Answer:
Number of hot dogs sold = 56
Number of hamburgers sold = 52
Step-by-step explanation:
Let
Number of hot dogs sold = x
Number of hamburgers sold = y
We can make equation from given equations:
(Hot dogs were sold for $.50 (fifty cents), and hamburgers were sold for $1 (one dollar). The total money raised by your class was $80. )
(Together you sold 108 hot dogs and hamburgers.)
Now we cam solve these system of equations to find value of x and y
![0.50x+y=80--eq(1)\\x+y=108--eq(2)](https://tex.z-dn.net/?f=0.50x%2By%3D80--eq%281%29%5C%5Cx%2By%3D108--eq%282%29)
Subtract both equations to get value of x:
![0.50x+y=80\\x\:\:\:\:\:\:\:\: + y=108\\-\:\:\:\:\:\:\:\: -\:\:\:\:\:\: -\\---------\\-0.5x=-28\\x=\frac{-28}{-0.5}\\x=56](https://tex.z-dn.net/?f=0.50x%2By%3D80%5C%5Cx%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%20%2B%20y%3D108%5C%5C-%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%20-%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%20-%5C%5C---------%5C%5C-0.5x%3D-28%5C%5Cx%3D%5Cfrac%7B-28%7D%7B-0.5%7D%5C%5Cx%3D56)
We get value of x = 56
Now putting value of x in equation 2 to find value of y
![x+y=108\\56+y=108\\y=108-56\\y=52](https://tex.z-dn.net/?f=x%2By%3D108%5C%5C56%2By%3D108%5C%5Cy%3D108-56%5C%5Cy%3D52)
So, we get y = 52
Therefore,
Number of hot dogs sold = x = 56
Number of hamburgers sold = y = 52
Answer:
The polynomial is:
![p(x) = -x^3 - 2x^2 + 5x + 6](https://tex.z-dn.net/?f=p%28x%29%20%3D%20-x%5E3%20-%202x%5E2%20%2B%205x%20%2B%206)
Step-by-step explanation:
Zeros of a function:
Given a polynomial f(x), this polynomial has roots
such that it can be written as:
, in which a is the leading coefficient.
Zeros of −3, −1, and 2
This means that
. Thus
![p(x) = a(x - x_{1})*(x - x_{2})*(x-x_3)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20a%28x%20-%20x_%7B1%7D%29%2A%28x%20-%20x_%7B2%7D%29%2A%28x-x_3%29)
![p(x) = a(x - (-3))*(x - (-1))*(x-2)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20a%28x%20-%20%28-3%29%29%2A%28x%20-%20%28-1%29%29%2A%28x-2%29)
![p(x) = a(x+3)(x+1)(x-2)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20a%28x%2B3%29%28x%2B1%29%28x-2%29)
![p(x) = a(x^2+4x+3)(x-2)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20a%28x%5E2%2B4x%2B3%29%28x-2%29)
![p(x) = a(x^3+2x^2-5x-6)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20a%28x%5E3%2B2x%5E2-5x-6%29)
Passes through the point (1,12).
This means that when
. We use this to find a.
![12 = a(1 + 2 - 5 - 6)](https://tex.z-dn.net/?f=12%20%3D%20a%281%20%2B%202%20-%205%20-%206%29)
![-12a = 12](https://tex.z-dn.net/?f=-12a%20%3D%2012)
![a = -\frac{12}{12}](https://tex.z-dn.net/?f=a%20%3D%20-%5Cfrac%7B12%7D%7B12%7D)
![a = -1](https://tex.z-dn.net/?f=a%20%3D%20-1)
Thus
![p(x) = -(x^3+2x^2-5x-6)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20-%28x%5E3%2B2x%5E2-5x-6%29)
![p(x) = -x^3 - 2x^2 + 5x + 6](https://tex.z-dn.net/?f=p%28x%29%20%3D%20-x%5E3%20-%202x%5E2%20%2B%205x%20%2B%206)
Answer:
49% of the lights are on!