Answer:
Step-by-step explanation:
it is maximum.
when leading coefficient of x² is negative,
It is downward parabola.
or
y=-2x²+10x+1
=-2(x²-5x+(-5/2)²-(-5/2)²)+1
=-2(x-5/2)²+2×25/4+1
=-2(x-5/2)²+25/2+1
=-2(x-5/2)²+27/2
maximum value of y is 27/2 and is attained at x=5/2
vertex is (5/2,27/2)
let's do so using substitution
![\bf \begin{cases} -3x-4y=-14\\ 9x+2y=22 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{solving for "y" in the 1st equation}~\hfill }{-3x-4y=-14\implies -3x+14-4y=0} \\\\\\ -3x+14=4y\implies \cfrac{14-3x}{4}=\boxed{y} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting "y" in the 2nd equation}}{9x+2\left( \boxed{\cfrac{14-3x}{4}} \right)=22}\implies 9x+\cfrac{14-3x}{2}=22](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20-3x-4y%3D-14%5C%5C%209x%2B2y%3D22%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsolving%20for%20%22y%22%20in%20the%201st%20equation%7D~%5Chfill%20%7D%7B-3x-4y%3D-14%5Cimplies%20-3x%2B14-4y%3D0%7D%20%5C%5C%5C%5C%5C%5C%20-3x%2B14%3D4y%5Cimplies%20%5Ccfrac%7B14-3x%7D%7B4%7D%3D%5Cboxed%7By%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsubstituting%20%22y%22%20in%20the%202nd%20equation%7D%7D%7B9x%2B2%5Cleft%28%20%5Cboxed%7B%5Ccfrac%7B14-3x%7D%7B4%7D%7D%20%5Cright%29%3D22%7D%5Cimplies%209x%2B%5Ccfrac%7B14-3x%7D%7B2%7D%3D22)
![\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( 9x+\cfrac{14-3x}{2}\right)=2(22)}\implies 18x+(14-3x)=44\implies 15x+14=44 \\\\\\ 15x = 30\implies x = \cfrac{30}{15}\implies \blacktriangleright x = 2\blacktriangleleft \\\\\\ \stackrel{\textit{since we know that }}{\cfrac{14-3x}{4}=y}\implies \cfrac{14-3(2)}{4}=y\implies \cfrac{14-6}{4}=y\implies \blacktriangleright 2 = y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (2,2)~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B2%7D%7D%7B2%5Cleft%28%209x%2B%5Ccfrac%7B14-3x%7D%7B2%7D%5Cright%29%3D2%2822%29%7D%5Cimplies%2018x%2B%2814-3x%29%3D44%5Cimplies%2015x%2B14%3D44%20%5C%5C%5C%5C%5C%5C%2015x%20%3D%2030%5Cimplies%20x%20%3D%20%5Ccfrac%7B30%7D%7B15%7D%5Cimplies%20%5Cblacktriangleright%20x%20%3D%202%5Cblacktriangleleft%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsince%20we%20know%20that%20%7D%7D%7B%5Ccfrac%7B14-3x%7D%7B4%7D%3Dy%7D%5Cimplies%20%5Ccfrac%7B14-3%282%29%7D%7B4%7D%3Dy%5Cimplies%20%5Ccfrac%7B14-6%7D%7B4%7D%3Dy%5Cimplies%20%5Cblacktriangleright%202%20%3D%20y%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%282%2C2%29~%5Chfill)
Welll....from the diagram, you can see you have two triangles (one on each side)
area of triangle = 1/2 base*height = 1/2 * 2 x 15 = 15ft2 each then you are left with a rectangle 13 ft x 15= 195 ft2
195+15+15=
225 ft2 <----- ANSWER
<span>Tali is running at 5 miles per hour.
In 12 minutes she runs 1 mile,
in 1 minute she runs 1/12 mile,
so in 60 minutes (one hour) she would run 60/12 = 5 mph
Sandra is running at 10 miles per hour, this is twice as fast as Tali (5 mph x 2 = 10 mph).
It takes Sandra 6 minutes to run a mile.
Sandra runs 10 miles in an hour, so to run one mile would take her one tenth of an hour or 6 minutes.</span>
<span>(SAT Prep) In the given figure, the reflex angle ∠DOB has measure of 3.5</span>y<span> while the measure of ∠AOD is </span>y. Find the measure of the non-reflex ∠DOB in degrees.
