Questions in mathematics

Questions in mathematics

📝 Answered - 3. The coefficient of [tex]$x^3$[/tex] in the expansion of [tex]$\left(x-\frac{a}{x^2}\right)^7$[/tex] is [tex]$\frac{14}{9}$[/tex]. (i) Find the possible values of [tex]$a$[/tex]. (ii) If [tex]$a\ \textgreater \ 0$[/tex], find the term independent of [tex]$x$[/tex]. (iii) Hence, for [tex]$a\ \textgreater \ 0$[/tex], find the term which is independent of [tex]$x$[/tex] in the expansion of [tex]$\left(7 x^3\right)\left(x-\frac{a}{x^2}\right)^7$[/tex]

📝 Answered - What is the equation of the line that is perpendicular to the given line and passes through the point $(5,3)$? $4 x-5 y=5$ $5 x+4 y=37$ $4 x+5 y=5$ $5 x-4 y=8$

📝 Answered - The given line passes through the points $(0,-3)$ and $(2, 3)$. What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point $(-1,-1)$? A. $y+1=-3(x+1)$ B. $y+1=-\frac{1}{3}(x+1)$ C. $y+1=\frac{1}{3}(x+1)$ D. $y+1=3(x+1)$

📝 Answered - Evaluate: [tex]\begin{array}{c} \sum_{n=1}^6 4(3)^{n-1} \ S=[?]\end{array}[/tex] Remember: for a geometric series, [tex]S=\frac{a\left(1-r^n\right)}{1-r}[/tex]

📝 Answered - Find the first 3 iterates of the function [tex]f(x)=-2 x+3[/tex] when [tex]x_0=0[/tex]. A. 1,1,1 B. 2,-1, 5 C. -2,0,2 D. 3,-3,9

📝 Answered - The volume of a cylinder can be found using the formula [tex]$V=\pi r^2 h$[/tex]. Which is the correct first step in finding the height of a cylinder with a volume of [tex]$192 \pi$[/tex] cubic inches and a radius of 5 inches? A. [tex]$5=\pi(192)^2 h$[/tex] B. [tex]$V=\pi+(5)^2+192 \pi$[/tex] C. [tex]$V=\pi(5)^2(192)$[/tex] D. [tex]$192 \pi=\pi(5)^2 h$[/tex]

📝 Answered - Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for $35, then took 5 hours of group snowboarding lessons. Victor paid $175 in all. Which equation can you use to find how much Snowy Ridge charges, $x$, for each hour of group snowboarding lessons? $35 x+5=175$ $35(x+5)=175$ $5 x+35=175$ $5(x+35)=175$ How much does Snowy Ridge charge for each hour of group snowboarding lessons? $ $\square$

📝 Answered - $(1,-3)$ is not a solution to the inequality $y>4x-3$. True or False?

📝 Answered - Find the equation of the line specified. The line passes through the points $(7,-7)$ and $(6,-5)$. a. $y=-2 x+7$ b. $y=2 x-21$ c. $y=-2 x-7$ d. $y=2 x-7$

📝 Answered - Simplify the following expression: $\frac{-8-\sqrt{-9}}{6}$. Give your answer in the form $a+b i$.