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Ainat [17]
3 years ago
15

Directions: Simplify each term by factoring.

Mathematics
1 answer:
Mrrafil [7]3 years ago
3 0

Answer:

Factoring means to factor a number means to break it up into numbers that can be multiplied together to get the original number.

To simplify each term by factoring:

1.

3rs = 3 \cdot r \cdot s

2.

12xy = 2 \cdot 2 \cdot 3 \cdot x \cdot y

3.

5x^2 = 5 \cdot x \cdot x

4.

36x^2 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot x \cdot x

5.

25x^2 = 5 \cdot 5 \cdot x \cdot x

6.

30x^2 = 2 \cdot 3 \cdot 5 \cdot x \cdot x

7.

5x^3 = 5 \cdot x \cdot x \cdot x

8.

24y^3 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot y \cdot y \cdot y

9.

9xy = 3 \cdot 3 \cdot x \cdot y

10.

12x^4 = 2 \cdot 2 \cdot 3 \cdot x \cdot x \cdot x \cdot x


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The area of a rectangular ceiling tile is 756 square inches. The perimeter is 114 inches. What are the dimensions of the tile?
kogti [31]

Here we need to use what we know about rectangles to make a system of equations.

By solving that system we found that the tile has a length of 36 inches and a width of 21 inches.

Remember that for a rectangle of length L and width W, the perimeter is:

P = 2*(L + W)

And the area is:

A = W*L

Here we know that the perimeter is 114 inches, then we can write:

114in = 2*(L + W)

We also know that the area is 756 in^2, then we can write:

756 in^2 = L*W

So we found two equations, which means that we have a system of two equations with two variables:

114in = 2*(L + W)

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To solve this, the first step is to isolate one of the variables in one of the equations, we can isolate L in the first equation:

114in = 2*(L + W)

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Now that we have an expression equivalent to L, we can replace it in the other equation to get:

756 in^2 = L*W

756 in^2 = (57in - W)*W

Now we can solve this for W.

756 in^2 = W*57in - W^2

W^2 - W*57in + 756 in^2 = 0

The solutions are given by the Bhaskara's formula:

W = \frac{57in \pm \sqrt{(-57in)^2 - 4*1*(756in^2)} }{2*1} = \frac{57in \pm 15in}{2}

Then the two possible values of the width will be:

W = (57in + 15in)/2 =  36 in

W = (57in - 15in)/2 = 21 in

Suppose that we choose the second solution, W = 21in

Now using the equation 57in - W = L we can find the value of L

L = 57in - W = 57in - 21in = 36in

L = 36in

Then we found that the tile has a length of 36 inches and a width of 21 inches.

If you want to learn more, you can read:

brainly.com/question/11137975

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