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 :)
325
Step-by-step explanation:
<h3>(x+8)2+(y+12)2=235</h3>
Answer:16.5
Step-by-step explanation:
Answer:
commission on the purchase = $559
gross cost = $9371
Step-by-step explanation:
Given data
Prime Cost = $8,600
Commission Rate = 6.5%
Local Delivery = 44
storage = 77
air freight = 91
to find out
Luis' commission on the purchase and the gross cost
solution
we find first commission on the purchase that is = commision @ 6.5%
commission on the purchase = 8600 × 0.065 = $559
commission on the purchase = $559
and
gross cost = Prime Cost + Commission + Local Delivery +storage +air freight
gross cost = 8600 + 559 + 44+ 77 + 91
gross cost = $9371
