68+70=180
=138=180
=180-138
=42 degrees (using angle sum property of triangles
Hope this helps you
Answer:
13! or 6227020800
Step-by-step explanation:
With no restrictions, we can figure out the answer to be 13! by the following analysis:
For the first position in line, there are 13 different students who could fill that spot. If we fill it and proceed to the next position in line, there are now only 12 students left who can fill it, since one is already in line. Then the next position only has 11 possibilities, and the next 10, and so on.
Multiplying all of this together gives us 13*12*11*10*9*8*7*6*5*4*3*2*1 or 13!
I that 'y' is 45 degrees because of alternate angles (I think its called).
If you look at the large triangle on the left where the corner angles are 35 and 80 and 20+an unknown angle. We can work out the missing angle by doing 180-80-35-20= 45.
And so if we use the fact that alternate angle must be equal then y= 45 degrees (I think!)
![\bf \stackrel{\textit{multiplying both sides by LCD of 3}}{3(y+5)=3\left[ \cfrac{5}{3}(x-3) \right]}\implies 3y+15=5(x-3) \\\\\\ 3y+15=5x-15\implies -5x+3y=-30\implies \stackrel{\textit{multiplying by -1}}{5x-3y=30}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20LCD%20of%203%7D%7D%7B3%28y%2B5%29%3D3%5Cleft%5B%20%5Ccfrac%7B5%7D%7B3%7D%28x-3%29%20%5Cright%5D%7D%5Cimplies%203y%2B15%3D5%28x-3%29%0A%5C%5C%5C%5C%5C%5C%0A3y%2B15%3D5x-15%5Cimplies%20-5x%2B3y%3D-30%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20by%20-1%7D%7D%7B5x-3y%3D30%7D)
bearing in mind the standard form uses all integers, and the x-variable cannot have a negative coefficient.
