Answer:
or 1.7 as a decimal (1.6 repeating)
Step-by-step explanation:
Answer:
Step-by-step explanation:
The parabola opens up and that is the answer on the quiz
Your welcome
Answer:
280 ft
Step-by-step explanation:
An auditorium is in the shape of an equilateral triangle with side length as 112 ft.
The stage extends from one vertex of the triangle to the mid-segment and the seating area extends from the mid-segment to the rear wall.
*The situation is represented in the attachment.
According to the midpoint theorem, the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.
Hence, the length of the mid-segment in this case is,
![\dfrac{1}{2}\times 112=56\ ft](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20112%3D56%5C%20ft)
Therefore, the perimeter of the seating area is,
![=112+56+56+56=280\ ft](https://tex.z-dn.net/?f=%3D112%2B56%2B56%2B56%3D280%5C%20ft)
²⁰¹²C₂₀₁₁ = (2012)! / [(2011)! (2012-2011)!]
²⁰¹²C₂₀₁₁ = (2012)! / [(2011)! (1)!]
Simplify 2012! / (2011)! = 2012
²⁰¹²C₂₀₁₁ = (2012)! / (1)! = 2012
Answer:
![y=\frac{9}{2}x+[tex]\frac{53}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B9%7D%7B2%7Dx%2B%5Btex%5D%5Cfrac%7B53%7D%7B2%7D)
![9x-2y=-53](https://tex.z-dn.net/?f=9x-2y%3D-53)
Step-by-step explanation:
The line is passing through
and
.
The equation of line in point-slope form can be obtained by using the following rule that says:
![(y-y_1)=m(x-x_1)](https://tex.z-dn.net/?f=%28y-y_1%29%3Dm%28x-x_1%29)
Lets say:
are
and
respectively.
Lets find the slope of the line:
![m=\frac{y_2-y_1}{x_2-x_1} =\frac{4-(-5)}{-5-(-7)} =\frac{4+5}{-5+7}=\frac{9}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%3D%5Cfrac%7B4-%28-5%29%7D%7B-5-%28-7%29%7D%20%3D%5Cfrac%7B4%2B5%7D%7B-5%2B7%7D%3D%5Cfrac%7B9%7D%7B2%7D)
So the slope of the line is
.
![(y-(-5))=\frac{9}{2}(x-(-7))](https://tex.z-dn.net/?f=%28y-%28-5%29%29%3D%5Cfrac%7B9%7D%7B2%7D%28x-%28-7%29%29)
![y+5=\frac{9}{2}(x+7)](https://tex.z-dn.net/?f=y%2B5%3D%5Cfrac%7B9%7D%7B2%7D%28x%2B7%29)
-5=\frac{9}{2}x+![\frac{53}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B53%7D%7B2%7D)
![y=\frac{9}{2}x+[tex]\frac{53}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B9%7D%7B2%7Dx%2B%5Btex%5D%5Cfrac%7B53%7D%7B2%7D)
So the required equation is
.
And the equation of line in standard form can be written as:
![\frac{-9}{2}x+y=[tex]\frac{53}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-9%7D%7B2%7Dx%2By%3D%5Btex%5D%5Cfrac%7B53%7D%7B2%7D)
Multiplying the equation by 2 we get:
![-9x+2y=53](https://tex.z-dn.net/?f=-9x%2B2y%3D53)
![9x-2y=-53](https://tex.z-dn.net/?f=9x-2y%3D-53)