Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
Answer:
-2
Step-by-step explanation:
Answer:
Step-by-step explanation: 1,860 Seconds Is Equal To 31 Minutes Hope It Helped
Answer:
Mean of the data would be 6c
Step-by-step explanation:
<u>Rule to Remember:</u> Whenever each term of the data is multiplied by the same number, the new mean is previous mean multiplied by that number.
In this case, original value of mean was c. Each value of the data is multiplied with 6 so a result the new mean would be 6 times the original mean i.e. 6c
Let us consider that original values in the data set are x, y and z. Their mean would be:
If each value of the data is multiplied with 6, the new values would be 6x, 6y and 6z. The mean in this case will be:
We can see from above that the new mean is 6 multiplied to the original mean.
Therefore, the answer to this question is 6c.
