Answer:
169 
Step-by-step explanation:
Surface area (SA) = 2B + PH
SA = 2 (
x 9 x 6) + (7+7+9) 5
= 2 (27) + (23) 5
= 54 + 115
SA = 169
Two strings are 15 inches and 7 inches long.
You could draw a diagram that has two rulers (that are longer than 12 inches).
Draw a piece of string that is exactly 15 inches on one ruler.
Draw another piece of string on the other ruler at exactly 7 inches.
Then you can find the total length of the two strings by adding 15 and 7 inches.
15 + 7 = 22
The total length of both the strings is 22 inches. You can draw a ruler and a piece of string on it at 22 inches.
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 :)
