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 :)
Part 1: 4 quarts in a gallon
4 * 5 = 20 quarts
Part 2: 20 * 2 = 40
They will make $40.00
Hey there!
You are trying to find the perimeter of triangle ABC. Each side is 2. Since there are 3 sides on a triangle, multiply 2 by 3 to get 6. You do not need the centroid for this problem.
I hope this helps!
Your equation is gonna be a^2-24^2=25^2 and your answer is 7.
Answer:
(1,2) is a solution to both equations
Step-by-step explanation:
To determine if (1,2) is a solution to both equations, substitute into the equation and see if it is true
2x+y =4
2(1) + 2 =4
2+2 =4
4=4
true
y =3x-1
2 = 3(1) -1
2 =3-1
2=2
true
Since both statements are true
(1,2) is a solution to both equations
