Answer:
see explanation
Step-by-step explanation:
to clear a square root on the denominator
Multiply the numerator and denominator by the square root, for example
![\frac{5}{\sqrt{3} }](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B%5Csqrt%7B3%7D%20%7D)
=
×
=
Answer:
ffffff cccc fff
Step-by-step explanation:
Answer:
5 31/30 or 181/30
Step-by-step explanation:
Step-by-step explanation:
![x^{2} - 4x - 7 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-%204x%20-%207%20%3D%200)
First, let's move the
to the right-hand side so we can determine what constant we'll need on the left-hand side to complete the square:
![x^{2} - 4x = 7](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-%204x%20%3D%207)
From here, since the coefficient of the
term is
, we know the square will be
(since
it's half of
).
To complete this square, we will need to add
to both sides of the equation:
![x^{2} - 4x + (-2)^2 = 7 + ^{-2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-%204x%20%2B%20%28-2%29%5E2%20%3D%207%20%2B%20%5E%7B-2%7D)
![x^{2} - 4x + 4 = 7 + 4](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-%204x%20%2B%204%20%3D%207%20%2B%204)
![(x - 2)^{2} = 11](https://tex.z-dn.net/?f=%28x%20-%202%29%5E%7B2%7D%20%3D%2011)
Now we can take the square root of both sides to figure out the solutions to
:
![x - 2 = \pm \sqrt{11}](https://tex.z-dn.net/?f=x%20-%202%20%3D%20%5Cpm%20%5Csqrt%7B11%7D)
![x = 2 \pm \sqrt{11}](https://tex.z-dn.net/?f=x%20%3D%202%20%5Cpm%20%5Csqrt%7B11%7D)
Henry runs at a rate of seven miles an hour. I think you meant the second sentence to be 'Blake', because there is not attatched graph. They are both running at the same speed in this case.
I got this because 14 (miles ran by Henry) / 2 (hours ran) you get 7. This same equation is applied to (Blake?) 35 (miles ran by [Blake?]) / 5 (hours ran) also equals seven.
If you meant the second statement to be Blake, they are both running at the same speed, and x=7.
If you didn't, then there is not enough information to determine Blake's speed.
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