let h(x)=x+6 and g(x)=x^2-4x+2. find h(x) * g(x)
To find h(x) * g(x), we need to multiply h(x) by g(x) first.
First, let's find h(x) * g(x):
h(x) = x + 6
g(x) = x^2 - 4x + 2
h(x) * g(x) = (x + 6) * (x^2 - 4x + 2)
= x*(x^2 - 4x + 2) + 6*(x^2 - 4x + 2)
= x^3 - 4x^2 + 2x + 6x^2 - 24x + 12
= x^3 + 2x^2 - 22x + 12
Therefore, h(x) * g(x) = x^3 + 2x^2 - 22x + 12.
Find the perimeter
length x^2-9
width x^2-4
The perimeter of a rectangle is calculated by adding up all the sides.
Given:
Length = x^2 - 9
Width = x^2 - 4
Perimeter = 2*(length + width)
Perimeter = 2*((x^2 - 9) + (x^2 - 4))
Perimeter = 2*(2x^2 - 13)
Perimeter = 4x^2 - 26
Therefore, the perimeter of the rectangle is 4x^2 - 26.
find the area
length x+7
width x+3
The area of a rectangle is calculated by multiplying the length by the width.
Given:
Length = x + 7
Width = x + 3
Area = Length * Width
Area = (x + 7) * (x + 3)
Area = x^2 + 3x + 7x + 21
Area = x^2 + 10x + 21
Therefore, the area of the rectangle is x^2 + 10x + 21.