Answer:
A
Step-by-step explanation:
Slope intercept form is y = mx + b
First find the slope or m with this equation
(plug in)
=
= ![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)
So your slope is ![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)
To find the y-intercept you use y= mx + b and plug in.
6 = 1/4(12) + b
6 = 3 + b (minus 3 on both sides)
3 = b
so 3 is the y-intercept
So the answer is A.
F(2) is the same as (3x-7)(3x-7)
Answer:
6
Step-by-step explanation:
Because my lucky num is 6
Step-by-step explanation:
Letting the variable x approach 1 will give us
, an indeterminate result. In such a case, we can use L'Hopital's rule where
![\displaystyle \lim_{x \to c} \dfrac{f(x)}{g(x)} = \lim_{x \to c} \dfrac{f'(x)}{g'(x)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20%5Cdfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%3D%20%5Clim_%7Bx%20%5Cto%20c%7D%20%5Cdfrac%7Bf%27%28x%29%7D%7Bg%27%28x%29%7D)
Let
and
![g(x) = \sqrt{ 2 - x} - 1](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Csqrt%7B%202%20-%20x%7D%20-%201)
We can see that
![f'(x) = -\frac{1}{2}(17 - x)^{-\frac{1}{2}}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%2817%20-%20x%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D)
and
![g'(x) = -\frac{1}{2}(2 - x)^{-\frac{1}{2}}](https://tex.z-dn.net/?f=g%27%28x%29%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%282%20-%20x%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D)
Applying L'Hopital's rule, we get
![\displaystyle \lim_{x \to 1} \dfrac{\sqrt{17 - x} - 4}{\sqrt{ 2 - x} - 1} = \lim_{x \to 1} \dfrac{-\frac{1}{2}(17 - x)^{-\frac{1}{2}}}{-\frac{1}{2}(2 - x)^{-\frac{1}{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%201%7D%20%5Cdfrac%7B%5Csqrt%7B17%20-%20x%7D%20-%204%7D%7B%5Csqrt%7B%202%20-%20x%7D%20-%201%7D%20%3D%20%5Clim_%7Bx%20%5Cto%201%7D%20%5Cdfrac%7B-%5Cfrac%7B1%7D%7B2%7D%2817%20-%20x%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B-%5Cfrac%7B1%7D%7B2%7D%282%20-%20x%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7D)
![\:\:\:\:\:\:\:\:= \displaystyle \lim_{x \to 1} \sqrt{\dfrac{2 - x}{17 - x}} =\sqrt{\dfrac{1}{16}} = \dfrac{1}{4}](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%3D%20%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%201%7D%20%5Csqrt%7B%5Cdfrac%7B2%20-%20x%7D%7B17%20-%20x%7D%7D%20%3D%5Csqrt%7B%5Cdfrac%7B1%7D%7B16%7D%7D%20%3D%20%5Cdfrac%7B1%7D%7B4%7D)
Therefore, as
the given expression approaches
.
Answer:
-4(-41)
Step-by-step explanation: