We'd need a value, a coefficient, that effectively tosses away the variable "y" and leaves "x" all by her lonesome.
and our sharpest value for that, is our very good friend Mr Zero, c = 0, cy = 0y = 0.
check the picture below.
Answer:
332=y
Step-by-step explanation:
Answer:
- 2x - 31
Step-by-step explanation:
Given
- 3(4x + 5) - 2(- 5x + 8)
Multiply the terms in the first parenthesis by - 3 and the terms in the second parenthesis by - 2
= - 12x - 15 + 10x - 16 ← collect like terms
= (- 12x + 10x) + (- 15 - 16)
= - 2x - 31
Given:
The equation of a circle is
![10y+x^2=-18+5x-y^2](https://tex.z-dn.net/?f=10y%2Bx%5E2%3D-18%2B5x-y%5E2)
To find:
The center and radius of the given equation by completing the square.
Solution:
The standard form of a circle is
...(i)
where, (h,k) is center and r is radius of the circle.
We have,
![10y+x^2=-18+5x-y^2](https://tex.z-dn.net/?f=10y%2Bx%5E2%3D-18%2B5x-y%5E2)
It can be written as
![(x^2-5x)+(y^2+10y)=-18](https://tex.z-dn.net/?f=%28x%5E2-5x%29%2B%28y%5E2%2B10y%29%3D-18)
![\left(x^2-5x+\left(\dfrac{5}{2}\right)^2\right)+\left(y^2+10y+\left(\dfrac{10}{2}\right)^2\right)=-18+\left(\dfrac{5}{2}\right)^2+\left(\dfrac{10}{2}\right)^2](https://tex.z-dn.net/?f=%5Cleft%28x%5E2-5x%2B%5Cleft%28%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%5Cright%29%2B%5Cleft%28y%5E2%2B10y%2B%5Cleft%28%5Cdfrac%7B10%7D%7B2%7D%5Cright%29%5E2%5Cright%29%3D-18%2B%5Cleft%28%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B10%7D%7B2%7D%5Cright%29%5E2)
![\left(x-\dfrac{5}{2}\right)^2+\left(y^2+10y+5^2\right)=-18+\dfrac{25}{4}+5^2](https://tex.z-dn.net/?f=%5Cleft%28x-%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%5Cleft%28y%5E2%2B10y%2B5%5E2%5Cright%29%3D-18%2B%5Cdfrac%7B25%7D%7B4%7D%2B5%5E2)
![\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=-18+\dfrac{25}{4}+25](https://tex.z-dn.net/?f=%5Cleft%28x-%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%28y%2B5%29%5E2%3D-18%2B%5Cdfrac%7B25%7D%7B4%7D%2B25)
![\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{-72+25+100}{4}](https://tex.z-dn.net/?f=%5Cleft%28x-%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%28y%2B5%29%5E2%3D%5Cdfrac%7B-72%2B25%2B100%7D%7B4%7D)
![\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{53}{4}](https://tex.z-dn.net/?f=%5Cleft%28x-%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%28y%2B5%29%5E2%3D%5Cdfrac%7B53%7D%7B4%7D)
...(ii)
On comparing (i) and (ii), we get
![h=\dfrac{5}{2},k=-5,r=\dfrac{\sqrt{53}}{2}](https://tex.z-dn.net/?f=h%3D%5Cdfrac%7B5%7D%7B2%7D%2Ck%3D-5%2Cr%3D%5Cdfrac%7B%5Csqrt%7B53%7D%7D%7B2%7D)
Therefore, the center is
and the radius is
units.
The correct answer is A. 120 ft squared because you must multiply the height times the width which comes to 120.