Answer:
HF = 15??
Step-by-step explanation:
i think the question is incorrect cause there's no solution, I've been struggling help u answer the question for 10 minute but... anyway please refer to the pic
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.
What I see here is a triangle sitting on top of a rectangle, and the
base of the triangle is equal to the length of the rectangle.
To see this, just draw a line between 'F' and 'S'. We can find the
area of the triangle, hen find the area of the rectangle, and then
add the two areas to get the area of the whole polygon.
The triangle:
. . . The base of the triangle is 9 units long.
. . . The height of the triangle is 6 units (from point 'N' down to the line FS).
. . . The area of a triangle is
(1/2) · (base · height)
= (1/2) · (9units · 6units)
= (1/2) · (54 units²) = 27 units².
The rectangle:
. . . The length of the rectangle = 9 units. (line FS)
. . . The height of the rectangle = 2 units. (line WF or line CS)
. . . The area of a rectangle is
(length) · (height)
= (9units · 2units)
= 18 units²
The whole polygon:
The area of the whole polygon is
(area of the triangle) + (area of the rectangle)
= (27 units²) + (18 units²) = 45 units²
