(5,9) (8,33)
(33-9)/(8-5)= 24/3= 8
y-9= 8(x-5)
y-9= 8x-40
y= 8x-31
Answer:
Because your sleep deprived and your head is clumped up with more equations. :( i wish school was easy
Step-by-step explanation:
so first off, let's simplify both equations, starting off by multiplying both sides by the LCD of all fractions, to do away with the denominators.
![\bf \cfrac{10(x-y)-4(1-x)}{3}=y\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{10(x-y)-4(1-x)=3y} \\\\\\ 10x-10y-4+4x=3y\implies \boxed{14x-13y=4} \\\\[-0.35em] ~\dotfill\\\\ 7+x-\cfrac{x-3y}{4}=2x-\cfrac{y+5}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( 7+x-\cfrac{x-3y}{4} \right)=12\left( 2x-\cfrac{y+5}{3} \right)} \\\\\\ 84+12x-3(x-3y)=24x-4(y+5) \\\\\\ 84+12x-3x+9y=24x-4y-20\implies \boxed{-15x+13y=-124}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B10%28x-y%29-4%281-x%29%7D%7B3%7D%3Dy%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B3%7D%7D%7B10%28x-y%29-4%281-x%29%3D3y%7D%20%5C%5C%5C%5C%5C%5C%2010x-10y-4%2B4x%3D3y%5Cimplies%20%5Cboxed%7B14x-13y%3D4%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%207%2Bx-%5Ccfrac%7Bx-3y%7D%7B4%7D%3D2x-%5Ccfrac%7By%2B5%7D%7B3%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B12%7D%7D%7B12%5Cleft%28%207%2Bx-%5Ccfrac%7Bx-3y%7D%7B4%7D%20%5Cright%29%3D12%5Cleft%28%202x-%5Ccfrac%7By%2B5%7D%7B3%7D%20%5Cright%29%7D%20%5C%5C%5C%5C%5C%5C%2084%2B12x-3%28x-3y%29%3D24x-4%28y%2B5%29%20%5C%5C%5C%5C%5C%5C%2084%2B12x-3x%2B9y%3D24x-4y-20%5Cimplies%20%5Cboxed%7B-15x%2B13y%3D-124%7D)
now, let's do some elimination on those two simplified equations.
![\bf \begin{array}{cllcl} 14x&-13y&=&4\\ -15x&+13y&=&-124\\\cline{1-4} -x&&=&-120 \end{array}~\hfill x=\cfrac{-120}{-1}\implies \blacktriangleright x=120 \blacktriangleleft \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{14(120)-13y=4}\implies 1680-13y=4\implies 1680-4=13y \\\\\\ 1676=13y\implies \blacktriangleright \cfrac{1676}{13}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 120~,~\frac{1676}{13} \right)~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bcllcl%7D%2014x%26-13y%26%3D%264%5C%5C%20-15x%26%2B13y%26%3D%26-124%5C%5C%5Ccline%7B1-4%7D%20-x%26%26%3D%26-120%20%5Cend%7Barray%7D~%5Chfill%20x%3D%5Ccfrac%7B-120%7D%7B-1%7D%5Cimplies%20%5Cblacktriangleright%20x%3D120%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsubstituting%20on%20the%201st%20equation%7D%7D%7B14%28120%29-13y%3D4%7D%5Cimplies%201680-13y%3D4%5Cimplies%201680-4%3D13y%20%5C%5C%5C%5C%5C%5C%201676%3D13y%5Cimplies%20%5Cblacktriangleright%20%5Ccfrac%7B1676%7D%7B13%7D%3Dy%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%5Cleft%28%20120~%2C~%5Cfrac%7B1676%7D%7B13%7D%20%5Cright%29~%5Chfill)
Answer:
y = 2.6x + 8
Plug 40 into y
40 = 2.6x + 8 and solve for x
x = 12.3 gallons
Answer:
90 degrees
Step-by-step explanation:
Sum of the angles in a triangle = 180°
Opposite angles are equal
For two parallel lines and a transversal,
corresponding angles are equal, and
alternate angles are equal.
45+45=90.
180-90=90
Plus, you can see that the angle forms a perfect 90 degree angle.
