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Questions in mathematics

[Done] Let $L(t)$ represent the number of likes on a social media post, $t$ hours after it is posted. Interpret the statement $L(4)=2 L(3)$.

[Done] Use integration by parts [tex]$\int_0^1 2 s e^{-5 s} d s=$[/tex]

[Done] Add: $\left(8 g^5-5 h\right)+-9 g^5$ Enter the correct answer.

[Done] Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. [tex]\begin{array}{l} y\ \textgreater \ -2 x-1 \\ y\ \textless \ \frac{1}{2} x+4 \end{array}[/tex]

[Done] 9. [tex]$-24 \times(-2)$[/tex] 10. [tex]$-11+24$[/tex] 11. [tex]$-9-13$[/tex] 12. [tex]$\frac{-63}{-9}$[/tex] 13. [tex]$-11 \cdot(-4)$[/tex] 14. [tex]$21-27$[/tex] 15. [tex]$84+(-4)$[/tex] 16. [tex]$5 \times(-5)$[/tex] 17. [tex]$\frac{-16}{8}$[/tex] 18. [tex]$49+-7$[/tex] 19. [tex]$120+6$[/tex] 20. [tex]$-3+(-5)$[/tex] 21. [tex]$26-19$[/tex] 22. [tex]$12-(-8)$[/tex] 23. [tex]$0 \cdot(-11)$[/tex] 24. [tex]$-18 \times(-2)$[/tex] Find the value for the rectangle that completes the equation. 25. [tex]$5-(\square)=-2$[/tex] 26. [tex]$-3 \cdot \square=-27$[/tex] 27. [tex]$\square+(-5)=45$[/tex] 28. [tex]$\square -(-8)=-3$[/tex] 29. [tex]$\square \cdot(-7)=70$[/tex] 30. [tex]$\frac{\square}{-4}=-24$[/tex]

[Done] In the complex plane, the rectangular coordinates $(x, y)$ represent a complex number. Which statement explains why polar coordinates $(r, \theta)$ represent the same complex number? A. $r$ is equivalent to $\sqrt{x^2+y^2}$ and $\theta$ is equivalent to $\tan ^{-1}(\frac{x}{y})$ B. $r$ is equivalent to $\sqrt{x^2+y^2}$ and $\theta$ is equivalent to $\tan ^{-1}(\frac{y}{x})$. C. $r$ is equivalent to $\sqrt{x^2-y^2}$ and $\theta$ is equivalent to $\tan ^{-1}(\frac{x}{y})$. D. $r$ is equivalent to $\sqrt{x^2-y^2}$ and $\theta$ is equivalent to $\tan ^{-1}(\frac{y}{x})$.

[Done] Determine any data values that are missing from the table, assuming that the data represent a linear function. \begin{tabular}{|l|l|} \hline$x$ & $y$ \\ \hline 1 & 6 \\ \hline 2 & 10 \\ \hline 3 & \\ \hline \end{tabular} A. 6 B. 15 C. 16 D. 14

[Done] The table below shows how much Joe earns, $y$, after working $x$ hours. Joe's Earnings \begin{tabular}{|c|c|} \hline Hours worked & Money earned \\ \hline 4 & $30 \\ \hline 10 & $75 \\ \hline 12 & $90 \\ \hline 22 & $165 \\ \hline \end{tabular} The relationship between money earned and hours worked is linear. Joe computes the slope between $(4,30)$ and $(12, 90)$, then computes the slope between $(4,30)$ and $(10,75)$. How do the two slopes compare? A. The slope between $(4,30)$ and $(12,90)$ is greater because the ordered pairs are farther apart on the $x$-axis. B. The slope between $(4,30)$ and $(12,90)$ is greater because the ordered pairs are farther apart on the $y$-axis. C. The slope between $(4,30)$ and $(12,90)$ and between $(4,30)$ and $(10,75)$ is the same. D. The slope between $(4,30)$ and $(12,90)$ is less because 4 is a factor of 12 and 30 is a factor of 90.

[Done] Evaluate the expression when [tex]$x=6$[/tex] and [tex]$z=4$[/tex]. [tex]$7 x^2+\frac{72}{z}$[/tex] Simplify your answer as much as possible.

[Done] What is the domain of the given function? $\left\{(3,-2),(6,1),(-1,4),(5,9),(-4,0)\right\}$ A. $\{x \mid x=-4,-1,3,5,6\}$ B. $\{y \mid y=-2,0,1,4,9\}$ C. $\{y \mid y=-4,-2,-1,0,1,3,4,5,6,9\}$ D. $\{x \mid x=-4,-2,-1,0,1,3,4,5,6,9\}$