Two of the vertices of a triangle are located at (6,0) and (5,10) on the coordinate plane. The third vertex is located at (x,20) , where x is a negative value. The area of the triangle is 60 square units.

Using the shoelace formula (Green’s Theorem) in counterclockwise fashion, write an equation that can be used to find the value of x .
PLEASE I NEED HELP! ASAP I WOULD REALLY APPRECIATE IT!!

Answers

Answer 1
The answer is 1,1 . 3,-3, 5, -3
Answer 2

Using the shoelace formula (Green’s Theorem) in counterclockwise fashion, the value of x is -8.

What is Shoelace formula ?

Area of Polygon can be calculated using Shoelace formula described by Mathematician and Physicist Carl Friedrich Gauss where polygon vertices are described by their Cartesian coordinates in the Cartesian plane.

A = [tex]\frac{1}{2} |x_{1} y_{2} +x_{2} y_{3}+........x_{n-1}y_{n} +x_{n} y_{1} -x_{2} y_{1} -x_{3} y_{2} - ........-x_{n}y_{n-1}-x_{2}y_{n} |[/tex]

Shoelace formula (Green’s Theorem)

A = [tex]\frac{1}{2} |x_{1} y_{2} +x_{2} y_{3}+........x_{n-1}y_{n} +x_{n} y_{1} -x_{2} y_{1} -x_{3} y_{2} - ........-x_{n}y_{n-1}-x_{2}y_{n} |[/tex]

Where A is the area of the polygon and n is the number of sides of the polygon.

Here A = 6, n = 3, [tex]x_{1}[/tex] = 6, [tex]y_{1}[/tex] = 0, [tex]x_{2}[/tex] = 5, [tex]y_{2}[/tex] = 10, [tex]x_{3}[/tex] = [tex]x[/tex], [tex]y_{3}[/tex] = 20

A = 60 = [tex]\frac{1}{2} |(6.10)+(5.20)+(x.0)-(5.0)-(x.0)-(6.20)|[/tex]

60 = [tex]\frac{1}{2} |60+100-10x-120|[/tex]

60 = [tex]\frac{1}{2} |40-10x|[/tex]

60 = [tex]|20-5x|[/tex]

So 20 - 5x = -60

5x  = 80

x = 16

20 - 5x = 60

5x  = -40

x = -8

since x is a negative value,

we can know x = -8

Hence the value of x is -8.

Find out more information about green's theorem here

brainly.com/question/27549150

#SPJ2


Related Questions

HELP HELP HELP HELP HELPPPP.

Answers

Answer:

letter d

................

Answer:

I think the answer is D - 0.6

What is the measure of angle x?

Enter your answer in the box.

Answers

Answer:

x = 48º

Step-by-step explanation:

x = 90 -42

x = 48º

will give more p0ints if correct

Answers

Answer:

REVENGE

Step-by-step explanation:

Answer:

Answer is im not sure

Plz stop deleting my questions! This is a urgent!!plz help meee!,

Answers

Answer:

B

Step-by-step explanation:

Its really not hard. Just look at the chart. Find the 96 in the chart. What is it under? Flowers ordered. Which flower? Petunias. So its B. I'm sure you could have figured that out on your own. Not being rude, just telling you.

i need help pls!
this test is about angles, and i am having trouble with it.

Answers

Answer:

alternate exterior angles

The answer is the first one

if you are to measure the following figure for real,what tool(ruler or meter stick) and unit of measur(m, cm, in,) will you use..........
help me guys plsss​

Answers

1. Meter stick(m) 2. Ruler (in) 3. Meter stick (m)

Why is 5992 divisible by 6​

Answers

Answer:

Because its 9987 * 6

Step-by-step explanation:

Well, you could use simple math.

6:

1,6

2,3

I'm sorry if this is what you weren't looking for.

PLEASE HELP! (No links!)
What is the volume of the salt shaker??

Answers

Answer:

10

Step-by-step explanation:

How much shorter of a kiloliter is 498 Litre?​

Answers

Answer:

hi

Step-by-step explanation:

Answer:498000

Step-by-step explanation:

solve for x 9.2, 16.5, x

Answers

Answer:

152

Step-by-step explanation:

A bag contains 56 marbles: 7 red, green, 11 yellow, 17 brown, and 13 blue.
If a marble is chosen at random, what is the probability that the marble is green?

Answers

Answer:

8/56

Step-by-step explanation:

Add up all other marble colors then find the difference from the total.

Answer:

1/7

Step-by-step explanation:

there are 8 green marbles out of 56 so the probability would be 8/56 which simpliefies to 1/7 or 14.285714%

give your answer as a mixed number

will someone show me how
to work out questions like this in the pictures step but step​

Answers

Answer:

The value of given expression is 13 / 3

Step-by-step explanation:

Given expression in the form of improper fraction;

17/3 - [tex]1\frac{1}{3}[/tex]

Find;

The value of given expression

Computation:

⇒ 17/3 - [tex]1\frac{1}{3}[/tex]

Step 1 ;

Change mixed fraction into simple fraction

⇒ 17/3 - 4/3

Step 2 ;

By taking LCM of denominators;

⇒ [17 - 4] / 3

Step 3 ;

Subtract 17 from 3

⇒ [13] / 3

The value of given expression is 13 / 3

Carlos va a comprar un televisor que tiene un costo de c doláres. El impuesto gubernamental
de valor añadido es del 16%. ¿Cuál es la ecuación que MEJOR modela el pago total en
dólares, p, que hará Carlos en está en esta compra? *

Answers

Answer:

b

Step-by-step explanation:

There are 67 rabbits in the garden. Round 67 to the nearest 10.

Answers

Answer:

70

Step-by-step explanation:

1-4 rounds down

5-9 rounds up

70

hope this helps!!!

How many million bacteria were in the dish at 10 a.m.?​

Answers

Answer:

Fraction form: 1/4

Exponential form: 2^-2

Expanded form: 1/4 (Not sure if thats correct)

Step-by-step explanation:

Answer:

Its 1/4 he was right

Step-by-step explanation:

Write a sine function that has an amplitude of 5, a midline of 2 and a period of 8pi/5.

Answers

Answer:

f(x) = 5*sin( (5/4)*x) + 2

Step-by-step explanation:

A general sine function can be written as:

f(x) = A*sin(w*x) + M

Where:

A is the amplitude

w is the frequency of the function

M is the midline

Here we know that we want to have:

An amplitude of 5. Then, A  = 5

A midline of 2, then M = 2

And a period of (8/5)*pi

For now, we can write our function as:

f(x) = 5*sin(w*x) + 2

Now, we know that for a function of period T, is always true that:

f(x) = f(x + T)

here, the period is T = (8/5)*pi

knowing that sin(0) = sin(2*pi)

Then we must have:

sin(0) = sin(w*0) = sin(w*( 0 +  (8/5)*pi)) = sin(2*pi)

Then the arguments of the third and fourt parts must be the same, thus:

w*(8/5)*pi = 2*pi

We can solve this for w now:

w*(8/5) = 2

w = 2*(5/8) = (5/4)

Then the function is:

f(x) = 5*sin( (5/4)*x) + 2

In a plane, line b is parallel to line f, line f is parallel to line g, and line h is perpendicular to line b. Which of the following cannot be true?

Answers

Answer: f is Parralel to g

Step-by-step explanation:

Answer:

You gave us no choices

Step-by-step explanation:

h is not parallel f

Suppose you invest $200 at a 7% annual rate for one year. How much interest would you earn?

Answers

Use a percentage calculator and an interest rate calculator to help you solve this

24 mi
32 mi
c


What is the length of the hypotenuse?

c =
miles

Answers

Answer:

40 mi

Step-by-step explanation:

a² + b² = c²

24² + 32² = c²

1600 = c²

√1600 = c

c = 40

The answer is 40 miles

Help me please this is very hard i got 8ft but it said I was wrong!?

Answers

Answer:

is the answer 200/3 Or 66.667 ft

One pipe fills an empty tank in 3 hours. A second pipe fills the same tank in 6 hours. A third pipe can empty the full tank in 5 hours. If all three valves were left open, how long would it take to fill the empty tank?

Answers

6 would be your answer

The value of a car is decreasing by 12​% per year. If the car is worth ​$11,000 ​today, what will it be worth in two​ years?

Answers

Answer:

$8518.40

Step-by-step explanation:

FV = PV(1+r)^n

FV = future value

PV = present value

r = rate

n = # of years

Value in 2 yrs = 11,000 x (1 - 0.12)^2 = 8518.4

Order from greatest to least: 12, -4,8, -3, 0.

Answers

Answer:

-4,-3,0,8,12 its backwards my bad

Step-by-step explanation:

because it is

Answer:

12, 8, 0, -3, -4

hope it helps

HELP. LIKE- WHICH ONE IS THE ANSWER? ALSO EXPLAIN A BIT

Answers

Answer:

perpendicular lines are when two lines intercect in a right angle. so it would be A then

Step-by-step explanation:

A has a right degree angle where the two lines cross, so this is the answer

B that is not a right angle it has acute and obtuse angles

C does not even have two lines that touch

D the two lines don't cross at all

E is an acute angle

B, C,D, and E are not the answers

In ΔMNO, the measure of ∠O=90°, OM = 69 feet, and NO = 16 feet. Find the measure of ∠N to the nearest tenth of a degree.

Answers

9514 1404 393

Answer:

  76.9°

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(N) = OM/ON

  N = arctan(OM/ON) = arctan(69/16)

  N ≈ 76.9°

solve for x if 2(1+3x) =3​

Answers

Answer:

x is 5

Step-by-step explanation:

Given the following regression output, what is the expected value for the change in daily circulation (the dependent variable) if a newspaper had 35 winners and finalists between 2004 and 2014 and 14 winners and finalists between 1990 and 2003?
Model parameters (Change in Daily Circulation, 2004-2013):
Source Value Standard error t Pr > |t| Lower Upper
bound (95%) bound (95%)
Intercept -0.328 0.042 -7.890 <0.0001 -0.412 -0.244
Pulitzer Prize
Winners and
Finalists,
1990-2003 -0.015 0.008 -1.873 0.067 -0.030 0.001
Pulitzer Prize
Winners and
Finalists,
2004-2014 0.024 0.008 2.837 0.007 0.007 0.040
Pulitzer Prize
Winners and
Finalists,
1990-2014 0.000 0.000

Answers

Answer:

0.512 ; - 0.538

Step-by-step explanation:

Using the standard linear regression relation :

y = bx + c

b slope ; c = intercept ; y = dependent ; x = independent variable.

For finalist between 2004 - 2014 ;

y = 0.024x - 0.328

x = 35

y = 0.024(35) - 0.328

y = 0.512

For finalist between 1990 - 2014 ; with 14 winners ; change in daily circulation :

y = -0.015x - 0.328

x = 14.

y = -0.015(14) - 0.328

y = - 0.538

A rectangular yard has dimensions 10 meters by 8 meters. In the middle of the yard is a rectangular pond of 8 square meters, leaving a uniform walkway around the pond. Write a quadratic equation in standard form to find the width of the walkway.

Answers

hahahaha i had this same question in my grade

For every 1000 videos a channel gets it makes £2.50 from ad revenue. How many videos will the channel need to make £1

Answers

Answer: 400 videos

Step-by-step explanation:

1000/1 x 1/2.5 = 400

50 points! Can you please be honest and answer these 3 questions.

Answers

Answer:

1. 5/10

2. 0.54

3. √3 and -1/16????

I think

sorry if I wrong

Other Questions
How many solutions are there to this system of equations? On a coordinate plane, 2 lines have equations y = one-fourth (x minus 4) and y = one-fourth x minus 1.a. one solutionb. no solutionc. infinitely many solutions d. it cannot be determined without solving (1) After our trip, the skyscraper visit was unanimously voted as our favorite. (2) The museum was supposed to be the highlight of the trip. (3) But those works of art were completed a long time ago. (4) At the skyscraper, we watched them in action building their masterpiece.Which sentence in the paragraph is in the active voice?Sentence 1Sentence 2Sentence 3Sentence 4 La chica _______________(estar) en el museo todos los das. When Natalie commutes to work, the amount of time it takes her to arrive is normallydistributed with a mean of 25 minutes and a standard deviation of 4 minutes. Usingthe empirical rule, what percentage of her commutes will be between 17 and 33minutes? i'm in desperate need of help !! if you are good with government issues pleeeeease help. (i will report if i get links or random answers)list the 3 levels of government Can someone please help me with math. Please help this is due today! 5-11-2021Observe the chemical reaction below, and identify if the equation is balanced or not. If it is not balanced, then what coefficient should you place for the reactants and products? Justify with scientific reasoning. Mg + O2---------> MgOMake sure to include the following details in your answer in complete sentences:- Is the chemical reaction balanced?- Is it following the law of conservation of mass, why is not following?- What can you do to make sure that the equation becomes balanced and follow the law? A solution with a pH of 5.30 has a H+ concentration of since im too lazy to do this order the points from least to greatest here are the stuff roo put in least to greatest -1/2-1.1250.3751/2-7/8 first come first served brainiest *easy* (10x^2+9)+(8x^2 5x+7) How to lower blood pressure? Tell answers down bdlow. the slope of the line joining points (3 ;2) and (0;a) is-1 determine the value of a During the 1986 World Cup, Argentina and England couldbest be described asAPolitical rivalsBWartime alliesCHost nationsDTeammates Passage AOne way to enjoy a healthier lifestyle is to grow your own vegetables. That way, you know they are free from harmful chemicals. Where do you start if you want to grow your own healthy food? Start with the soil.If this is your first adventure in gardening, start small. Choose plants that are easy to tend and that will grow well in the soil you have. Deciding what to grow is the first step and it will help decide how big of a garden you want. Not all plants grow in the same way. You have to consider which plants prefer sunlight and which prefer shade. This will help with picking the best spot for your garden.Once you have decided where you will plant your garden, you can move on to planning your garden's layout. You don't want your tall plants growing next to the shorter ones and blocking out the sun. You also want to make sure there is enough room between the rows to allow for weeding. Proper planning makes planting a breeze.Passage BIt is more expensive to build a green roof than it is to lay asphalt or shingles on a roof, but the trend is growing. The basic green roof requires a frame, waterproof membrane, gravel for drainage, fibrous material to retain moisture, soil for planting, and a barrier that prevents roots from penetrating the building.Green roofs started in Europe and are now gaining a strong foothold in the United States. The largest green roof in New York City is built on the roof of a processing and distribution facility. It is actually the biggest green roof in the country. Being in New York, it has faced snow, rain, freezing, and thawing. It has survived it all.The city of Chicago, Illinois, now has more green roofs than any other U.S. city. There are 7 million square feet of green roofs planted across the city. Toronto, Canada, is the first city in the western hemisphere to mandate green roofs on all new tall buildings. Green roofs are beneficial, not only to the environment, but also to the cities that build them. A recent study in Toronto suggested that if 75 percent of the flat roofs were greened, the city could save $37 million a year on storm water management and energy bills.Explain why people are building green roofs to live healthier lives. Use information from both texts in your answer. How was the Cold War a conflict of political ideas? Which of the following words is an interjection? Diamond Flat Phew Tree Solve the following system of equations using the elimination method.5x + y = 9 what is the function of myonemes in the euglena You roll a 6-sided number cube with faces numbered 1-6. What is (P)5?