Answer:
see explanation
Step-by-step explanation:
(i)
to find h(g(x)) , substitute x = g(x) into h(x) , that is
h(g(x))
= h(2x - 3)
= 4(2x - 3)
= 8x - 12
(ii)
given
h(g(x)) =
g(x) , then
8x - 12 =
(2x - 3) ← multiply both sides by 2 to clear the fraction
16x - 24 = 2x - 3 ( subtract 2x from both sides )
14x - 24 = - 3 ( add 24 to both sides )
14x = 21 ( divide both sides by 14 )
x =
=
= 1.5
In geometry, the area enclosed by a circle of radius r is πr2. Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.

Here's the explanation ~
Zeros or roots of a function is the value of independent variable (usually x - coordinate or absicca) where the value of dependent variable (y - coordinate or ordinate) is 0.
That is :
The point where it cuts the x - axis, it has an x - coordinate = -6
Therefore, we can conclude that The zero of given function is -6
Our equation for the area of a rectangle is l x w = A (length times width equals area)
We know that l=w+20 so we can plug this into our equation.
It is now, (w+20) x w =800
We can then solve for w
w^2 +20w =800
We can subtract 800 on each side to get
w^2 +20w - 800 =0
We then factor to get
(w-20)(w+40)=0
This gives us w =20 and w = -40
Width cannot be negative so our width will be 20 feet
Since our length is 20 more than this, then our length will be 40feet
So the dimensions of the rectangle are 20 ft wide by 40 ft long