To solve, use the difference of squares rule. (a^2-b^2)=(a-b)(a+b). In your equation, your a^2=81x^2 and your b^2=4y^2, making your a=9x and your b=2y. This makes your factored form (9x-2y)(9x+2y).
Answer:
a. $600
b. 173.33%
Step-by-step explanation:
The computation is shown below:
a. For amount owed at the end of six weeks is
= The amount borrowed + interest amount
where,
The amount borrowed is $500
And, the interest is
= $100
So, the amount owed is
= $500 + $100
= $600
b. Now the APR is
Since 20% denotes for the six weeks
So, the annual percentage rate is
= 
= 173.33%
Can you put the question in English?
For the carpet:
Given:
Area = x^2 + x - 20 ft^2
Length = x+ 5 ft
As a carpet is rectangular, the area is defined as the product of the length and the width. To obtain an expression of the carpet's width, the area is to be divided by the length, which is shown below:
__x_-_4___x + 5|x^2 + x - 20 x^2 + 5x -------- -4x - 20 -4x - 20 -------- 0
Therefore, the expression of width = x - 4.
Applying the value of x = 20 to obtain the measurements of the carpet, we obtain the following:
Width = x - 4 = 20 - 4 = 16ft
Length = x+ 5 = 20 + 5 = 25ft.
Therefore, the carpet is 25ft x 16ft.
For the wall:
The same principles apply to the wall as it is also assumed to be rectangular.
Given:
Area = <span>x^2 + 17x + 30 ft^2
Width = x + 2
To obtain the expression for the wall's length, Area is to be divided by the Width, which is shown below:
__x_+_15______x + 2|x^2 + 17x + 30 x^2 + 2x -------- 15x + 30 15x + 30 --------- 0
Therefore, the expression for the wall's length is x + 15.
Applying the value of x = 20 to obtain the wall's dimensions:
Length = x + 15 = 20 + 15 = 35ft.
Width = x + 2 = 20 + 2 = 22ft.
Therefore the wall has measurements of 35ft x 22ft.</span>