-4= Contraction
2.5=Expansion
2/3= Contraction
-3/4= Contraction
Best way to solve this, if the scale factor is less than one, is a contraction. If it is greater than one, than it is an expansion.
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Answer:
The correct answer is C.
Step-by-step explanation:
The given equation is;
![r=\frac{1}{1-\sin(\theta)}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1%7D%7B1-%5Csin%28%5Ctheta%29%7D)
This implies that;
![r(1-\sin(\theta)=1](https://tex.z-dn.net/?f=r%281-%5Csin%28%5Ctheta%29%3D1)
![r-r\sin(\theta)=1](https://tex.z-dn.net/?f=r-r%5Csin%28%5Ctheta%29%3D1)
Let us write in Cartesian coordinates by substituting;
![r=\sqrt{x^2+y^2} ,y=r\sin(\theta)](https://tex.z-dn.net/?f=r%3D%5Csqrt%7Bx%5E2%2By%5E2%7D%20%2Cy%3Dr%5Csin%28%5Ctheta%29)
![\sqrt{x^2+y^2}-y=1](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%2By%5E2%7D-y%3D1)
![\sqrt{x^2+y^2}=y+1](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%2By%5E2%7D%3Dy%2B1)
Square both sides;
![(\sqrt{x^2+y^2})^2=(y+1)^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bx%5E2%2By%5E2%7D%29%5E2%3D%28y%2B1%29%5E2)
This implies that;
![x^2+y^2=y^2+2y+1](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3Dy%5E2%2B2y%2B1)
![x^2=2y+1](https://tex.z-dn.net/?f=x%5E2%3D2y%2B1)
![y=\frac{1}{2}x^2-\frac{1}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%5E2-%5Cfrac%7B1%7D%7B2%7D)
This is an equation of a parabola that opens upwards with a y-intercept of
.
The correct choice is C
Answer:
see below
Step-by-step explanation:
![1) -4x + 9x = 5x\\\\2) 6y -8y = -2y\\\\3) -7x+x = -6x\\\\4) 9y-y = 8y\\\\5) -5x-5x = -10x\\\\6) 3y-7y = -4y\\\\7) -x-8x+7 = -9x +7\\\\8) y-2y -3 = -y -3\\\\9) 5+5x-4x = 5 + x\\\\10) 3y-6 +7y-4y = 6y -6\\\\11) -9x-5-8+x = -13 -8x\\\\12) 6-y+5y-6y = 6 -2y\\\\13) 3x-8y+2x-5-5y = 5x -13y -5\\\\14)-9x +3 +2x-9y-8 = -7x -9y -5\\\\15) 5 +6x -3y +x +8y = 7x +5y+5\\\\16) -4x -4 +x -2y +7x = 4x -2y -4\\\\17) -8x +7y-x-6y+4x = -5x +y\\\\18) x+5-2x+3y-y=2y-x+5\\\\19) 9x-3y+7-4x+y-3 = 5x-2y+4\\\\](https://tex.z-dn.net/?f=1%29%20-4x%20%2B%209x%20%3D%205x%5C%5C%5C%5C2%29%206y%20-8y%20%3D%20-2y%5C%5C%5C%5C3%29%20-7x%2Bx%20%3D%20-6x%5C%5C%5C%5C4%29%209y-y%20%3D%208y%5C%5C%5C%5C5%29%20-5x-5x%20%3D%20-10x%5C%5C%5C%5C6%29%203y-7y%20%3D%20-4y%5C%5C%5C%5C7%29%20-x-8x%2B7%20%3D%20-9x%20%2B7%5C%5C%5C%5C8%29%20y-2y%20-3%20%3D%20-y%20-3%5C%5C%5C%5C9%29%205%2B5x-4x%20%3D%205%20%2B%20x%5C%5C%5C%5C10%29%203y-6%20%2B7y-4y%20%3D%206y%20-6%5C%5C%5C%5C11%29%20-9x-5-8%2Bx%20%3D%20-13%20-8x%5C%5C%5C%5C12%29%206-y%2B5y-6y%20%3D%206%20-2y%5C%5C%5C%5C13%29%203x-8y%2B2x-5-5y%20%3D%205x%20-13y%20-5%5C%5C%5C%5C14%29-9x%20%2B3%20%2B2x-9y-8%20%3D%20-7x%20-9y%20-5%5C%5C%5C%5C15%29%205%20%2B6x%20-3y%20%2Bx%20%2B8y%20%3D%207x%20%2B5y%2B5%5C%5C%5C%5C16%29%20-4x%20-4%20%2Bx%20-2y%20%2B7x%20%3D%204x%20-2y%20-4%5C%5C%5C%5C17%29%20-8x%20%2B7y-x-6y%2B4x%20%3D%20-5x%20%2By%5C%5C%5C%5C18%29%20x%2B5-2x%2B3y-y%3D2y-x%2B5%5C%5C%5C%5C19%29%209x-3y%2B7-4x%2By-3%20%3D%205x-2y%2B4%5C%5C%5C%5C)
![20) -x-3+5x+6y+8x-9\\\\21) 4x-4-8y+8-5x+1 = -x-8y+5\\\\22) 3x-x+6y-4x-y = -2x+5y\\\\23) 2x+2y-x-y-7+5y = x+6y-7\\\\24) 6x-8x-4y -x+5y-2y = -3x-y\\\\](https://tex.z-dn.net/?f=20%29%20-x-3%2B5x%2B6y%2B8x-9%5C%5C%5C%5C21%29%204x-4-8y%2B8-5x%2B1%20%3D%20-x-8y%2B5%5C%5C%5C%5C22%29%203x-x%2B6y-4x-y%20%3D%20-2x%2B5y%5C%5C%5C%5C23%29%202x%2B2y-x-y-7%2B5y%20%3D%20x%2B6y-7%5C%5C%5C%5C24%29%206x-8x-4y%20-x%2B5y-2y%20%3D%20-3x-y%5C%5C%5C%5C)
I think the answer is that they all ran the same
I cant answer the other part