A because if you use T3 it wouldn’t have make sense so only reasonable and solution that works is A
Answer
y=mx+b
y=2x-7
Explanation
m = the “common difference” between two points
In this graph, it’s 2 because every time the line moves across the x axis by 1, it increases in 2 in the y axis
b = the point that intercepts the y axis; the y-intercept
In this graph, the point intercepts the y axis at -7 (the y-intercept is -7)
If the hot air balloon can only hold 3 students and there is a total of 126, there will have to be 42 rides in order for every student to have a turn.
Answer:
89
Step-by-step explanation:
To find the value of the
<h3>
Quadratic expression</h3>
when x = 5 we substitute x = 5 into the expression.
4x^2 - 3x + 4
putting x = 5
4(5)^2 - 3(5) + 4
4(25) - 15 + 4
100 - 11 = 89
Answer:
Step-by-step explanation:
The derivative of 
is calculated as follows:
![\dfrac{dF(x)}{dx}=\dfrac{d}{dx} [(5e^{4x})+(e^{-x^6})]](https://tex.z-dn.net/?f=%5Cdfrac%7BdF%28x%29%7D%7Bdx%7D%3D%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%285e%5E%7B4x%7D%29%2B%28e%5E%7B-x%5E6%7D%29%5D)
![\dfrac{dF(x)}{dx}=\dfrac{d}{dx} [(5e^{4x})]+\dfrac{d}{dx} [(e^{-x^6})]](https://tex.z-dn.net/?f=%5Cdfrac%7BdF%28x%29%7D%7Bdx%7D%3D%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%285e%5E%7B4x%7D%29%5D%2B%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%28e%5E%7B-x%5E6%7D%29%5D)
![\dfrac{dF(x)}{dx}=5\dfrac{d}{dx} [(e^{4x})]+\dfrac{d}{dx} [(e^{-x^6})]](https://tex.z-dn.net/?f=%5Cdfrac%7BdF%28x%29%7D%7Bdx%7D%3D5%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%28e%5E%7B4x%7D%29%5D%2B%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%28e%5E%7B-x%5E6%7D%29%5D)
using the chain rule we find that
![\dfrac{d}{dx} [(e^{4x})]= \dfrac{d}{d(4x)} [(e^{4x})]+ \dfrac{d}{dx} [4x] = 4e^{4x},](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%28e%5E%7B4x%7D%29%5D%3D%20%5Cdfrac%7Bd%7D%7Bd%284x%29%7D%20%5B%28e%5E%7B4x%7D%29%5D%2B%20%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B4x%5D%20%3D%204e%5E%7B4x%7D%2C)
![\dfrac{d}{dx} [(e^{-x^6})] = \dfrac{d}{d(-x^6)} [(e^{-x^6})]+\dfrac{d}{dx} [(-x^6})]= -6x^5e^{-x^6};](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%28e%5E%7B-x%5E6%7D%29%5D%20%3D%20%5Cdfrac%7Bd%7D%7Bd%28-x%5E6%29%7D%20%5B%28e%5E%7B-x%5E6%7D%29%5D%2B%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%28-x%5E6%7D%29%5D%3D%20-6x%5E5e%5E%7B-x%5E6%7D%3B)
therefore,
![\dfrac{dF(x)}{dx}=5\dfrac{d}{dx} [(e^{4x})]+\dfrac{d}{dx} [(e^{-x^6})] =5(4e^{4x})-6x^5e^{x^{-6}}](https://tex.z-dn.net/?f=%5Cdfrac%7BdF%28x%29%7D%7Bdx%7D%3D5%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%28e%5E%7B4x%7D%29%5D%2B%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%28e%5E%7B-x%5E6%7D%29%5D%20%3D5%284e%5E%7B4x%7D%29-6x%5E5e%5E%7Bx%5E%7B-6%7D%7D)
