Greatest Common Factors are the greatest numbers that go into a given group of numbers. The GCF of 54 and 84 is 6.
Divide by 4 if it has 4 equal sides and the answer is 13.5.
Given:
The equation of a circle is:
![x^2+y^2-x-2y-\dfrac{11}{4}=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-x-2y-%5Cdfrac%7B11%7D%7B4%7D%3D0)
To find:
The center of the circle and its radius.
Solution:
The standard form of a circle is:
...(i)
Where, (h,k) is center and r is the radius of the circle.
The given equation of the circle is:
![x^2+y^2-x-2y-\dfrac{11}{4}=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-x-2y-%5Cdfrac%7B11%7D%7B4%7D%3D0)
Write the given equation in standard form of a circle.
![(x^2-x)+(y^2-2y)-\dfrac{11}{4}=0](https://tex.z-dn.net/?f=%28x%5E2-x%29%2B%28y%5E2-2y%29-%5Cdfrac%7B11%7D%7B4%7D%3D0)
![\left(x^2-x+\left(\dfrac{1}{2}\right)^2\right)+(y^2-2y+1^2)-\dfrac{11}{4}-\left(\dfrac{1}{2}\right)^2+1^2=0](https://tex.z-dn.net/?f=%5Cleft%28x%5E2-x%2B%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%5E2%5Cright%29%2B%28y%5E2-2y%2B1%5E2%29-%5Cdfrac%7B11%7D%7B4%7D-%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%5E2%2B1%5E2%3D0)
![\left(x-\dfrac{1}{2}\right)^2+(y-1)^2-\dfrac{11}{4}-\dfrac{1}{4}-1=0](https://tex.z-dn.net/?f=%5Cleft%28x-%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%5E2%2B%28y-1%29%5E2-%5Cdfrac%7B11%7D%7B4%7D-%5Cdfrac%7B1%7D%7B4%7D-1%3D0)
![\left(x-0.5\right)^2+(y-1)^2-\dfrac{12}{4}-1=0](https://tex.z-dn.net/?f=%5Cleft%28x-0.5%5Cright%29%5E2%2B%28y-1%29%5E2-%5Cdfrac%7B12%7D%7B4%7D-1%3D0)
On further simplification, we get
![\left(x-0.5\right)^2+(y-1)^2-3-1=0](https://tex.z-dn.net/?f=%5Cleft%28x-0.5%5Cright%29%5E2%2B%28y-1%29%5E2-3-1%3D0)
![\left(x-0.5\right)^2+(y-1)^2-4=0](https://tex.z-dn.net/?f=%5Cleft%28x-0.5%5Cright%29%5E2%2B%28y-1%29%5E2-4%3D0)
![\left(x-0.5\right)^2+(y-1)^2=4](https://tex.z-dn.net/?f=%5Cleft%28x-0.5%5Cright%29%5E2%2B%28y-1%29%5E2%3D4)
...(ii)
On comparing (i) and (ii), we get
![h=0.5,k=1,r=2](https://tex.z-dn.net/?f=h%3D0.5%2Ck%3D1%2Cr%3D2)
Therefore, the center of the circle is (0.5,1) and radius is 2 units.
Answer/Step-by-step explanation:
1.a)(iv). ![\frac{1}{6} + (-\frac{7}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B6%7D%20%2B%20%28-%5Cfrac%7B7%7D%7B8%7D%20)
Positive multiplied by negative = negative
![\frac{1}{6} - \frac{7}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B6%7D%20-%20%5Cfrac%7B7%7D%7B8%7D%20)
![\frac{4 - 21}{24} = \frac{-17}{24} = -\frac{17}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B4%20-%2021%7D%7B24%7D%20%3D%20%5Cfrac%7B-17%7D%7B24%7D%20%3D%20-%5Cfrac%7B17%7D%7B24%7D)
2a.) 73.48 +(-37.3)
![Note: + * - = -](https://tex.z-dn.net/?f=%20Note%3A%20%2B%20%2A%20-%20%3D%20-%20)
73.48 - 37.3 = 36.18
3c.)
÷
Convert to proper fraction
÷
Change ÷ to × and flip the fraction on your right upside down
![-\frac{1*7}{4*2} = -\frac{7}{8}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B1%2A7%7D%7B4%2A2%7D%20%3D%20-%5Cfrac%7B7%7D%7B8%7D%20)
3d.) -52.25 ÷ (-5.5) = ![\frac{-52.25}{-5.5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-52.25%7D%7B-5.5%7D%20)
(Note: - ÷ - = + )
![\frac{-52.25}{-5.5} = 9.5](https://tex.z-dn.net/?f=%20%5Cfrac%7B-52.25%7D%7B-5.5%7D%20%3D%209.5%20)