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 :)
<h2>
Stella is correct about center and wrong about radius </h2>
Step-by-step explanation:
Equation of circle with (h,k) as center and radius r is given by,
(x-h)²+(y-k)² = r²
Here equation is
x²−8x+y²+2y=5
Changing in to (x-h)²+(y-k)² = r² form
x²−8x + 16 - 16 +y²+2y+1 - 1=5
(x-4)² - 16 + (y+1)² -1 = 5
(x-4)² + (y+1)² = 22
(x-4)² + (y+1)² = 4.69²
Center is (4,-1) and radius is 4.69
Stella is correct about center and wrong about radius
Answer:
So, where is the question that you are talking about?
To solve this problem we can use simple proportion
If
270$ -------------------------3000 pesos
x $ ---------------------------100 pesos (x$ means that we dont know how much)
Now we crossmultiplying to get proportion
x*3000=270*100
Now we just to solve eq
3000x=27000 /:3000
x=27000:3000
x=9$ - its the result
Answer:
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Step-by-step explanation:
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