R = l + (3w)/2
Subtract 'l' to both sides:
r - l = (3w)/2
Multiply 2 to both sides:
2r - 2l = 3w
Divide 3 to both sides:
w = (2r - 2l)/3
Tha answer is 15 apple pies. Divide 118 pies by 8 apples. You will get 14 and a remainder. Add one more to the quotient.
Answer:
(4, 0)
Step-by-step explanation:
Using the vertex of the quadratic equation, it is found that the maximum profit she can earn is of $106.
<h3>
What is the vertex of a quadratic equation?</h3>
A quadratic equation is modeled by:
![y = ax^2 + bx + c](https://tex.z-dn.net/?f=y%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c)
The vertex is given by:
![(x_v, y_v)](https://tex.z-dn.net/?f=%28x_v%2C%20y_v%29)
In which:
![x_v = -\frac{b}{2a}](https://tex.z-dn.net/?f=x_v%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
![y_v = -\frac{b^2 - 4ac}{4a}](https://tex.z-dn.net/?f=y_v%20%3D%20-%5Cfrac%7Bb%5E2%20-%204ac%7D%7B4a%7D)
Considering the coefficient a, we have that:
- If a < 0, the vertex is a maximum point.
- If a > 0, the vertex is a minimum point.
In this problem, her profit is modeled by:
![P(x) = -x^2 + 14x + 57](https://tex.z-dn.net/?f=P%28x%29%20%3D%20-x%5E2%20%2B%2014x%20%2B%2057)
Which is a quadratic equation with coefficients a = -1, b = 14, c = 57, hence, her maximum profit in dollars is given by:
![y_v = -\frac{14^2 - 4(-1)(57)}{4(-1)} = 106](https://tex.z-dn.net/?f=y_v%20%3D%20-%5Cfrac%7B14%5E2%20-%204%28-1%29%2857%29%7D%7B4%28-1%29%7D%20%3D%20106)
More can be learned about the vertex of a quadratic equation at brainly.com/question/24737967