Answer:
$978
Step-by-step explanation:
Given:
- y = amount of profit
- x = selling price of each widget
![y=-x^2+78x-543](https://tex.z-dn.net/?f=y%3D-x%5E2%2B78x-543)
To find the maximum amount of profit, differentiate the equation, set it to zero and solve for x. Substitute found value of x into the original equation.
<u>Differentiate equation</u>
![y=-x^2+78x-543](https://tex.z-dn.net/?f=y%3D-x%5E2%2B78x-543)
![\implies \dfrac{dy}{dx}=-2x+78](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bdy%7D%7Bdx%7D%3D-2x%2B78)
<u>Set differentiated equation to zero and solve for x</u>:
![\dfrac{dy}{dx}=0](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D0)
![\implies -2x+78=0](https://tex.z-dn.net/?f=%5Cimplies%20-2x%2B78%3D0)
![\implies 2x=78](https://tex.z-dn.net/?f=%5Cimplies%202x%3D78)
![\implies x=39](https://tex.z-dn.net/?f=%5Cimplies%20x%3D39)
<u>Maximum profit</u>
Substitute x = 39 into the equation:
![\implies -(39)^2+78(39)-543=978](https://tex.z-dn.net/?f=%5Cimplies%20-%2839%29%5E2%2B78%2839%29-543%3D978)
Therefore, max profit is $978
Answer:
x = 1
y = 0
Step-by-step explanation:
You did a great job solving one of the equations for a single variable. You solved for x. But what your paper shows is that...it jind of looks like you were going to substitute the 2y+1 into y. BUT you need to substitute it into x.
-4x + 3y = -4
x = 2y + 1
Fill in 2y + 1 into x in the first equation.
-4(2y+1) + 3y = -4
Now you have an equation in one variable. There are only y's in this equation. Next, distribute.
-8y - 4 + 3y = -4
combine like terms.
-5y - 4 = -4
add 4 to both sides.
-5y = 0
divide by -5
y = 0
It's okay that it cam out to be zero. Its fine!
y=0
Put it back in one of the original equations to find x.
x = 2y + 1
x = 2(0) + 1
x = 1
The solution is
x=1
y=0
You can write this as an ordered pair.
(1,0)
Step-by-step explanation:
10 red 6 blue so 16 altogether.
apologies if I'm wrong
Answer: $25,875 - 15% = 21 993.75 0r $25,875 + 15% = 29 756.25
Step-by-step explanation:
Answer: B, C, AND A
Step-by-step explanation: