Given triangle abc with vertices A(2,-1), B(5,6), C(-1,4) as shown. Find the number of square units in the area of triangle abs in simplest form.

Answers

Answer 1

Answer:

The area of the triangle is 18 square units.

Step-by-step explanation:

First, we determine the lengths of segments AB, BC and AC by Pythagorean Theorem:

AB

[tex]AB = \sqrt{(5-2)^{2}+[6-(-1)]^{2}}[/tex]

[tex]AB \approx 7.616[/tex]

BC

[tex]BC = \sqrt{(-1-5)^{2}+(4-6)^{2}}[/tex]

[tex]BC \approx 6.325[/tex]

AC

[tex]AC = \sqrt{(-1-2)^{2}+[4-(-1)]^{2}}[/tex]

[tex]AC \approx 5.831[/tex]

Now we determine the area of the triangle by Heron's formula:

[tex]A = \sqrt{s\cdot (s-AB)\cdot (s-BC)\cdot (s-AC)}[/tex] (1)

[tex]s = \frac{AB+BC + AC}{2}[/tex] (2)

Where:

[tex]A[/tex] - Area of the triangle.

[tex]s[/tex] - Semiparameter.

If we know that [tex]AB \approx 7.616[/tex], [tex]BC \approx 6.325[/tex] and [tex]AC \approx 5.831[/tex], then the area of the triangle is:

[tex]s \approx 9.886[/tex]

[tex]A = 18[/tex]

The area of the triangle is 18 square units.


Related Questions

24- Cada uma das letras, a, b, c e d, no diagrama abaixo, representa um único número de conjunto {√7, -9,0, 5/6}. Determine o valor que cada uma dessas letras representa

Answers

Answer:

i

no hablo español-by-step explanation:

Jenna's only source of income is from her job at a car wash, where she works 25 hours each week. She is paid $9.90 per hour. What is her net weekly income if she pays $30.70 in payroll tax each week?

Answers

Answer: 216.8$

Step-by-step explanation:

25 x 9.9 = 247.5

247.5 - 30.70 = 216.8

State the Postulate or Theorem

Answers

Answer:

7. Corresponding Angles Theorem

8. Alternate Interior Angles Theorem

9. Alternate Exterior Angles Theorem

10. Supplementary Angles Theorem

Step-by-step explanation:

In triangle ABC, the length of side AB is 10 inches and the length of side BC is 17 inches. Which of the following could be the length of side AC?

Answers

Answer:

16 inches

Step-by-step explanation:

The length of the side AC is 16 inches.

Calculation of the length of side AC:

Since

we know that two side lengths of a triangle as x and y (x greater than y), the third side z should  satisfy the inequality

So, it can be like

x - y ≤ z ≤ x + y

Also,

The side lengths are x=17 and y=10,

So,

17 - 10 ≤ z ≤ 17 + 10

7 ≤ z ≤ 27

Therefore, the AC should be 16 inches.

learn more about length here: https://brainly.com/question/24545771

Find the area and circumference of the circle from the problem to the left. h 14 in Area= Circumferencer​

Answers

Answer:

r is 14÷2=7in

r is 7

area of circle is pie R square

22÷7×7×7

154 in

since area = circumference

154=154

hope it helps

(10pts) find all the solutions to the equations.

Answers

all of your solution is right
I think they are all correct

Choose the system of equations to solve the following: Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. Determine the total number of adult and student tickets. *

A: 7.25a + 5.50s = 8 and a + s = 52.75
B: 7.25a + 5.50s = 52.75 and a + s = 52.75
C: 7.25a + 5.50s = 52.75 and a + s = 8

Answers

UMMMMMMMMMMMMMMM I don't know

A triangular prism and a plane cutting a triangular prism is shown which shape represents the cross section formed by the plane

Answers

Answer: Tringle

Step-by-step explanation:

I think

Can someone help please!

Answers

Answer:

Step-by-step explanation:

extend the line on the 5ft side to create a triangle and a rectangle.

Area of a rectangle is l x b

10 x 4 = 40ft^2

Area of a triangle is 1/2 base x height

the height of the triangle will be 10 - 5 = 5ft

the base of the triangle will be 12 - 4 = 8

1/2 (8) x (5)

20ft^2

Total area = area of triangle + area of rectangle

Total area  = 20ft^2 + 40ft^2

Total area = 60 ft^2

Someone please please..help me I don’t want to fail this..

Answers

Step-by-step explanation:

hope it helps you........

These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?

Answers

Answer:

2/10 * 2/10 = 1/25

Step-by-step explanation:

Suppose you have 10 marbles in a bag. 5 black , 2 pink and 3 blue

As if two pink marbles are selected then for one pink marble probability = event occurred / total outcome = 2/10

Similar probability for an other pink marbles Probability for the drawing two pink marbles is P = 2/10 * 2/10  = 1/25

Reparte 280 euros entre 3 personas, de forma que la 1º reciba el triple que la 2º y esta el doble de la3º

Answers

Answer:

x = 31.11

Step-by-step explanation:

Let us assume the third person receives be  x

Now the second person receives be 2x

And, the second  be 3(2x) = 6x

The total is 280

Now the equation is

x + 2x + 6x = 280

9x = 280

x = 31.11

5/x+4=9/x-8. Solve for x.

Answers

Answer: x = 1/3

Step-by-step explanation:

5/x - 9/x = -8 - 4

-4/x = -12

x = -4/-12

x = 1/3

Answer:

-19

Step-by-step explanation:

symbolab- a website that you enter an equation in and it solves it for you it's free and no videos or anything :)

PLEASE HELP...!!!!!!!!!!

Answers

Answer:

5 and 10

Step-by-step explanation:  

You have all the information you need to find the area of the circle and then subtracting that from 77 you'll have the area of the rectangle and will be able to figure out the length and height by looking at the answer options.

So the area of a triangle is 1/2(b x h) or (b x h)/2 so the base is 6 and the height is 9 so the area is 54/2 which equals 27. 77 - 27 = 50 so the area of the rectangle is 50. With the answer options provided I can see that the height of the rectangle is 5 and the length is 10.

PLEASE HELP DUE AT MIDNIGHT

Answers

Answer:

268.1

Step-by-step explanation:

Area of Sphere =

[tex] \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \pi {4}^{3} \\ = 268.1 {units}^{3} (nearest \: tenth)[/tex]

Find two integers whose sum is -20 and product is 99

Answers

Answer:

Step-by-step explanation:

let the integers be x and y

x+y=-20

y=-20-x

xy=99

x(-20-x)=99

-20x-x²=99

x²+20x+99=0

x²+11x+9x+99=0

x(x+11)+9(x+11)=0

(x+11)(x+9)=0

x=-11,-9

when x=-11

-11+y=-20

y=-20=11=-9

when x=-9

-9+y=-20

y=-20+9=-11

so integers  are -11,-9

A child has a box of colored building blocks. He will choose one block without looking. The odds against choosing a blue block are 13/4. What is the probability of choosing a blue block?

Answers

Answer:

The answer is "0.2352".

Step-by-step explanation:

Given:

The chance of selecting a odds blue block [tex]= \frac{13}{4}[/tex]

[tex]=\frac{\text{Amount of unfavourable blue block evets} \ (13)}{\text{Amount of unfavourable blue block evets} \ (4)}[/tex]

total number of events are 13+4= 17

Calculating the probability of choosing the blue block  

[tex]=\frac{\text{Amount of unfavourable blue block evets} }{\text{Amount of unfavourable blue block evets} } \\\\ = \frac{4}{17} \\\\ =0.2352[/tex]

3: Find the slope:
(2, 18), (4, 28)
What’s the slope ?

Answers

Answer:

5

Step-by-step explanation:

use the formula y2-y1/x2-x1 = 28-18/4-2=10/2=5

Answer: The slope is equal to 5.

Step-by-step explanation: Remember rise over run or y^1 - x^1/y^2 - x^2.

Hope that helps you :)

Calculate the unknown sides and angles of the triangle ABC given.
Given the final answer correct to three significant figures.
C= 25.7° , b= 3.5cm, a = 6cm​

Answers

Answer:See below

Step-by-step explanation:

to understand thisyou need to know about:law of sinelaw of cosinePEMDASlet's solve:

there are 3 ways to solve SAS triangle

use The Law of Cosines to calculate the unknown side,then use The Law of Sines to find the smaller of the other two anglesand then use the three angles add to 180° to find the last angle.

first figure out [tex]\angle C [/tex]

to do so we will use the formula of law of cosine of C angle

[tex] {c}^{2} = {a}^{2} + {b}^{2} - 2ab.\cos(C) [/tex]

substitute the given values of a,b and [tex]\angle C[/tex]

[tex] \sf{c}^{2} = {6 }^{2} + {3.5}^{2} - 2.6.(3.5). \cos( {25.7}^{ \circ} ) [/tex]

simplify squares:

[tex]c^{2}=36+12.25-42.\cos(25.7^{\circ})[/tex]

simplify addition:

[tex]c^{2}=48.25-42.\cos(25.7^{\circ})[/tex]

square root both sides

[tex] \sf \: \sqrt{ {c}^{2} } = \sqrt{ 48.25-42. \cos(25.7^{\circ})}[/tex]

simplify:

therefore

[tex]\bold{c=3.23}[/tex]

use law of sine to figure out angle A

[tex] \dfrac{6}{\sin( \angle \: A) } = \dfrac{3.23}{\sin(25.7)} [/tex]

therefore

[tex]\bold{\angle A=53.66°}[/tex](use calculater to simplify it)

therefore

[tex]\angle B\: is\: 180^{o}-25.70^{o}-53.66^{o}[/tex]

[tex]\bold{= 100.64}[/tex]

Will give Brainliest, A car wash has a weekly ad in the local newspaper that is 2 inches wide and 4 inches high and costs $36.75 per week. The cost of each ad is based on its area. If the owner of the car wash decides to double the width and height of the ad, how much will the new ad cost?

Answers

Answer:

4+2+$36.75= $42.75

Step-by-step explanation:

4+2+36.75

6+36.75

42.75

Alternative Form

171/4,42 3/4

Answer:

4+2+$36.75=$42.75.

Step-by-step explanation:

6+36.75=42.75

Round your answer to the nearest hundredth if necessary. A figure is shown. 8X 44.49 What is the measure, in degrees, of the shaded angle?​

Answers

You can download answer here

tinyurl.com/wpazsebu

Question 6
Which expression is equivalent to the expression shown?
2
7147²
712
17
716
77

Answers

Answer:

7^12

Step-by-step explanation:

if you are dividing the base numbers then you are subtracting the exponents

90% of what = 81,000​

Answers

Answer:

90000

Step-by-step explanation:

Answer:

90,000

Step-by-step explanation:

81000=0.9*X

81000/0.9=X

X=90000

Hope this helps!

Samuel needs 233 feet of wood to build a fence.The wood comes in lengths of 11 feet. How many prices will samuel need to buy?

Answers

Answer:

21 pieces

Step-by-step explanation:

Given that,

Length of wood needed = 233 feet

The wood comes in lengths of 11 feet.

We need to find the number of pieces samuel need to buy. It can be done as follows :

Let he needed x peices. So

[tex]x=\dfrac{233}{11}\\\\x=21.18\\\\or\\\\x=21[/tex]

So, he will need approx 21 peices.

HELPPP please!!! need answer fast, very confused

Answers

Answer:

I think D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Its d

x: y = 8:1
Which is the correct equation?
A. y=8x
B. x=8y
C. y=7x

Answers

B) x*1=y*8 -> x=8y that’s the right answer

Answer:

B. x=8y

Step-by-step explanation:

X*1=y*8

X=8y

I hope so that i help you

Which of these is a unit of density?
Please help.

Answers

Answer:

I think is C.

Step-by-step explanation:

Hope it's help you ❤️❤️❤️❤️❤️❤️❤️

C

SI unit of density
= kilogram per cubic meter

What is the volume of this composite solid?
4 m
6 m
10 m
6 m
O A. 372 cubic meters
B. 144 cubic meters
Ο Ο Ο Ο
O C. 600 cubic meters
D. 480 cubic meters

Answers

D. 480 cubic meters. Using the volume formula LxWxH we can find the volume of the rectangular prism on the bottom. Using the triangle area formula, we know the face of the triangle has an area of 12. Multiply this twelve by 10 and you get 120. 120+360 = 480

Answer:

its D. 480 cubic meters for Ape.x

Step-by-step explanation:

Find the value of x in the isosceles triangle shown below.
V74
V74

Answers

Answer:

C. x = 10

Step-by-step explanation:

By Pythagoras Theorem:

[tex] \bigg( \frac{x}{2} \bigg)^{2} = {( \sqrt{74} )}^{2} - {7}^{2} \\ \\ \frac{ {x}^{2} }{4} = 74 - 49 \\ \\ \frac{ {x}^{2} }{4} = 25 \\ \\ {x}^{2} = 25 \times 4 \\ \\ {x}^{2} = 100 \\ \\ x = \sqrt{100} \\ \\ x = 10[/tex]

Answer:

C. x = 10

Step-by-step explanation:

Use Pythagorean theorem.

(x/2)² = (√74)² - 7²(x/2)² = 25x/2 = √25x/2 = 5x = 10

Correct choice is C

Answer this Quickly Please 50 points !!!!!!!!!!!!!!!
A seagull is flying in the sky 10 meters above sea level. Directly below the
seagull, a dolphin is jumping 2.5 meters above sea level. Directly below these
animals, is an octopus, swimming 10 feet below sea level. Select all the true
statements. *
10
k
S
vertical position (meters)
-5
-10
The difference in height between the seagull and the dolphin is -7.5 feet.
The difference in height between the seagull and the dolphin is 7.5 feet.
The difference in height between the dolphin and the octopus is -12.5 feet.
The difference in height between the dolphin and the octopus is 12.5 feet.

Answers

Nsnananqnqnqnnqnqnqnqnkkkk
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