In a grid of an auditorium, the vertices of a section of seats are A(40, 20) , B(80, 20) , C(100, 70) , and D(40, 70) . The coordinates are measured in feet. Find the area of the section.

Answers

Answer 1

Answer:

[tex]Area = 2900[/tex]

Step-by-step explanation:

Given

[tex]A (x_1,y_1) = (40,20)[/tex]

[tex]B (x_2,y_2) = (80,20)[/tex]

[tex]C (x_3,y_3) = (100,70)[/tex]

[tex]D (x_4,y_4) = (40,70)[/tex]

Required

Determine the Area

The area of the section is:

[tex]Area = \frac{1}{2}|(x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1) - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1)|[/tex]

Substitute values for the x's and y's

[tex]Area = \frac{1}{2}|(40 * 20 + 80*70 + 100*70 + 40*40) - (20*80 + 20*100 + 70*40 + 70*40)|[/tex]

[tex]Area = \frac{1}{2}|15000 - 9200|[/tex]

[tex]Area = \frac{1}{2}|5800|[/tex]

[tex]Area = \frac{1}{2} * 5800[/tex]

[tex]Area = 2900[/tex]

Hence, the area of the section is 2900ft^2


Related Questions

A salesperson makes a 35% commission and makes a sale for $425. Determine the commission the salesperson will make.​

Answers

$425-35%= $276.25
hope this helped

What is the surface area of a cylinder with a radius of 12 centimeters and a height of 7 centimeters? Use terms of pi.

I’ll give brainliest to whoever answers 1st! :)

Answers

Answer:

1432.57cm²

Step-by-step explanation:

3h+5 when h =4 23 points

Answers

Answer:

3*4= 12 12+5=17

Step-by-step explanation:

hav a great day :P

Answer:

17

Step-by-step explanation:

3h + 5    h=4

plug in 4 for h

3(4) + 5

12 + 5

17

Hope this Helps!!!

Sophia scored 33 points in a basketball game. She scored four
more two-point baskets than three-point baskets.
Write a system of equations in standard form that models this
situation.
How many three-point baskets did Sophia make?

Answers

Answer:

Let's try to set up some equations. We'll say a is the number of 1-point shots, b the number of 2-point shots, and c the number of 3-point shots.

A basketball player scored 33 points in one game.

So a + 2b + 3c = 33

He scored four more 2-point baskets than he did 3-point baskets.

So b = c + 4

The number of free-throws equaled the sum of the number of 2-point and 3-point shots made.

So a = b + c

and since b = c + 4,

a = (c + 4) + c = 2c + 4

Substituting in a + 2b + 3c = 33,

(2c + 4) + 2 * (c + 4) + 3c = 33

which simplifies to

7c + 12 = 33

So c = 3, b = 7, a = 10

Answer:

The system of equations in standard form that models this situation are:

2x+3y=33

x-y=4

OMG WILL SOMEONE PLEASE HELP I NEED THIS!!!!!!!!!!! I WILL GIVE A LOAD OF POINTS!!! The price for X pounds of almonds at the Snack Shack is represented by y = 6.5x. Which store sell almonds at a lower unit rate cost? How much lower?

Answers

c

Step-by-step explanation:

because th x value of 9 will determine rhe shape of s

A pair of basketball shoes's normal price is $120. Jordan bought it at a discount of 10%. He had to pay 8% tax on the discounted price. If jordan put 15% of the final cost (including tax) as a down payment, how much money did he have to pay for the down payment?

Answers

Answer:

$17.50

Step-by-step explanation:

If the shoes are discounted at 10%, the price would be 90% of the original price

Discounted price = 0.9 x 120 = 108

Tax increases the price of the good. so, the discounted price would increase by 8%

1.08 x 108 =116.64

If Jordan pays 15% as a down payment, he would pay :

0.15 x 116.64 = 17.496

A truck is carrying cranberry juice, grape juice, and pineapple juice bottles in a ratio of
7 : 2 : 3. If there are 40 grape juice bottles, then how many juice bottles in total are there?

Answers

Answer:

140

Step-by-step explanation:

7- Cranberry

2:Grape = 40 so 40/2 = 1

3:Pineapple

1= 20 juices

7+2+3 is 12

20 x 12 is 140

40/2=a factor of 20

7+2+3=12, so multiply that by a factor of 20.

20*12=240 total juice bottles is the answer

What is the circumference of a circle with a diameter of 3 feet? Use 3.14 for
TT

Pls help

Answers

918155555332feet +3.14

Answer:

9.42

Step-by-step explanation:

1. Jacob has $500 saved. He receives a gift of $100 as a graduation present.
Write an expression for the total amount of money he has.

Answers

Jacob now has 600 dollars.

What is the slope of the line that passes through the points (-3, 4) and (5, -2)?

Answers

Answer:

  m = 0 , this is a horizontal line, y = 5

Step-by-step explanation:

Find the slope of the line that passes through the pair of points

(-3,5),

(-4,5)   m = 0/1 = 0  

m=y2-y1/x2-x1

 m = 0 , this is a horizontal line, y = 5

Hopefully that helps!!!!!

A spinner with the numbers 1 through 8 is spun 25 times. What is the experimental probability of the spinner stopping on the number 4?

Answers

Answer: Because if you think about it it would be 4 because of the fact that it is in the middle of 1-8. So there is a higher chance to land on 4 than any other number.

Step-by-step explanation:

The experimental probability of the spinner stopping on the number 4 is 1/25.

What is experimental probability?

Experimental probability is a probability that is determined on the basis of a series of experiments.

A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial.

Given that, a spinner with the numbers 1 through 8 is spun 25 times.

we need to find the experimental probability of the spinner stopping on the number 4

So,

Experimental Probability =

P(E) = Number of times an event occurs / Total number of trials.

Number of times an event occurs = 1

Total number of trials = 25

Therefore,

P(E) = 1/25

Hence, the  experimental probability of the spinner stopping on the number 4 is 1/25.

Learn more about experimental probability click;

https://brainly.com/question/30694293

#SPJ3

7 more than a number w is -2

Answers

Answer:

w+7=-2

Step-by-step explanation:

If f(x) = -x + 5 and g(x) = x^2, what is (g° (-1)?

Answers

Answer:

[tex](g\circ f)(-1)=36[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]f(x)=-x+5\text{ and } g(x)=x^2[/tex]

And we want to find:

[tex](g\circ f)(-1)[/tex]

This is equivalent to:

[tex]=g(f(-1))[/tex]

So, evaluating f(-1) first, we acquire:

[tex]f(-1)=-(-1)+5=6[/tex]

Then by substitution:

[tex]=g(6)[/tex]

So:

[tex]=(6)^2=36[/tex]

Therefore:

[tex](g\circ f)(-1)=36[/tex]

Your answer is indeed correct.

Answer:

please refer to the above attachment.

36 is the right answer.

DUE IN 5 MINUTES MATH QUESTION ​

Answers

Answer:

x= -10

Step-by-step explanation:

So because the angle 55 is part of the same line as one of the unknown angles you can do 180-55 to find that first angle at the top, which is 125.

Next add all three angles (125 + x + 35 + x + 40)=180

Combine the x values to get 2x and subtract the three values from 180

Then 2x= -20, x should be equal to -10

You can plug x back into the values and check your work by adding all the values again, making it all equal to 180 degrees again

Determine the domain of the following graph:

Answers

Answer:

Domain: (-7, 4]

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Step-by-step explanation:

According to the graph, the line's x-values span from -7 to 4. Since -7 is open dot, it is exclusive from the domain; since 4 is closed dot, it is inclusive in the domain:

Interval Notation: (-7, 4]

Inequality Notation: -7 < x ≤ 4

How many groups of 1/4 are in 3?”

Answers

Answer: 12

Step-by-step explanation:

there are 12 because

1/4 = 0.25
2/4 = 0.50
3/4 = 0.75
4/4 = 1.00

If you do this three times, It will have an end result of twelve

hope this helps!!

how do you solve this using the substitution method?

Answers

Answer:

x=13, y=36

Step-by-step explanation:

y−2x=10

6x−2y=6  −2x+y=10

6x−2y=6

6x=2y+6

x=  1/6(2y+6)

x=1/3y+1

-2(1/3y+1)+y=10

-2/3y-2+y=10

1/3y=12

y=36

Substitute y  to check your answer

x=1/3*36+1

x=12+1

x=13

And to go further if you wish to check your answer you can substitute x

PLEASE HELP MEE I NEED TO TURN THIS IN SOON

Answers

Answer:

7x=7

Step-by-step explanation:

Solve using quadratic formula.
[tex]4 {s}^{2} + 8s + 4 = 0[/tex]

Answers

s = - 1
Hope this help!

A 4-pound bag of carrots costs $2.48. What is the unit price? *

Answers

Answer:

0.62 cents per pound

Step-by-step explanation:

2.48/4

to find price per pound which is the unit price

2.48/4=0.62

brainliest appreciated

Juan made $115 for 5 hours of work how many hours would he have to work to make $414

Answers

Answer:

He would need to work for 18 hours.

Step-by-step explanation:

115÷5=23 (dollars)

414÷23=18 (hours)

Answer:

18 hours because Juan makes $23 an hours and if you divide the $414 by 23 you get 18 so he needs to work 18 hours to get $414

Step-by-step explanation:

The value of n is a distance of 1.5 units from -2 on a number line. Click on the number line to show the possible values of n. -5 - 4 -3 -2 -1 0 1 2 3 4 5​

Answers

Answer:

Its Going to be -4

Step-by-step explanation:

PLEASE HELP ME!!! I need the answer quick please if you can!

Answers

Answer:

angle 1 is 145°

Step-by-step explanation:

this is because à horizontal line is always 180° so you jus have to subtract 35 from 180

4. An annual pass covering emtrance fees to more than
2,000 national parks costs $80. If the total income from
the annual passes is $12,800 in one month, which equation
can you use to find the number of passes purchased that month?
F. 12,800p = 80
H. 80p = 12,800
G. 12,800 – p = 80
J. 80 + p = 12,800

Answers

Answer:

Search it up

Step-by-step explanation:

Someone already answered it on brainly

The initial amount of bacteria in a culture is 12,000. The culture grows at a rate of 45% each day. Write an exponential function to model the population of y bacteria after x days. How many bacteria are there after 6 days?

Answers

Answer:

FV= 111,529.37 = 111,529

Step-by-step explanation:

Giving the following information:

Initial amount (PV)= 12,000

Growth rate (g)= 45% = 0.45

First, we will establish the future value formula:

FV= PV*(1+g)^n

FV= future value

n= number of days

FV= 12,000*(1.45^n)

For 6 days:

FV= 12,000*(1.45^6)

FV= 111,529.37

if I buy 54 packs of cookies and 15 cookies are in each pack how many cookies do I have all together?!!?!?!

Answers

Answer:

810

Step-by-step explanation:

54x15=810.

hope this helps

Step-by-step explanation:

54 x 15 = 810

all you have to multiply

Please help me! Please and thank you!

Answers

Answer:

4m+0.50

Step-by-step explanation:

i realllllllllllllllllllllly neeeeeeddddd help on this one pleaseeeeeeeeeeeeeeeeeeeeee
Carlos traveled at an average speed of 70 miles per hour for 2.5 hours and then traveled at an average speed of 80 miles per hour for 3.5 hours. What was the total distance in miles that Carlos traveled during that time

Answers

Answer:

70 * 2.5 = 175

80 * 3.5 = 280

175 + 280 = 455 miles all together

Step-by-step explanation:

I hope this helps :)


What is the domain of h?h(x)=4/x-5

Answers

Answer:

(−∞, 5) ∪ (5, ∞)

Step-by-step explanation:

I really hope it helps!

Good Luck!

MARKING BRAINLIEST!!!!

Answers

Answer:

12

Step-by-step explanation

Other Questions
Monty bought a small swimming pool, as shown below, for his Labradorpuppy. He fills the pool halfway to the top. If one cubic foot of water isapproximately 7.5 gallons of water, about how many gallons of water willbe in the pool?6 ft2 ft Which of the following is an example of physical weathering? Frost wedging Acid rain Oxidation Carbonic acid PLEASE HELP ASApSophia has a shelf that is 51 over 2 inches wide. How many notebooks can Sophia arrange on the shelf if each notebook is 3 over 2 inches thick? 38, because the number of notebooks is 51 over 2 3 over 2 153, because the number of notebooks is 51 over 2 3 over 2 102, because the number of notebooks is 51 over 2 3 over 2 17, because the number of notebooks is 51 over 2 3 over 2 Can some one give me 3 breakfast options 3 lunch options 3 dinner options And what comes in the meal? Which of the following changes in a dilation? (Help fast please)A. shapeB. slopeC. sizeD. angle measures Why people prefer buses What lesson or lessons were contained in Nokomis story? how many calories in the average fast food meal CIAA has been established as a constitutional organ to check corruption in Nepal. Illustrate the roles played by it to control corruption in Nepal. Solve number 8 (geometry) Find the value of the expression whenx=1, y=-1,z =0a)5y y b) 3x +2y + 3z c) 2y -3xyz Which best describes the relationship between digestion and cellular respiration? O A. Digestion breaks foods down to simple sugar molecules, and respiration uses the sugar molecules to produce energy. O B. Digestion creates nutrients from food particles, and respiration uses the nutrients to produce energy. O C. Digestion releases oxygen molecules from food, and respiration uses oxygen molecules to produce energy. D. Digestion produces waste materials, and respiration uses the waste materials to produce energy. which of the following drinks should you NOT order if you are outside in the sun and need something cold and refreshing?una cola un the heladoun caf con lecheuna limonada the regular price of a bicycle is $120.the bicycle is on sale for 20% off.which expression is equal to the sale price,in dollars,of the bicycle A computer normally costs$650, but it is on sale for15% off. What is the saleprice of the computer? Pierce Which of the following statements is therefore necessarily true for Pierce? has a concave utility of wealth function, u(x). Pierce prefers prospect X to prospect Y. a. CE(X) > CE(Y). b. U(EV(X)) > U(EV(Y)) c. EU(X) < EU(Y) d. Y is a mean preserving spread of X. Please help me. I might die it was due a week ago Does (2, 3) make the equation y = x true? Which statement best explains what happened during the collision ? Which answer choice shows an inequality that represents the problem below? Marcus needs more than 550 tickets to get the prize he wants at the arcade. He already has 125 tickets and can earn 24 tickets each time he plays an arcade game. How many games will he have to play in order to have enough tickets to win the prize he wants? 24x + 125 > 550 24x + 125 >_ 550 24x + 125 < 550 125x + 24 > 550