07.04.2021

The combined area of a pair of congruent rectangles can be represented, in square units, by the expression 18y^2-818y 2 −8. The length and side of each rectangle can be represented as a difference of squares. What is the perimeter of one of the rectangles?

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Step-by-step answer

24.06.2023, solved by verified expert
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The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

Step-by-step explanation:

Given

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53 -- two rectangles

Required

Determine the perimeter of one of the rectangles

First, calculate the area (A) of 1 rectangle

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

Express as difference of two squares

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

Area is calculated as:

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

So, by comparison:

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

The perimeter is:

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

Collect Like Terms

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

The combined area of a pair of congruent rectangles, №17886546, 07.04.2021 12:53

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Mathematics
Step-by-step answer
P Answered by PhD

Perimeter = 12y

Step-by-step explanation:

Given

Area = 18y^2 - 8 -- two rectangles

Required

Determine the perimeter of one of the rectangles

First, calculate the area (A) of 1 rectangle

A =\frac{1}{2}Area

A =\frac{1}{2}(18y^2 - 8)

A =9y^2 - 4

Express as difference of two squares

A =(3y - 2)(3y+2)

Area is calculated as:

A = Length * Width

So, by comparison:

Length = 3y - 2

Width = 3y + 2

The perimeter is:

Perimeter = 2 *(Length + Width)

Perimeter = 2 *(3y-2+3y+2)

Collect Like Terms

Perimeter = 2 *(3y+3y-2+2)

Perimeter = 2 *(6y)

Perimeter = 12y

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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