The Answer is C
R is (2,-1)
2*2=4
-1*2=-2
2r=(4,-2)
t=(-7,5)
-7-4=-11
5-(-2)=5+2=7
t-r=(-11,7)
Since we are multiplying r by two, we have to multiply its x and y values by two to be 2r
With t-2r, we have to subtract 2r's x value from t's x value and 2r's y value fro t's y value to get the x value -11 and the y value 7
Therefore, the x and y values for the answer is -11 and 7, and to put them in the proper form required, which is (x,y), input -11 into x's spot and 7 in y's spot, giving you and answer of (-11,7)
I definitely just took an exam with this question. The answer is definitely C. Trapezoid.
A population of 2,000 mosquitos grows at a rate of 15% per month. Which equation models the population, p(t), of the mosquitos after t months?
1 yard = 36 inches
Then 12 characters/inch * 36 inch/yard = 432 characters / yard.
The answer is 432 characters per yard of text.
Check the picture below.
so the hyperbola looks more or less like so, with a = 6, and its center at the origin.
![\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bhyperbolas%2C%20vertical%20traverse%20axis%20%7D%20%5C%5C%5C%5C%20%5Ccfrac%7B%28y-%20k%29%5E2%7D%7B%20a%5E2%7D-%5Ccfrac%7B%28x-%20h%29%5E2%7D%7B%20b%5E2%7D%3D1%20%5Cqquad%20%5Cbegin%7Bcases%7D%20center%5C%20%28%20h%2C%20k%29%5C%5C%20vertices%5C%20%28%20h%2C%20k%5Cpm%20a%29%5C%5C%20c%3D%5Ctextit%7Bdistance%20from%7D%5C%5C%20%5Cqquad%20%5Ctextit%7Bcenter%20to%20foci%7D%5C%5C%20%5Cqquad%20%5Csqrt%7B%20a%20%5E2%20%2B%20b%20%5E2%7D%5C%5C%20asymptotes%5Cquad%20y%3D%20k%5Cpm%20%5Ccfrac%7Ba%7D%7Bb%7D%28x-%20h%29%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\bf \begin{cases} a=6\\ h=0\\ k=0\\ \stackrel{asymptotes}{y=\pm\frac{3}{4}x} \end{cases}\implies \stackrel{\textit{using the positive asymptote}}{0+\cfrac{6}{b}(x-0)=\cfrac{3}{4}x}\implies \cfrac{6x}{b}=\cfrac{3x}{4}\implies 24x=3xb \\\\\\ \cfrac{24x}{3x}=b\implies 8=b \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(y- 0)^2}{ 6^2}-\cfrac{(x- 0)^2}{ 8^2}=1\implies \cfrac{y^2}{36}-\cfrac{x^2}{64}=1](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20a%3D6%5C%5C%20h%3D0%5C%5C%20k%3D0%5C%5C%20%5Cstackrel%7Basymptotes%7D%7By%3D%5Cpm%5Cfrac%7B3%7D%7B4%7Dx%7D%20%5Cend%7Bcases%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20positive%20asymptote%7D%7D%7B0%2B%5Ccfrac%7B6%7D%7Bb%7D%28x-0%29%3D%5Ccfrac%7B3%7D%7B4%7Dx%7D%5Cimplies%20%5Ccfrac%7B6x%7D%7Bb%7D%3D%5Ccfrac%7B3x%7D%7B4%7D%5Cimplies%2024x%3D3xb%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B24x%7D%7B3x%7D%3Db%5Cimplies%208%3Db%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B%28y-%200%29%5E2%7D%7B%206%5E2%7D-%5Ccfrac%7B%28x-%200%29%5E2%7D%7B%208%5E2%7D%3D1%5Cimplies%20%5Ccfrac%7By%5E2%7D%7B36%7D-%5Ccfrac%7Bx%5E2%7D%7B64%7D%3D1)