Hey there!
40 - 23 = 17
x = 17
Hope this helps
Have a great day (:
I think the answer is x=-8
you are basically simplifying both sides of the equation..then isolating the variable
F(x) is a piecewise function defined as:
f(x) = (3/2)x when 0 <= x <= 2
or
f(x) = -(3/2)x+6 when 2 < x <= 4
g(x) is defined as:
g(x) = -(1/4)x+1 when 0 <= x <= 4
Based on the graph or through the equations we can say:
f(1) = (3/2)*1 = 1.5
g(1) = -(1/4)*1+1 = 0.75
f(3) = (3/2)*3 = 4.5
g(3) = -(1/4)*3+1 = 0.25
And the derivative values are:
f ' (1) = 3/2 = 1.5
f ' (3) = -3/2 = -1.5
g ' (1) = -1/4 = -0.25
g ' (3) = -1/4 = -0.25
which are the slopes of each line
So...
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x) ... product rule
h ' (1) = f ' (1)*g(1) + f(1)*g ' (1)
h ' (1) = 1.5*0.75 + 1.5*(-0.25)
h ' (1) = 0.75
and,
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)
h ' (3) = f ' (3)*g(3) + f(3)*g ' (3)
h ' (3) = -1.5*0.25 + 4.5*(-0.25)
h ' (3) = -1.5
Answer:
the options are missing, so I looked for a similar question:
- 4 inches by 3 inches
- 3 inches by 1 inch
- 6 inches by 2 inches
the correct options are:
3 inches by 1 inch
6 inches by 2 inches
A scaled copy means that the values of rectangle A are related to the value of rectangle B by a scaling factor. In this case, the scaling factor is 3:1. This means that for every 3 inches in rectangle A, you will have 1 inch in rectangle B.
E.g. imagine that instead of making the rectangle smaller, you would make it larger. Using the same scale 3:1, rectangle B could be 30 inches by 10 inches, or 600 inches by 200 inches.
