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:
53
Step-by-step explanation:
When subtracting 97-56=41+12=53. The answer is 53. Consider using a calculator or mental math next time rather than asking it as a question.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Answer:
c) (-2, 1)
Step-by-step explanation:
3x - 3y = -9
2x + y = -3
2x + y = -3
-2x -2x
y = -2x - 3
3x - 3y = -9
y = -2x - 3
3x - 3(-2x - 3) = -9
3x + 6x + 9 = -9
9x + 9 = -9
- 9 -9
9x = -18
/9 /9
x = -2
y = -2x - 3
y = -2(-2) -3
y = 4 - 3
y = 1
(x, y) --> (-2,1)
Check your answer:
y = -2x - 3
1 = -2(-2) - 3
1 = 4 - 3
1 = 1
This statement is true
Hope this helps!
The smallest possible value of z is the denominator of the reduced fraction x/y. We note the prime factors of the members of set y are
... 2², 7, 2³, 3²
so if there are any even members of set x, the fraction can be reduced to something divided by 2. The number 6 in set x is even, so we have
... 6z/4 = 6·2/4 = 3 (an integer) when z=2
The lowest possible value of z is ...
... B) 2
