Step-by-step explanation:
First thing first, let find the x value of where P and Q both meet y=5, we know that y=5, and y=2x^2+7x-4, so using transitive law,
![5 = 2 {x}^{2} + 7x - 4](https://tex.z-dn.net/?f=5%20%3D%202%20%7Bx%7D%5E%7B2%7D%20%20%2B%207x%20-%204)
![2 {x}^{2} + 7x - 9](https://tex.z-dn.net/?f=2%20%7Bx%7D%5E%7B2%7D%20%20%2B%207x%20-%209)
![2 {x}^{2} - 2x + 9x - 9](https://tex.z-dn.net/?f=2%20%7Bx%7D%5E%7B2%7D%20%20-%202x%20%2B%209x%20-%209)
![2x(x - 1) + 9(x - 1)](https://tex.z-dn.net/?f=2x%28x%20-%201%29%20%2B%209%28x%20-%201%29)
![(2x + 9)(x - 1) = 0](https://tex.z-dn.net/?f=%282x%20%2B%209%29%28x%20-%201%29%20%3D%200)
![x = 1](https://tex.z-dn.net/?f=x%20%3D%201)
![2x + 9 = 0](https://tex.z-dn.net/?f=2x%20%2B%209%20%3D%200)
![x = - \frac{9}{2}](https://tex.z-dn.net/?f=x%20%3D%20%20-%20%20%5Cfrac%7B9%7D%7B2%7D%20)
Now, to find the gradient of the curve let take the derivative of both sides
![5 = 2 {x}^{2} + 7x - 4](https://tex.z-dn.net/?f=5%20%3D%202%20%7Bx%7D%5E%7B2%7D%20%20%2B%207x%20-%204)
![0 = 4x + 7](https://tex.z-dn.net/?f=0%20%3D%204x%20%2B%207)
![4x + 7](https://tex.z-dn.net/?f=4x%20%2B%207)
Plug in -9/2, let call that point P
![4( \frac{ - 9}{2} ) + 7 = - 11](https://tex.z-dn.net/?f=4%28%20%5Cfrac%7B%20-%209%7D%7B2%7D%20%29%20%2B%207%20%3D%20%20-%2011)
Plug in 1, let call that point Q
![4(1) + 7 = 11](https://tex.z-dn.net/?f=4%281%29%20%2B%207%20%3D%2011)
So the gradient of the curve at point P (-9/2,5) is -11
The gradient of the curve at point Q (1,5) is 11.
Answer:8
Step-by-step explanation:
72/9=8
Answer: Emma’s mean is 189. Devins mean is 186.
Step-by-step explanation:
Emma: 147+143+181+232+193+207+205+221+172= 1701. 1701 divided by nine: 189.
Devin: 185+186+194+197+198+155+194+163+202= 1674 divided by nine: 186.
Coach should choose Emma.
Hope i helped have an awesome Friday!
Answer:
m∠BFE = 171º
BE = 219º
Step-by-step explanation:
∠BFE is supplementary to ∠EFC
m∠BFE = 180 - 9
m∠BFE = 171º
--------------------------
The angle between two chords is equal to half the sum of the intercepted arcs:
∠BFE = (DC + BE)2
171 = (123 + BE)/2
342 = 123 + BE
219º = BE