Arectangle’s length is 2 units more than twice its width. its area is 40 square units. the equation w(2w + 2) = 40 can be used to find w, the width of the rectangle.

what is the width of the rectangle?

4 units
5 units
10 units
12 units

Option 1 is correct that is 4 units

Explanation:

Given equation is w(2w+2) = 40

we can simplify the equation by opening the brackets on left hand side of the equation we get + 2w =40

taking 2 as common factor from both the sides we will get

+ w=20

after middle term split we will get

+ 5w-4w -20=0

after simplification we will get (w+5)(w-4)

we will two values w= -5 , 4

-5 will be neglected because width can not be negative

Hence, width is 4 units.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

the function makes a strait line horizontally with no x intercept but a y intercept at 9.