Answer:
![F(x)=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.](https://tex.z-dn.net/?f=F%28x%29%3D2%5Cleft%28x%2B%5Cdfrac%7B13%7D%7B4%7D%5Cright%29%5E2-%5Cdfrac%7B9%7D%7B8%7D.)
Step-by-step explanation:
Consider the function ![F(x)=2x^2+13x+20.](https://tex.z-dn.net/?f=F%28x%29%3D2x%5E2%2B13x%2B20.)
Rewrite it as follows:
![F(x)=(2x^2+13x)+20=2\left(x^2+\dfrac{13}{2}x\right)+20=2\left(x^2+\dfrac{13}{2}x+\left(\dfrac{13}{4}\right)^2-\left(\dfrac{13}{4}\right)^2\right)+20=2\left(x^2+\dfrac{13}{2}x+\dfrac{169}{16}\right)-2\cdot \dfrac{169}{16}+20.](https://tex.z-dn.net/?f=F%28x%29%3D%282x%5E2%2B13x%29%2B20%3D2%5Cleft%28x%5E2%2B%5Cdfrac%7B13%7D%7B2%7Dx%5Cright%29%2B20%3D2%5Cleft%28x%5E2%2B%5Cdfrac%7B13%7D%7B2%7Dx%2B%5Cleft%28%5Cdfrac%7B13%7D%7B4%7D%5Cright%29%5E2-%5Cleft%28%5Cdfrac%7B13%7D%7B4%7D%5Cright%29%5E2%5Cright%29%2B20%3D2%5Cleft%28x%5E2%2B%5Cdfrac%7B13%7D%7B2%7Dx%2B%5Cdfrac%7B169%7D%7B16%7D%5Cright%29-2%5Ccdot%20%5Cdfrac%7B169%7D%7B16%7D%2B20.)
Since
![x^2+\dfrac{13}{2}x+\dfrac{169}{16}=\left(x+\dfrac{13}{4}\right)^2,](https://tex.z-dn.net/?f=x%5E2%2B%5Cdfrac%7B13%7D%7B2%7Dx%2B%5Cdfrac%7B169%7D%7B16%7D%3D%5Cleft%28x%2B%5Cdfrac%7B13%7D%7B4%7D%5Cright%29%5E2%2C)
you get
![F(x)=2\left(x+\dfrac{13}{4}\right)^2+20-\dfrac{169}{8}=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.](https://tex.z-dn.net/?f=F%28x%29%3D2%5Cleft%28x%2B%5Cdfrac%7B13%7D%7B4%7D%5Cright%29%5E2%2B20-%5Cdfrac%7B169%7D%7B8%7D%3D2%5Cleft%28x%2B%5Cdfrac%7B13%7D%7B4%7D%5Cright%29%5E2-%5Cdfrac%7B9%7D%7B8%7D.)
Answer:
LCM is 30.
Step-by-step explanation:
She forgot that they both can multiply into 30. She listed all their multiples and their LCM is 30. Not 60. That's her error.
<u>Hope this helps and have a nice day!</u>
Answer:
that's wrong, its 217 1/2 miles
Step-by-step explanation:
3/4 of a minute is 45 seconds
the easiest way to this is you figure there is 15 intervals of 3 seconds in 45 seconds so do 15 times 14.5 and get 217 1/2 miles
Answer:
range in age = 5
Step-by-step explanation:
The range of a set of data is the difference between the highest and lowest values in the set.
we can see that the highest age is 29 and the smallest age is 24.
29 - 24 = 5
range = 5