Answer:
20
Step-by-step explanation:
Step 1: find the derivative of y = x^2 + 12x - 7; it is 2x + 12.
This function represents the slope of the tangent line to the given curve at x.
Step 2: Substitute 4 for x in f '(x) = 2x + 12: f '(4) = 2(4) + 12 = 20
The slope of the tangent line to the graph of y = x^2 + 12x - 7 at x = 4 is 20.
3-(2x-5)<-4(x+2)
8-2x<-8-4x
16<-2x
-8 > x. or equivalently x<-8
Answer:
(See explanation and attachment below for further details)
Step-by-step explanation:
The parabola must satisfy the following conditions:


The expression for the x-intercepts are, respectively:
x = -3
![4 = C\cdot [(-3)^{2} - 2\cdot k\cdot (-3)+k^{2}]](https://tex.z-dn.net/?f=4%20%3D%20C%5Ccdot%20%5B%28-3%29%5E%7B2%7D%20-%202%5Ccdot%20k%5Ccdot%20%28-3%29%2Bk%5E%7B2%7D%5D)

x = 5
![4 = C\cdot [5^{2}-2\cdot k \cdot (5)+k^{2}]](https://tex.z-dn.net/?f=4%20%3D%20C%5Ccdot%20%5B5%5E%7B2%7D-2%5Ccdot%20k%20%5Ccdot%20%285%29%2Bk%5E%7B2%7D%5D)

By equalizing both expressions:



And,


The equation of parabola is:

Whose graph is included as attachment.
-7.2 because you have to multiply-2.4 by 3