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Ghella [55]
3 years ago
13

Figure ABCDE has vertices a(-3, 3), b(2, 3), c(5, -2), d(0, -3), and e(-3, -2). Plot the points on your own coordinates grid and

connect in alphabetical order. Decompose figure ABCDE into rectangles and triangles.

Mathematics
1 answer:
Ilya [14]3 years ago
5 0
<h2>Answer:</h2>

Shown below

<h2>Step-by-step explanation:</h2>

First of all, we have the following points:

a(-3, 3) \\ \\ b(2, 3) \\ \\ c(5, -2) \\ \\ d(0, -3) \\ \\ e(-3, -2)

To plot these points, we need to graph a coordinate grid. Recall that a coordinate grid is composed of two perpendicular lines, that we call the axes and are labeled like number lines. The horizontal axis is called the x-axis while the vertical axis is called the y-axis, and these two axes intersect at a point called the origin. Next, let's plot each point as follows:

<h2>PART 1. Plot the points on your own coordinates grid and connect in alphabetical order. </h2><h2></h2>

Point a:

Let's stand at the origin and then move three units to the left and three units up. The resulting point is shown in the firs figure below.

Point b:

Let's stand at the origin and then move two units to the right and three units up. The resulting point is shown in the firs figure below.

Point c:

Let's stand at the origin and then move five units to the right and two units down. The resulting point is shown in the firs figure below.

Point d:

Let's stand at the origin and then move three units to down. The resulting point is shown in the firs figure below.

Point e:

Let's stand at the origin and then move three units to the left and two units down. The resulting point is shown in the firs figure below.

Next, let's connect connect the points in alphabetical order, so that the line are connected from a to b, from b to c, from c to d, from d to e and from e to a again. So the resulting graph is shown in the second figure. As you can see, this is an irregular pentagon.

<h2>PART 2. Decompose figure ABCDE into rectangles and triangles.</h2>

Every pentagon can be divided up into three triangles. Hence, from the third figure. the triangles are:

ΔABE

ΔBDE

ΔBCD

Since a rectangle is a quadrilateral whose angles are all right angles, then there is no chance to obtain a rectangle from ABCDE. To obtain a rectangle, we'd need other points and this is not what the problem asks.

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8 0
3 years ago
The square of a number is 12 less than 7 times the number. What is the number?
hjlf

<u><em>Answer:</em></u>

The number is either 3 or 4


<u><em>Explanation:</em></u>

Assume that the number we are looking for is x

The square of the number would be x²

7 times the number would be 7x


<u>We are given that:</u>

square of the number (x²) is 12 less than 7 times the number (7x)


<u>Translating this into an equation, we would have:</u>

x² = 7x - 12


<u>Rearranging the quadratic equation:</u>

x² - 7x + 12 = 0


<u>Now, we factor the equation:</u>

(x-4)(x-3) = 0


<u>This means that:</u>

either x-4 = 0 ..................> x = 4

or x-3 = 0 ........................> x = 3


<u>Let's check if any of the solutions is an extrovert:</u>

For x = 3 .............> (3)² = 7(3) - 12 .........> 9 = 21 - 12 .......> 9 = 9 .......> not extrovert

For x = 4 .............> (4)² = 7(4) - 12 .........> 16 = 28 - 12 .....> 16 = 16 ....> not extrovert


Since we have no restrictions on the number, therefore, both solutions would be accepted


Hope this helps :)


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