Find the area, in square units, of ABC plotted below.
A(0,7)
B(7,-2)
D(2, -3)
C(-3,-4)

The area of the triangle ABC for the considered triangle plotted in the considered image is 66.5 sq. units approximately.

The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

The coordinates of the points A, B, C, and D in the given figure are:

Finding the length of the line segments AD and CB, which will be the distance between A and D, and C and B respectively.

Thus, we get:

Length of line segment AD = |AD| = distance between A and D = [tex]\sqrt{(0-7)^2 + (7-(-2))^2} = \sqrt{7^2 + 9^2} = \sqrt{130} \: \rm units.[/tex]

Similarly, we get:
|CB| = [tex]\sqrt{(-3-7)^2 + (-4-(-2))^2} = \sqrt{10^2 + 6^2} = \sqrt{136} \: \rm units.[/tex]

If we take CB as the base of ABC triangle, then as AD is perpendicular on CB, and touches the peak of the triangle ABC from its base, so AD is height of the triangle.

Thus, as we know know that:

Thus, the area of the triangle ABC is:

[tex]A = \dfrac{base \times height}{2} = \dfrac{\sqrt{130} \times \sqrt{136}}{2} \approx 66.5 \: \rm unit^2[/tex]

Thus, the area of the triangle ABC for the considered triangle plotted in the considered image is 66.5 sq. units approximately.

Learn more about distance between two points here:

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2 An art studio charges $65 per month for art lessons. There is also an additional supply fee of $25 at the time of registration. Which equation best describes the total cost, c, given the number of months, m?​

a: -20
b:-8
c:8
d:48
¿?
​

Write down the gradient of the line y =-4r+7.​

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r + 7 < 6 or r + 8 > 18
Write your answer as a compound inequality with integers.

Silvi has a coupon for $5 off any one item at her favorite store. She must pay 6% sales tax on the discounted price. Which of the following functions represents Silvi's final cost, c, for an item with an original price of x dollars?

which time has the definition the location where the X and Y axis intersect the ordered pair is (0,0)"? A Ordinate B Abscissa C Origin D Quadrant​

If 4x + 3x - 2(x + 5) = -9, then x = ?
A-12
B
C
Is
D
213
E
"15

Describe how the values of a and k affect the graphical and tabular representations of the functions y=ax^2, y=x^2+k, and y=ax^2+k.

As Mexican troops drew closer to the Alamo, the Texans ________________.
a.
retreated to smaller quarters within the mission chapel
b.
sent word to Gonzales for reinforcements
c.
sent word to the United States requesting statehood
d.
suffered a rebellion from within the fort

Which unit of measurement would be the most appropriate to measure a bottle of nail polish

A. Choudhury’s bowling ball factory in Illinois makes bowling balls of adult size and weight only. The standard deviation in the weight of a bowling ball produced at the factory is known to be 0.12 pounds. Each day for 24 days, the average weight, in pounds, of nine of the bowling balls produced that day has been assessed as follows:

Day Average (LB) Day Average (LB)
1 16.3 13 16.3
2 15.9 14 15.9
3 15.8 15 16.3
4 15.5 16 16.2
5 16.3 17 16.1
6 16.2 18 15.9
7 16.0 19 16.2
8 16.1 20 15.9
9 15.9 21 15.9
10 16.2 22 16.0
11 15.9 23 15.5
12 15.9 24 15.8

Required:
a. Establish a control chart for monitoring the average weights of the bowling balls in which the upper and lower control limits are each two standard deviations from the mean. What are the values of the control limits?
b. If three standard deviations ate used in the chart, how do these values change? Why?

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Dylan solved the following problem:



258
34
X
----------------------------
1032

+ 774
-------------------

Aubrey says that Dylan is incorrect. What was Dylan’s mistake? What could you do to fix it? Explain your thinking





Please help ASAP

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OX=-3
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AAAAAAAAAAAAAAAAAAHHHHHHHHHHHH

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what’s the decimal expansion of 4/11

Area =
44 ft?
(x - 12) ft
(x - 5) ft
length:
width:
ft

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multiply. Express your answer in the simplest form

PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((