C=(-10;5). If you want an explanation I would be happy to explain it
Give a reason for each step of the proof.
Given: <1 and <2 are complimentary
<1 is congruent to <3,
<2 is congruent to <4
Prove: <3 and <4 are complimentary
Statements: Reasons:
1. <1 and <2 are complimentary 1.Given
2. m<1 + m<2=90* 2.<u>DEFINITION OF COMPLEMENTARY ANGLES</u>
3. <1 is congruent to <3, <2 is congruent to <4 3.__GIVEN______
4. m<1=m<3, m<2=m<4 4.<u>DEFINITION OF CONGRUENT ANGLES_</u>
5. m<3 + m<2=90* 5. <u>SUBSTITUTION PROPERTY (m<1 is replaced by m<3.) </u>
6. m<3 +m<4=90* 6. <u>DEFINITION OF COMPLEMENTARY ANGLES </u>
7. <3 and <4 are complimentary 7.<u> DEFINITION OF COMPLEMENTARY ANGLES</u>
From 8.30 pm to 12 : 00
Difference = 12 : 00 - 08:30 = 3 : 30
3 hours 30 minutes = 3.5 hours.
Total for those hours = 3.5 * 1000 = $3500
From 12:00 to 1:00 am = 1 hour.
50% increase = 50% of 1000 = .50 * 1000 = 500
So it will increase to 1000 + 500 = $1500 per hour.
For the 1 hour extra, 1 * 1500 = $1500
Total = $3500 + $1500 = $5000
She will be paid $5000
Given:
The revenue function is
![R(x)=126.98x-0.5x^2](https://tex.z-dn.net/?f=R%28x%29%3D126.98x-0.5x%5E2)
The cost function is
![C(x)=3809.40+0.7x^2](https://tex.z-dn.net/?f=C%28x%29%3D3809.40%2B0.7x%5E2)
To find:
The profit function.
Solution:
We know that, the total profit P is defined as total revenue R minus total cost C.
So, the profit function is
![P(x)=R(x)-C(x)](https://tex.z-dn.net/?f=P%28x%29%3DR%28x%29-C%28x%29)
![P(x)=126.98x-0.5x^2-(3809.40+0.7x^2)](https://tex.z-dn.net/?f=P%28x%29%3D126.98x-0.5x%5E2-%283809.40%2B0.7x%5E2%29)
![P(x)=126.98x-0.5x^2-3809.40-0.7x^2](https://tex.z-dn.net/?f=P%28x%29%3D126.98x-0.5x%5E2-3809.40-0.7x%5E2)
![P(x)=-3682.42-1.2x^2](https://tex.z-dn.net/?f=P%28x%29%3D-3682.42-1.2x%5E2)
Therefore, the profit function is
.