2(m - 5) + 6PEMDASu multiply 2 into (m-5)2*m and 2*-5that would be 2m-10 + 6now subtract common variables-10 + 6 = -42m - 4
9514 1404 393
Answer:
- 2 6/11 days
- 1 2/3 hours
Step-by-step explanation:
1. Add the rates in terms of houses per day.
1/4 + 1/7 = (7+4)/28 = 11/28
Then the time required in terms of days per house is the reciprocal of this:
28/11 = 2 6/11 . . . . days to paint a house, working together
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2. Each hour, the vehicles separate by 55 -40 = 15 miles. Then the time required for a separation of 25 miles is ...
time = distance/speed = (25 mi)/(15 mi/h_ = 5/3 h = 1 2/3 h
The vehicles will be separated by 25 miles after 1 2/3 hours.
The answer is c. I just did the math it is hard to explain how I did it though. Hopefully this helps you! :)
Answer:
![\large\boxed{-\bigg[(x-3)^2+2x\bigg]+1}\\\\\boxed{-x^2+4x-8}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B-%5Cbigg%5B%28x-3%29%5E2%2B2x%5Cbigg%5D%2B1%7D%5C%5C%5C%5C%5Cboxed%7B-x%5E2%2B4x-8%7D)
Step-by-step explanation:
![f(x)=(x-3)^2+2x\\\\g(x)=-x+1\\\\g\ \circ\ f\to\text{put f(x) instead of x in the function g(x)}:\\\\(g\ \circ\ f)(x)=-\bigg[\underbrace{(x-3)^2+2x}_{x}\bigg]+1](https://tex.z-dn.net/?f=f%28x%29%3D%28x-3%29%5E2%2B2x%5C%5C%5C%5Cg%28x%29%3D-x%2B1%5C%5C%5C%5Cg%5C%20%5Ccirc%5C%20f%5Cto%5Ctext%7Bput%20f%28x%29%20instead%20of%20x%20in%20the%20function%20g%28x%29%7D%3A%5C%5C%5C%5C%28g%5C%20%5Ccirc%5C%20f%29%28x%29%3D-%5Cbigg%5B%5Cunderbrace%7B%28x-3%29%5E2%2B2x%7D_%7Bx%7D%5Cbigg%5D%2B1)
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![-\bigg[(x-3)^2+2x\bigg]+1=-(x-3)^2-2x+1\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=-(x^2-(2)(x)(3)+3^2)-2x+1=-(x^2-6x+9)-2x+1\\\\=-x^2-(-6x)-9-2x+1=-x^2+6x-9-2x+1\\\\\text{combine like terms}\\\\=-x^2+(6x-2x)+(-9+1)=-x^2+4x-8](https://tex.z-dn.net/?f=-%5Cbigg%5B%28x-3%29%5E2%2B2x%5Cbigg%5D%2B1%3D-%28x-3%29%5E2-2x%2B1%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2%5C%5C%5C%5C%3D-%28x%5E2-%282%29%28x%29%283%29%2B3%5E2%29-2x%2B1%3D-%28x%5E2-6x%2B9%29-2x%2B1%5C%5C%5C%5C%3D-x%5E2-%28-6x%29-9-2x%2B1%3D-x%5E2%2B6x-9-2x%2B1%5C%5C%5C%5C%5Ctext%7Bcombine%20like%20terms%7D%5C%5C%5C%5C%3D-x%5E2%2B%286x-2x%29%2B%28-9%2B1%29%3D-x%5E2%2B4x-8)
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Answer:
√65 ft = 8.1 ft
Step-by-step explanation:
We solve using Pythagoras Theorem
c² = a² + b²
c = √a² + b²
Where c = Length of the Hypotenuse
a = 4ft , b = 7ft
Hence
c = √4² + 7²
c = √16 + 49
c = √(65)
c = 8.0622577483 ft
Approximately = 8.1 ft
Therefore, the length of the hypotenuse is √65 ft = 8.1 ft
