchanged without changing the result.

[Answered] Points $P, Q, R$, and $S$ are collinear. Point $Q$ is between $P$ and $R, R$ is between $Q$ and $S$, and $\overline{P Q} \cong \overline{R S}$. If $P S=24$ and $P R=20$, what is the value of $Q R$?

[Answered] Select the correct answer. Which logarithmic equation is equivalent to this exponential equation? [tex]$2,400=7,500(10)^{-x}$[/tex] A. [tex]$x=-\log \left(\frac{25}{8}\right)$[/tex] B. [tex]$x=\log \left(-\frac{25}{8}\right)$[/tex] C. [tex]$x=\log \left(\frac{8}{25}\right)$[/tex] D. [tex]$x=-\log \left(\frac{8}{25}\right)$[/tex]