Answer:
57.72 in^2
Step-by-step explanation:
Question 1. Shapes are triangle, semi-circle, and rectangle.
Question 2.Find area of rectangle first. Then area of triangle and circle. Subtract area of triangle and circle. Then add the difference with the rectangles area.
Question 3.
Rectangle's area:<u>48 in^2</u>
Triangles area:8*4/2= <u>16 in^2</u>
Circle Area: pi*r^2/2(since its a semi-circle)
3.14*2^2=3.14*4=12.56/2=<u>6.28 in^2</u>
Question 4.
16-6.28=9.72
9.72+48=57.72 in^2
For this case we have the following quadratic functions:
Revenue: ![3x ^ 2 + 4x - 60](https://tex.z-dn.net/?f=%203x%20%5E%202%20%2B%204x%20-%2060%20%20)
Cost: ![3x ^ 2 - x + 200](https://tex.z-dn.net/?f=%203x%20%5E%202%20-%20x%20%2B%20200%20%20)
Then, we observe that the profit is given by the following mathematical relationship:
![Profit = Revenue - Cost](https://tex.z-dn.net/?f=%20Profit%20%3D%20Revenue%20-%20Cost%20%20)
Substituting values we have:
![Profit = (3x ^ 2 + 4x - 60) - (3x ^ 2 - x + 200)](https://tex.z-dn.net/?f=%20Profit%20%3D%20%283x%20%5E%202%20%2B%204x%20-%2060%29%20-%20%283x%20%5E%202%20-%20x%20%2B%20200%29%20%20)
Making the corresponding calculations we have:
![Profit = x ^ 2 (3-3) + x (4 + 1) + (-60-200)\\Profit = 5x - 260](https://tex.z-dn.net/?f=%20Profit%20%3D%20x%20%5E%202%20%283-3%29%20%2B%20x%20%284%20%2B%201%29%20%2B%20%28-60-200%29%5C%5CProfit%20%3D%205x%20-%20260%20%20)
Answer:
An expression that represents the profit is:
![Profit = 5x - 260](https://tex.z-dn.net/?f=%20Profit%20%3D%205x%20-%20260%20)
Answer:
![x = \frac{-7 +\sqrt{489} }{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-7%20%2B%5Csqrt%7B489%7D%20%7D%7B2%7D)
![x = \frac{-7 - \sqrt{489} }{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-7%20-%20%5Csqrt%7B489%7D%20%7D%7B2%7D)
Step-by-step explanation:
2x² +21x-61 = (x+7)²
expand
2x² + 21x - 61 = x² + 14x +49
move everything to one side
x² + 7x - 12 = 0
use quadratic formula
![x = \frac{-b +- \sqrt{b^{2}-4ac } }{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%2B-%20%5Csqrt%7Bb%5E%7B2%7D-4ac%20%7D%20%7D%7B2a%7D)
plug in the values
![x = \frac{-7 +- \sqrt{7^{2}-4(1)(-110) } }{2(1)}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-7%20%2B-%20%5Csqrt%7B7%5E%7B2%7D-4%281%29%28-110%29%20%7D%20%7D%7B2%281%29%7D)
solve
![x = \frac{-7 +- \sqrt{49-4(1)(-110) } }{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-7%20%2B-%20%5Csqrt%7B49-4%281%29%28-110%29%20%7D%20%7D%7B2%7D)
![x = \frac{-7 +- \sqrt{49 + 440 } }{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-7%20%2B-%20%5Csqrt%7B49%20%2B%20440%20%7D%20%7D%7B2%7D)
![x = \frac{-7 +- \sqrt{489} }{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-7%20%2B-%20%5Csqrt%7B489%7D%20%7D%7B2%7D)
Answer:
![\huge \boxed{\mathrm{500 \ miles}}](https://tex.z-dn.net/?f=%5Chuge%20%5Cboxed%7B%5Cmathrm%7B500%20%5C%20miles%7D%7D)
Step-by-step explanation:
A right triangle is formed.
300 miles and 400 miles are the legs of the triangle.
We can apply Pythagorean theorem.
![c=\sqrt{300^2 +400^2 }](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B300%5E2%20%2B400%5E2%20%7D)
![c=\sqrt{90000 +160000}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B90000%20%2B160000%7D)
![c=\sqrt{250000}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B250000%7D)
![c=500](https://tex.z-dn.net/?f=c%3D500)
0.0909090909 Is the answer my friend plz mark brainliest