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Questions in Grade College

📝 Answered - 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]

📝 Answered - 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 $\tan ^{-1}(\frac{y}{x})$.

📝 Answered - 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

📝 Answered - 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.

📝 Answered - 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.

📝 Answered - What was the first animal to orbit the earth? A. rat B. pig C. dog D. monkey

📝 Answered - 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. $\{x \mid x=-4,-2,-1,0,1,3,4,5,6,9\}$

📝 Answered - Divide. [tex]$\frac{15}{35} \div \frac{3}{11}$[/tex]

📝 Answered - Complete the table of inputs and outputs for the function. [tex]f(x)=-5(x+7)[/tex] | x | f(x) | | --- | ---- | | -9 | | | | 0 | | 0 | | | | -60 |

📝 Answered - Find the point of local maxima (LM) and local minima (lm) of the function [tex]$x^3-x^2-5 x$[/tex] using the second derivative test. a) $(L M, l m)=(\frac{5}{3}, 1)$ b) $(L M, l m)=(1, \frac{5}{3})$ c) $(L M, l m)=(-1, \frac{5}{3})$ d) $(L M, l m)=(\frac{5}{3},-1)$