Answer:
D
Step-by-step explanation:
To obtain vertex form from the given equation use the method of completing the square
given 8y + x² = - y² - 181 + 26x
rearrange having the x terms and y terms together
add y² to both sides
8y + x² + y² = - 181 + 26x ( subtract 26x from both sides )
x² - 26x + y² + 8y = - 181
add (half the coefficient of the x/y terms )² to both sides
x² + 2(- 13)x + 169 +y² + 2(4)y + 16 = - 181 + 169 + 16
completing the square on both the x and y terms
(x - 13)² + (y + 4)² = 4 → D
Answer:
6 + 3
or 6 - 3
Step-by-step explanation:
x^2 - 12x + 36 = 90
x^2 - 12x - 54 = 0
x = ![\frac{-b +/- \sqrt{b^{2} + 4ac }}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%20%2B%2F-%20%5Csqrt%7Bb%5E%7B2%7D%20%2B%204ac%20%7D%7D%7B2a%7D)
a = 1, b= -12, c= -54
6 + 3
or 6 - 3
In the given graph, lets mark two points:
Let
and ![B = (4,-2)](https://tex.z-dn.net/?f=B%20%3D%20%284%2C-2%29)
The slope of the line is given by:
![m = \frac{(-2)-(-3)}{(4)-(0)}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B%28-2%29-%28-3%29%7D%7B%284%29-%280%29%7D)
![m = \frac{-2+3}{4}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-2%2B3%7D%7B4%7D)
![m = \frac{1}{4}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1%7D%7B4%7D)
The equation of the line is given by:
![(y-y_1)=m(x-x_1)](https://tex.z-dn.net/?f=%28y-y_1%29%3Dm%28x-x_1%29)
![(y-(-3))=(\frac{1}{4})(x-0)](https://tex.z-dn.net/?f=%28y-%28-3%29%29%3D%28%5Cfrac%7B1%7D%7B4%7D%29%28x-0%29)
![4(y+3)=x](https://tex.z-dn.net/?f=4%28y%2B3%29%3Dx)
![4y+12=x](https://tex.z-dn.net/?f=4y%2B12%3Dx)
![4y=x-12](https://tex.z-dn.net/?f=4y%3Dx-12)
![y= \frac{1}{4}x-3](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7B4%7Dx-3)
Therefore, the function equation represented by the graph is: ![f(x)= \frac{1}{4}x-3](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Cfrac%7B1%7D%7B4%7Dx-3)
Answer:
Which One ?
Step-by-step explanation:
Answer:
0.486% of world population lives in Canada.
Step-by-step explanation:
Given: World Population= 7691 million.
Canada Population= 37.4 million.
Now, finding the percentage of world population lives in Canada.
![Population\ percentage= \frac{Canada\ population}{World\ population} \times 100](https://tex.z-dn.net/?f=Population%5C%20percentage%3D%20%5Cfrac%7BCanada%5C%20population%7D%7BWorld%5C%20population%7D%20%5Ctimes%20100)
⇒ ![Population\ percentage= \frac{37.4}{7691} \times 100](https://tex.z-dn.net/?f=Population%5C%20percentage%3D%20%5Cfrac%7B37.4%7D%7B7691%7D%20%5Ctimes%20100)
⇒ ![Population\ percentage= 0.00486\times 100](https://tex.z-dn.net/?f=Population%5C%20percentage%3D%200.00486%5Ctimes%20100)
∴ ![Population\ percentage= 0.486\%](https://tex.z-dn.net/?f=Population%5C%20percentage%3D%200.486%5C%25)
Hence, 0.486% of world population lives in Canada.