Answer:
x=y-4
Step-by-step explanation:
y=x+4
-4
y-4=x
9514 1404 393
Answer:
f(x) = 0.15x +25
Step-by-step explanation:
We are given two points:
(x, y) = (180, 52) or (350, 77.50)
The slope is given by ...
m = (y2 -y1)/(x2 -x1)
m = (77.50 -52)/(350 -180) = 25.50/170 = 0.15
The y-intercept is given by ...
b = y -mx
b = 52 -0.15×180 = 25
Then the equation for the linear function is ...
f(x) = mx +b
f(x) = 0.15x +25
The generic equation for a linear function can be expressed in the slope intercept form f(x) = mx + b, where m is the slope and b is the y intercept. For this problem we can first find the equation of the line. Then we substitute x = 7 to get the f(x) value, which is n at the point x = 7.
To find the equation of the linear function we first find the slope. Slope is defined as the change in f(x) divided by the change in x. As we are given a linear function, the slope at every point is the same. We can pick any two points known to find the slope.
Let's pick (3, 7) and (9, 16). The slope m is m = (16-7)/(9-3) = 9/6 = 3/2.
Now that we have the slope, we can plug in the slope and one of the points to find b. Let's use the point (3, 7).
f(x) = mx + b
7 = (1/2)(3) + b
b = 11/2
Now we can write the equation
f(x) = (1/2)x + 11/2
Plugging in x = 7 we find that f(7) = 9. n = 9
Dy/dx=2x+2
So velocity will be zero when 2x+2=0, x=-1
Since d2y/dx2=2, it has a constant positive acceleration of 2, so that when dy/dx=0 it is at an absolute minimum value for f(x), which is also the vertex.
y(-1)=1-2+3=2
So the vertex is at (-1,2), which is an absolute minimum so the parabola opens upwards.
And by symmetry we can say that f(0)=f(-2)=3 so you have another two points that you can see (-2,3) and (0,3)