What is the factored form of the expression. 4n^2 + 24n + 36

Mathematics

1 answer:

skad [1K]3 years ago

6 0

Answer:

(2n+6)^2

Step-by-step explanation:

To solve this, you can use the given formula: x^2 + 2xy + y^2

In this case, 4n^2 is x^2, 24n is 2xy, and 36 is y^2. The next step is:

(2n)^2 + 2(2n)(6) + (6)^2

Since this equation fits into this formula ( x^2 + 2xy + y^2), we can do:

(2n+6)(2n+6) =

(2n+6)^2

Hence, the answer is (2n+6)^2

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A, b, c, and d please

DIA [1.3K]

<h2>Answers / Step-by-step explanation:</h2><h3>a. What is the length of one side of the square.</h3>

Looking at the image, the radius (r) of the circle appears to cover half of the length of a side of the square. Hence, the side of the square has a length of 2r.

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<h3>b. The formula A= πr² is used to find the area of a circle. The formula A=4r² can be used to find the area of the square. Write the ratio of the area of the circle to the area of the square in the simplest form.</h3>

$Ratio=\frac{\pi r^{2} }{4r^2} =\frac{\pi}{4}$ .

Notice that the value "r²" disappears from the expression because is being multiplied and divided by it at the same time.

$Ratio=\frac{4\pi }{16} =0.7854.$

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c. Complete the table.

To complete each cell of the table, simply take the equation of the asked parameter and substitute the value of r by the number indicated in the title of the column. For example, column 3 should be filled out like this:

Area of Circle (units²): π(3)²or 9π.

Length of 1 Side of the Square: 2r= 2(3)= 6.

Area of Square (units²)= 4r²= 4(3)²= 36.

Ratio: $\frac{\pi}{4}$ .

Do the same for all the other columns.

The answers to the table are presented on the attached image.

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d. What can you conclude about the relationship between the area of the circle and the square?

They will always have the same value, π/4, regardless of the size of the square and circle. As long as the circle borders meet the square's at the middle of each side of the square, the relationship will be the same.