Hello there, and thank you for posting your question here on brainly.
The smallest number out of the bunch is 40.
Hope this helps!
Answer:
Step-by-step explanation:
Essentially, begin by flipping the x and y terms:
x = (1 - 2y)^2 + 5
Then, solve for y:
![\ x = (1-2y)^2 + 5\\\sqrt{x-5} = 1 - 2y\\\sqrt{x-5} - 1 = 2y\\\frac{\sqrt{x-5} - 1}{2} = y^-1\\](https://tex.z-dn.net/?f=%5C%20x%20%3D%20%281-2y%29%5E2%20%2B%205%5C%5C%5Csqrt%7Bx-5%7D%20%3D%201%20-%202y%5C%5C%5Csqrt%7Bx-5%7D%20-%201%20%3D%202y%5C%5C%5Cfrac%7B%5Csqrt%7Bx-5%7D%20-%201%7D%7B2%7D%20%3D%20y%5E-1%5C%5C)
Because we know there is only 1 y-value for any given x-value, the inverse of the given function is also a function.
The formula to find how many different ways are there to choose a subgroup of r things from a group of n things is
![\frac{n!}{(n-r)!}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
Here, you have 7 trophies and you want to choose 4 of them, so you have
![\frac{7!}{(7-4)!}\text{ = }\frac{5040}{6}=840](https://tex.z-dn.net/?f=%5Cfrac%7B7%21%7D%7B%287-4%29%21%7D%5Ctext%7B%20%3D%20%7D%5Cfrac%7B5040%7D%7B6%7D%3D840)
So there are 840 ways to choose your 4 trophies out of the 7 you have.
because ( (-2)³+8))/(-2+2)=0/0,
you use formula a³+b³°(a+b)(a²-ab+b²).
therefore (x³+8)/(x+2) = ( (x+2)(x²-2x+4))/(x+2) = x²-2x+4
so lim x->-2 (x²-2x+4) = (-2)²-2*(-2)+4=
=4+4+4=12.
Answer:
![y - 35 = 6(x - 5)](https://tex.z-dn.net/?f=%20y%20-%2035%20%3D%206%28x%20-%205%29%20)
Step-by-step explanation:
The point-slope equation of a line is
,
where
![m = slope = \dfrac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=%20m%20%3D%20slope%20%3D%20%5Cdfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20)
and the point is
![(x_1, y_1)](https://tex.z-dn.net/?f=%20%28x_1%2C%20y_1%29%20)
Let's find the slope.
![m = slope = \dfrac{-31 - 35}{-6 - 5}](https://tex.z-dn.net/?f=%20m%20%3D%20slope%20%3D%20%5Cdfrac%7B-31%20-%2035%7D%7B-6%20-%205%7D%20)
![m = \dfrac{-66}{-11}](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cdfrac%7B-66%7D%7B-11%7D%20)
![m = 6](https://tex.z-dn.net/?f=%20m%20%3D%206%20)
We are asked to use the first point in the equation, so
and ![y_1 = 35](https://tex.z-dn.net/?f=%20y_1%20%3D%2035%20)
The equation is:
![y - 35 = 6(x - 5)](https://tex.z-dn.net/?f=%20y%20-%2035%20%3D%206%28x%20-%205%29%20)