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stira [4]
2 years ago
5

Pentagon TEXAS has vertices at T(1, 8), E(3, 8), X(6, 2), A(3, 2), and S(1, 4). What is the area of Pentagon TEXAS?

Mathematics
1 answer:
Tamiku [17]2 years ago
7 0

The area of the pentagon is 19 square units

The coordinates of the pentagon are given as:

T = (1, 8)

E =(3, 8)

X =(6, 2)

A=(3, 2)

S = (1, 4)

The area of the pentagon is then calculated using:

Area = \frac 12|(x_1y_2+x_2y_3+x_3y_4+x_4y_5+x_5y_1) -(y_1x_2+y_2x_3+y_3x_4+y_4x_5+y_5x_1)|

So, we have:

Area = \frac 12|(1 \times 8 +3 \times 2+6\times2+3 \times 4 + 1 \times 8) -(8\times3+8\times6+2\times3+2\times1+4\times1)|

Simplify the expressions in both brackets

Area = \frac 12|46 -84|

Area = \frac 12|-38|

Remove absolute bracket

Area = \frac 12 \times 38

Area = 19

Hence, the area of the pentagon is 19 square units

Read more about areas at:

brainly.com/question/1423568

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A system of inequalities is shown.
Doss [256]

The system of inequalities which is represented in the graph shown (see attachment) is:

  1. y ≥ x² -2x -3
  2. y ≤ x +3

<h3>What is an inequality?</h3>

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

  • Less than (<).
  • Greater than (>).
  • Less than or equal to (≤).
  • Greater than or equal to (≥).

<h3>What is a graph?</h3>

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

By critically observing the graph which models the system of inequalities shown, we can infer and logically deduce the following points:

  • Both boundary lines on the cartesian coordinate are solid. Thus, the inequalities will both have the "equal to" sign.
  • The shading occurred above the quadratic boundary line. Thus, the inequalities below the linear boundary line is given by y ≥ x² + and y ≤ x +

In conclusion, we can infer and logically deduce that the system of inequalities which is represented in the graph shown (see attachment) is:

  1. y ≥ x² -2x -3
  2. y ≤ x +3

Read more on graphs here: brainly.com/question/25875680

#SPJ1

6 0
2 years ago
Simplify the expression by combining like terms. -3y - 2 - 3 + 17y
Nookie1986 [14]

Answer:

14y -5

Step-by-step explanation:

Given:

-3y - 2 - 3 + 17y   (rearrange so that like terms are together)

= 17y - 3y -2 -3  (group like terms)

= (17y - 3y) + (-2 -3 )   simplify

= 14y + (-5)

= 14y -5

4 0
3 years ago
Using eight eights and addition only, can you make 1000?
Serga [27]

Answer:

..........................................................................................................................................................................................No

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Instructions: Find the value of 2.
frosja888 [35]

Answer:

x = 50°

2x = 100°

Step-by-step explanation:

Chords AB and DC are equidistant (3 units) from the center E of the circle.

Since, the chords equidistant from the center of the circle are congruent.

Congruent chords intercepts congruent arcs.

Hence, x = 50°

2x = 2*50° = 100°

3 0
3 years ago
√144² = <br>√9 + √16 = <br>√9 + √16 × √400 = ​
Morgarella [4.7K]

Answer:

Step-by-step explanation

√144²

12²

144

√9 + √16

3 + 4

7

√9 + √16 × √400 = ​

3 + 2^{4} x 5

3 + 80

83

7 0
3 years ago
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