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.
<span>y=x^2+5x+6
y=4x+12
Solution = (-3,0) and (2,20)
</span><span>y=x^2-3x-1
y=8x-1
Solution = (0,-1) and (11,87)</span>
Because this is a right angle triangle, we can use the Pythagorean theorem to find the missing leg.
The Pythagorean theorem is this:

The Pythagorean theorem tells us if you square both the legs then add them up together, you will get the length of the hypotenuse squared.
We know one leg is 24 and the hypotenuse is 26. Plug them into the equation.
24^2 + b^2 = 26^2
Solve for b.
24^2 + b^2 = 26^2
576 + b^2 = 26^2
576 + b^2 = 676
b^2 = 100
Take the square root of both sides.
b = 10
So, the other leg of the triangle is 10 units long.
STEP 1:
Divide the length of the ribbon by the size of the pieces.
12 inches= 1 foot
= 9 ft ÷ 15 inch pieces
convert ft to inches
= (12)(9) ÷ 15
= 108 ÷ 15
= 7.2 pieces from one roll
STEP 2:
multiply the number of pieces that can be cut from one roll by the number of rolls
= 7.2 pieces * 5 rolls
= 36 pieces total from 5 rolls
ANSWER: The greatest number of 15-inch pieces that can be cut from five 9-foot rolls is 36.
Hope this helps! :)
Answer:
y = 7
Step-by-step explanation:
15 - 8 =7