Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
To isolate x, we will first subtract 0.8 from both sides.
0.6x + 0.8 = 1.4
-0.8 -0.8
0.6x = 0.6
Now all we have to do is divide both sides by 0.6, because it is the number besides x.
0.6x/0.6 = 0.6/0.6
x = 1
So you get the answer of x = 1.
Answer:
D. (2, 0)
Step-by-step explanation:
The solutions are the two points of intersection of the graphs:
(-2, -4) and (2, 0)
The latter of these corresponds to choice D, the one you have marked.
Answer:
Part A 70x+50=250
Part B(75x + 35) = 250 - 5x
Step-by-step explanation:
Here to form an equation you must add all the money that she earned and subtract the money that she had to spend We dont know how many car washes she did, so we must represent it with a variable, or x.
Find the volume of the rectangular prism.
V = lwh
V = (9)(16)(4)
V = 756 ft^3
Convert to cubic yards:
1 ft^3 = 0.037037037 yd^3
756 * 0.037037037 = 28
So there are 28 cubic yards of dirt he needs.
Multiply this to 25 to find the total cost of the dirt:
28 * 25 = 700
So the project will cost $700
