hello :<span>
<span>an equation of the circle Center at the
A(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a =4 and b = -1 (Center at the origin)
r = AP.... P(0.1)
r² = (AP)²
r² = (4-0)² +(-1-1)² = 16+4=20
an equation of the circle that satisfies the stated conditions.
Center at A(4,-1), passing through P(0, 1) is : </span></span>(x-4)² +(y+1)² = 20
15 3/4 or 63/4 also works
Answer with Step-by-step explanation:
We are given that
Discriminant, D=![b^2-4ac](https://tex.z-dn.net/?f=b%5E2-4ac)
When ![D\geq 0](https://tex.z-dn.net/?f=D%5Cgeq%200)
Then, the function have two real zeroes.
1.![f(x)=x^2+6x+8](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2B6x%2B8)
By comparing withe general quadratic equation
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
We get a=1,b=6,c=8
Using the discriminant formula
![D=(6)^2-4(1)(8)=36-32=4>0](https://tex.z-dn.net/?f=D%3D%286%29%5E2-4%281%29%288%29%3D36-32%3D4%3E0)
Hence, function have two real zeroes.
2.![g(x)=x^2+4x+8](https://tex.z-dn.net/?f=g%28x%29%3Dx%5E2%2B4x%2B8)
![D=(4)^2-4(1)(8)=16-32](https://tex.z-dn.net/?f=D%3D%284%29%5E2-4%281%29%288%29%3D16-32)
![D=-16](https://tex.z-dn.net/?f=D%3D-16%3C0)
Hence, the function have no two real number zeroes.
3.![h(x)=x^2-12x+32](https://tex.z-dn.net/?f=h%28x%29%3Dx%5E2-12x%2B32)
![D=(-12)^2-4(1)(32)=144-128=16](https://tex.z-dn.net/?f=D%3D%28-12%29%5E2-4%281%29%2832%29%3D144-128%3D16)
![D>0](https://tex.z-dn.net/?f=D%3E0)
Hence, function have two real zeroes.
4.![k(x)=x^2+4x-1](https://tex.z-dn.net/?f=k%28x%29%3Dx%5E2%2B4x-1)
![D=(4)^2-4(1)(-1)=16+4=20](https://tex.z-dn.net/?f=D%3D%284%29%5E2-4%281%29%28-1%29%3D16%2B4%3D20)
![D>0](https://tex.z-dn.net/?f=D%3E0)
Hence, function have two real zeroes.
5.![p(x)=5x^2+5x+4](https://tex.z-dn.net/?f=p%28x%29%3D5x%5E2%2B5x%2B4)
![D=(5)^2-4(5)(4)=25-80](https://tex.z-dn.net/?f=D%3D%285%29%5E2-4%285%29%284%29%3D25-80)
![D=-55](https://tex.z-dn.net/?f=D%3D-55%3C0)
Hence, the function have no two real number zeroes.
6.![r(x)=x^2-2x-15](https://tex.z-dn.net/?f=r%28x%29%3Dx%5E2-2x-15)
![D=(-2)^2-4(1)(-15)=4+60=64](https://tex.z-dn.net/?f=D%3D%28-2%29%5E2-4%281%29%28-15%29%3D4%2B60%3D64)
![D>0](https://tex.z-dn.net/?f=D%3E0)
Hence, function have two real zeroes.
Answer:
Each guest must bring 5 cans.
Step-by-step explanation:
1000-565=435
435/87=5
The answer is A, Brainliest please