Definition: Vertical Angles
Vertical angles are a pair of non-adjacent angles formed when two lines intersect.
Answer:
Widgets should be sold by $38.88 to maximize the profit.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
![f(x) = ax^{2} + bx + c](https://tex.z-dn.net/?f=f%28x%29%20%3D%20ax%5E%7B2%7D%20%2B%20bx%20%2B%20c)
It's vertex is the point ![(x_{v}, y_{v})](https://tex.z-dn.net/?f=%28x_%7Bv%7D%2C%20y_%7Bv%7D%29)
In which
![x_{v} = -\frac{b}{2a}](https://tex.z-dn.net/?f=x_%7Bv%7D%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
![y_{v} = -\frac{\Delta}{4a}](https://tex.z-dn.net/?f=y_%7Bv%7D%20%3D%20-%5Cfrac%7B%5CDelta%7D%7B4a%7D)
Where
![\Delta = b^2-4ac](https://tex.z-dn.net/?f=%5CDelta%20%3D%20b%5E2-4ac)
If a<0, the vertex is a maximum point, that is, the maximum value happens at
, and it's value is
.
In this question:
The profit is given by:
![y = -9x^2 + 700x - 6005](https://tex.z-dn.net/?f=y%20%3D%20-9x%5E2%20%2B%20700x%20-%206005)
Which is a quadratic function with ![a = -9, b = 700, c = -6005](https://tex.z-dn.net/?f=a%20%3D%20-9%2C%20b%20%3D%20700%2C%20c%20%3D%20-6005)
The maximum profit happens at the x of the vertex. Thus
![x_{v} = -\frac{b}{2a} = -\frac{700}{2(-9)} = 38.88](https://tex.z-dn.net/?f=x_%7Bv%7D%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D%20%3D%20-%5Cfrac%7B700%7D%7B2%28-9%29%7D%20%3D%2038.88)
Widgets should be sold by $38.88 to maximize the profit.
Answer:
a. 20h + 8
Step-by-step explanation:
-2(-7h-4) + 6h = 14h + 8 + 6h = 20h + 8