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 :)
The value of 3 in 6,300 is 10 times the value of 3 in 530. And your welcome.
Answer:
no solution
Step-by-step explanation:
p-4=-9+p
p=-5+p
0=-5
Answer:
y=2, x=-1
Step-by-step explanation:
We can add the two equations together to eliminate x:
6x+5y+(-6x)+7y=4+20
12y=24
y=2
We plug y into the first equation and get
6x+5(2)=4
6x+10=4
6x=-6
x=-1
The total number of chocolates is 15 + 16 + 19 = 50
There are 15 + 16 = 31 [dark chocolates + caramel chocolates]
The probability of picking one of them is 31 / 50.
