Answer:
Number of ovens must be manufactured in a given week to generate a profit of $1610 is 70
Step-by-step explanation:
We are given
A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given by the formula
![P=\frac{1}{10}x(300-x)](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B10%7Dx%28300-x%29)
provided that 0 ≤ x ≤ 200
We are given
profit is $1610
so, we can set P=1610
and then we can solve for x
![1610=\frac{1}{10}x(300-x)](https://tex.z-dn.net/?f=1610%3D%5Cfrac%7B1%7D%7B10%7Dx%28300-x%29)
Multiply both sides by 10
![1610\cdot \:10=\frac{1}{10}x\left(300-x\right)\cdot \:10](https://tex.z-dn.net/?f=1610%5Ccdot%20%5C%3A10%3D%5Cfrac%7B1%7D%7B10%7Dx%5Cleft%28300-x%5Cright%29%5Ccdot%20%5C%3A10)
![16100=x\left(300-x\right)](https://tex.z-dn.net/?f=16100%3Dx%5Cleft%28300-x%5Cright%29)
![16100=300x-x^2](https://tex.z-dn.net/?f=16100%3D300x-x%5E2)
![-x^2+300x-16100=0](https://tex.z-dn.net/?f=-x%5E2%2B300x-16100%3D0)
now, we can factor it
![(x-70)(x-230)=0](https://tex.z-dn.net/?f=%28x-70%29%28x-230%29%3D0)
we can solve for x
and we get
![x=70,x=230](https://tex.z-dn.net/?f=x%3D70%2Cx%3D230)
Since, x=230 does not lie on 0 ≤ x ≤ 200
So, we will consider only x=70
So,
Number of ovens must be manufactured in a given week to generate a profit of $1610 is 70
You must use Pythagorean theorem, which is ![a^{2} +b^{2} =c^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%2Bb%5E%7B2%7D%20%3Dc%5E%7B2%7D)
a and b are both legs (the two legs are the sides that form a perpendicular right angle) while c is the hypotenuse (side opposite the right angle)
In this case...
a = y
b = 8
c = 12
^^^Plug these numbers into Pythagorean theorem
![y^{2} +8^{2} =12^{2}](https://tex.z-dn.net/?f=y%5E%7B2%7D%20%2B8%5E%7B2%7D%20%3D12%5E%7B2%7D)
Simplify as much as possible
+ 64 = 144
Isolate y by subtracting 64 to both sides
+ (64 - 64) = 144 - 64
= 80
Further isolate y by taking the square root of both sides. This will take away the square from the left side
y = ![\sqrt{80}](https://tex.z-dn.net/?f=%5Csqrt%7B80%7D)
<<< Can be further simplified
4√5 = y
Hope this helped!
~Just a girl in love with Shawn Mendes
Step-by-step explanation:
Let set up the two column proof
Statements. Reasons
1. m 1+ m∠5 = 180° and m∠1 + m∠4=180° Given
2. 2. m∠1 + m∠5 = m∠1 + m∠4. Substitution
3.m∠5 = m∠4. Subtraction Property of Equal
4.is Parallel to Given. 4.If alternate interior angles equal, then lines are ||.
First thing you have to do is take the 5 + -8 which equals -3 then you have to 33-18 which equals 15 then u have to divide by the -3 which gives you equal your answer of -5
Answer:
4, 096
2¹²
Step-by-step explanation:
i notice the pattern . each time the cells increase by 4 times :
Day:
- 4
- 4 × 4 =16
- 16 × 4 = 64
- 64 × 4 = 256
- 256 × 4 = 1024
- 1024 × 4 = 4096