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Questions in mathematics

📝 Answered - Solve the equation. Express numbers as integers or simplified fractions. $-\frac{3}{4} t-5=-\frac{9}{10} t+\frac{2}{5}$ The solution set is $\square$

📝 Answered - Evaluate [tex] \int \frac{48 x+30}{8 x^2+10 x+4} d x [/tex] where [tex] 8 x^2+10 x+4\ \textgreater \ 0 [/tex] First substitute [tex]u =[/tex] $\square$ Then [tex]\int \frac{48 x+30}{8 x^2+10 x+4} d x=\int[/tex] $\square$ du Now integrate with respect to u to get $\square$ [tex]+C[/tex] So [tex]\int \frac{48 x+30}{8 x^2+10 x+4} d x=[/tex] $\square$ [tex]+ C[/tex]

📝 Answered - Lee surveyed students at school about whether they buy lunch or bring lunch from home. The data she gathered is shown in the two-way table below. Source of Student Lunches | | Bring Lunch to School | Buy Lunch in the Cafeteria | |---|---|---| | Boys | 12 | 18 | | Girls | 20 | 30 | According to the data in the table, what percentage of boys bring lunch to school? A. 15% B. 37.5% C. 40% D. 66.7%

📝 Answered - A factory has fixed costs of $1,275 per month. The cost of producing each unit of its product is $2.50. Each unit sells for $10. The equations that model the cost and revenue for producing $x$ units are shown. Cost: [tex]C (x)=1275+2.5 x[/tex] Revenue: [tex]R(x)=10 x[/tex] If the company sells every unit it produces, how many units must it sell in order to break even? [tex]\square[/tex] units

📝 Answered - The median of $9, 5, 7, 11, 13, 3$ is... a) 7 b) 8 c) 9 d) 11

📝 Answered - A collection of 108 coins containing only quarters and nickels is worth $21. Coin Collection \begin{tabular}{|r|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & \begin{tabular}{c} Number \\ of \\ Coins \end{tabular} & Value & Total \\ \hline Nickels & $n$ & 0.05 & $0.05 n$ \\ \hline Quarters & $q$ & 0.25 & $0.25 q$ \\ \hline Total & & & \\ \end{tabular} Which value could replace $q$ on the chart? A. 21 B. 108 C. $21-n$ D. $108-n$

📝 Answered - Let $f(x)=x^2-7x$ and $g(x)=6+x$. Find the following. (a) $(f + g)(x)$ (b) $(f - g)(x)$ (c) $(f \cdot g)(x)$ (d) $\left(\frac{f}{g}\right)(x)$ (e) The domain of $\frac{f}{g}$

📝 Answered - Find the solution to the system of equations: [tex]x+3 y=7[/tex] and [tex]2 x+4 y=8[/tex] 1. Isolate [tex]x[/tex] in the first equation: 2. Substitute the value for [tex]x[/tex] into the second equation: 3. Solve for [tex]y[/tex]: [tex] \begin{array}{l} x=7-3 y \\ 2(7-3 y)+4 y=8 \\ 14-6 y+4 y=8 \\ 14-2 y=8 \\ -2 y=-6 \\ y=3 \\ x+3(3)=7 \end{array} [/tex] 4. Substitute [tex]y[/tex] into either original equation: 5. Write the solution as an ordered pair:

📝 Answered - Identify the coefficient of [tex]$17 x y^3 z^{12}$[/tex] A) 12 B) 17 C) 3 D) 1

📝 Answered - Materials Needed: pen and paper Instructions: Complete the table below. Show all solutions. | H Sides | Interior Angle Sum | Measure of ONE INTERIOR Angle (Regular Polygon) | Exterior Angle Sum | Measure of ONE EXTERIOR Angle (Regular Polygon) | | --------- | ------------------- | --------------------------------------------- | ------------------ | ---------------------------------------------- | | 1) | - | $(n-2) 180^{\circ}$ | 340 | | | 2) 14 | 、 | $\square$ | $\square$ | $\qquad$ | | 3) 24 | i | - | - | , | | 4) 17 | - | $\square$ | | $\qquad$ | | 5) 8 | $1080^{\circ}$ | | | | | 6) 7 | $900^{\circ}$ | | | | | 7) 30 | $5040^{\circ}$ | | | | | 8) 11 | $1620^{\circ}$ | | | | | 9) 12 | | $150^{\circ}$ | | | | 10) 6 | | $120^{\circ}$ | | | | 11) 15 | | $156^{\circ}$ | | | | 2) SO | | | | $10^{\circ}$ | | ) $\frac{360}{x}$ | | | | $7.2^{\circ}$ | | | | | | $90^{\circ}$ | | | | | | $5^{\circ}$ | uarter 1