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4 years ago

Use a geometric model to factor x + x - 2 by following these

Mathematics

2 answers:

Dima020 [189]4 years ago

8 0

Answer:

Mark Brainliest

Step-by-step explanation:

Factoring Trinomials using Algebra Tiles

Algebra tiles can be used as a model for factoring trinomials. When you multiply two binomials, your result is a trinomial. We used area models to multiply binomials. Therefore, to be able to factor a trinomial using algebra tiles, you must first rearrange the tiles into the shape of a rectangle.

1. Factor the expression x2 2x 1 .

a. This trinomial is made up of one x2 tile, two x tiles, and one unit tile.

b. Arrange these tiles to form a rectangle.

c. Use algebra tiles to identify the width and length of the rectangle.

d. The width has one x tile and one unit tile. The length has one x tile and one unit tile. Therefore, the factors of x2 2x 1 are x 1 and x 1. This means that:

x2 2x1x12

2. Factor the expression x2 8x 15.

a. This trinomial is made up of one x2 tile, eight x tiles, and fifteen unit tiles.

b. Arrange these tiles to form a rectangle. The key is to correctly arrange the unit tiles to match the number of x tiles.

c. Use algebra tiles to identify the width and length of the rectangle.

d. Write an equation to show the meaning of the model for this problem.

3. Special care must be taken when the c value in ax2  bx  c is negative. Let’s begin by factoring x2  x 6.

a. This trinomial is made up of one x2 tile, one x tile, and six negative unit tiles. It may be helpful to begin with the x2 tile and six negative unit tiles. Arrange these tiles to form a rectangle. (Note: There may be multiple ways to arrange the unit tiles so some trial and error may be necessary).

b. Since there are negative unit tiles, this means we will have to introduce some negative x tiles to create the rectangle. Just keep in mind – for every negative x tile you introduce, you must introduce a positive x tile. Otherwise, you are changing the value of the expression.

c. Identify the width and length of the rectangle and then write an equation to represent the model.

Practice: Factor each expression using algebra tiles.

1. x2 5x6 2. x2 5x4 3. x2 4x12

4. x2 7x8 5. 2x2 7x6 6. 2x2 5x12

Nikolay [14]4 years ago

6 0

Answer:

This should help

Step-by-step explanation:

Download pdf

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What's negative multiples of 3 in set builder-notation

BlackZzzverrR [31]

<span>Multiples of 3 are {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, …….} , these are all the multiples of 3.
Now, we are looking a negative multiple of 3, which means, we need to a negative value of 3 multiples.
=> -3 {-3, -6, -9, -12, -15, -18, -21, -24, -27, -30,…..} These are all the negative multiple of 3 in set builder notation.
Notice, that the numbers are of divisible by 3. Any number that Is divisible by 3 is called multiple of 3.

</span>

7 0

3 years ago

What is the volume of the cone?

Pavlova-9 [17]

Answer:

$Volume = 1017.36\ in^3$ -- Cone

$Volume = 3052.08\ in^3$ -- Cylinder

$Volume = 3052.08\ in^3$ -- Sphere

<em>Best Buy: Sphere Clay</em>

Step-by-step explanation:

Given

Solid Shapes: Cone, Cylinder, Sphere

Cost of Cone Clay = $12

Cost of Cylinder Clay = $30

Cost of Sphere Clay = $28

Required

Determine the volume of each shape

Which is the best buy

<h2>CONE</h2><h3>Calculating Volume</h3>

The volume of a cone is calculated as thus;

$Volume = \frac{1}{3}\pi r^2h$

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and $\pi = 3.14$

Substitute these values in the above formula;

$Volume = \frac{1}{3} * 3.14 * 9^2 * 12$

$Volume = \frac{3052.08}{3}$

$Volume = 1017.36\ in^3$

<h3>Calculating Volume:Price Ratio</h3>

The unit cost of the cone is calculated as thus;

$Volume:Price = \frac{Volume}{Total\ Cost}$

Where

$Volume = 1017.36\ in^3$

$Total\ Cost = \$12$ (Given)

$Volume:Price = \frac{1017.36\ in^3}{\$ 12}$

$Volume:Price = 84.78 in^3/\$$

$Volume:Price = 84.78 in^3:\$1$

<h2>CYLINDER</h2><h3>Calculating Volume</h3>

The volume of a cylinder is calculated as thus;

$Volume = \pi r^2h$

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and $\pi = 3.14$

Substitute these values in the above formula;

$Volume = 3.14 * 9^2 * 12$

$Volume = 3052.08\ in^3$

<h3>Calculating Volume:Price Ratio</h3>

The unit cost of the cone is calculated as thus;

$Volume:Price = \frac{Volume}{Total\ Cost}$

Where

$Volume = 3052.08\ in^3$

$Total\ Cost = \$30$ (Given)

$Volume:Price = \frac{3052.08\ in^3}{\$ 30}$

$Volume:Price = 101.736\ in^3/\$$

$Volume:Price = 101.736\ in^3:\$1$

<h2>SPHERE</h2><h3>Calculating Volume</h3>

The volume of a sphereis calculated as thus;

$Volume = \frac{4}{3}\pi r^3$

From the attached diagram

Radius, r = 9 inches; and $\pi = 3.14$

Substitute these values in the above formula;

$Volume = \frac{4}{3} * 3.14 * 9^3$

$Volume = \frac{9156.24}{3}$

$Volume = 3052.08\ in^3$

<h3>Calculating Volume-Price ratio</h3>

The unit cost of the cone is calculated as thus;

$Volume:Price = \frac{Volume}{Total\ Cost}$

Where

$Volume = 3052.08\ in^3$

$Total\ Cost = \$28$ (Given)

$Volume:Price = \frac{3052.08\ in^3}{\$ 28}$

$Volume:Price = 109.003\ in^3/\$$

$Volume:Price = 109.003\ in^3:\$1$

Comparing the Volume:Price ratio of the three clay;

<em>The best buy is the sphere because it has the highest volume:price ratio.</em>

<em>Having the highest volume:price ratio means that with $1, one can get more clay from the sphere compared to other types of clay</em>

3 0

3 years ago

Can someone help me with this. Will Mark brainliest.

VikaD [51]

Answer:

(7.5, 3)

Step-by-step explanation:

(5,5) and (10, 1)

Midpoint:

$(\frac{x1 + x2}{2} ,\frac{y1+y2}{2} )\\\\(\frac{5 + 10}{2} ,\frac{5+1}{2} )\\\\(\frac{15}{2} ,\frac{6}{2} )\\\\(7.5,3)$

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3 years ago

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Is 8 yd greater than 288 in.

jonny [76]

3 feet is equal to 1 yard and 3 feet is 36 inches. 288 inches divided by 36 is 8 so 8 yards is equal to 288 inches.

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3 years ago

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Setler79 [48]

The answer is -5x,,,,,,,,,

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3 years ago