The vertex is at -b/(2A). if you use the foil method it will come out to -(x^2+2x+1)+4. then distribute the negative and simplify the equation (add the four) the equation comes out to be -x^2-2x+3. The vertex is at x=2/(2*-1), which is -1. plug -1 into the original equation to find y, (y=-(-1)^2-2*(-1)+3) which is y=4. so the vertex is at (-1,4). then since the parabola opens down (negative a value) and has a maximum at 4, y is always less than or equal to 4. x is all real numbers as it goes on forever. so b is your answer.
Answer:
![A=906.9\ cm^2](https://tex.z-dn.net/?f=A%3D906.9%5C%20cm%5E2)
Step-by-step explanation:
A do-decagon is a polygon with 12 straight sides and 12 equal angles.
-The general formula for finding area of a do-decagon is given as:
![A=3(2+\sqrt{3})s^2](https://tex.z-dn.net/?f=A%3D3%282%2B%5Csqrt%7B3%7D%29s%5E2)
where s is the sides length.
-Given the sides dimension is 9cm, the area is calculated as;
![A=3(2+\sqrt{3})s^2\\\\=3(2+\sqrt{3})\times 9^2\\\\=906.8883462\approx906.9\ cm^2](https://tex.z-dn.net/?f=A%3D3%282%2B%5Csqrt%7B3%7D%29s%5E2%5C%5C%5C%5C%3D3%282%2B%5Csqrt%7B3%7D%29%5Ctimes%209%5E2%5C%5C%5C%5C%3D906.8883462%5Capprox906.9%5C%20cm%5E2)
Hence, the do-decagon's area is ![906.9\ cm^2](https://tex.z-dn.net/?f=906.9%5C%20cm%5E2)
the answer to your question is
Unit walking rate in miles per hour = 5 2/3 / 2 2/3 = 17/3 / 8/3 = 17/3 x 3/8 = 17/8 = 2 1/8 miles per hour.
Unit walking rate in hours per mile = 1/ 17/8 = 8/17 hours per mile
Answer:
12x
Step-by-step explanation:
Combine Like Terms
10x + 2x = 12x
The slopes of parallel line are the same.
We have
therefore the equation of parallel line is ![y=\dfrac{1}{4}x+b](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B4%7Dx%2Bb)
We know. The line passes throught (4; -2). Substitute the coordinates of the point to the equation:
![-2=\dfrac{1}{4}\cdot4+b\\\\-2=1+b\ \ \ |-1\\\\b=-3](https://tex.z-dn.net/?f=-2%3D%5Cdfrac%7B1%7D%7B4%7D%5Ccdot4%2Bb%5C%5C%5C%5C-2%3D1%2Bb%5C%20%5C%20%5C%20%7C-1%5C%5C%5C%5Cb%3D-3)
Answer: ![y=\dfrac{1}{4}x-3](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B4%7Dx-3)