Mathematics High School

John was visiting four cities that form a rectangle on a coordinate grid at A(0, 4), B(4, 2), C(1, -4) and D(-3, -2). What is the area of the space that cities enclose? Round your answer to the nearest whole number. Do not include units in your answer.

Answers

Answer 1

Answer:

[tex]Area = 30[/tex]

Step-by-step explanation:

Given

Rectangle coordinates

[tex]A = (0,4)[/tex]

[tex]B = (4,2)[/tex]

[tex]C = (1,-4)[/tex]

[tex]D =(-3,-2)[/tex]

Required

The area of the rectangle

The area is calculated as:

[tex]Area = Length* Width[/tex]

The length of the rectangle will be represented as:

[tex]Length = AB = CD[/tex]

And the width is:

[tex]Width = BC = AD[/tex]

Calculate distance AB using:

[tex]AB = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }[/tex]

Where:

[tex]A = (0,4)[/tex] --- [tex](x_1,y_1)[/tex]

[tex]B = (4,2)[/tex] [tex]--- (x_2,y_2)[/tex]

[tex]AB = \sqrt{(0 - 4)^2 +(4 - 2)^2 }[/tex]

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

[tex]AB = \sqrt{16 +4 }[/tex]

[tex]AB = \sqrt{20}[/tex]

Calculate distance BC using:

[tex]BC = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }[/tex]

[tex]C = (1,-4)[/tex] [tex]---(x_1,y_1)[/tex]

[tex]B = (4,2)[/tex] [tex]--- (x_2,y_2)[/tex]

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

[tex]BC = \sqrt{(- 3)^2 +(-6)^2 }[/tex]

[tex]BC = \sqrt{9 +36}[/tex]

[tex]BC = \sqrt{45}[/tex]

So, the area is:

[tex]Area = Length * Width[/tex]

[tex]Area = AB * BC[/tex]

[tex]Area = \sqrt{20} * \sqrt{45}[/tex]

[tex]Area = \sqrt{20 * 45}[/tex]

[tex]Area = \sqrt{900[/tex]

[tex]Area = 30[/tex]

Related Questions

Three functions are shown below.
3
A: g(x) = -5x+4
B: f(x) = (x + 2)(x+6)
hix)
C:
Which statement is true?
1) B and C have the same zeros.
2) A and B have the same y-intercept.
16.
3) B has a minimum and C has a maximum.
4) Chas a maximum and A has a minimum.

Answers

Thanks, I help you get correct

NEED HELP ASAP!The maker of a cell phone screen protector would like to estimate the proportion of customers who file a warranty claim. To do so, they select a random sample of 200 customers and determine that the 96% confidence interval for the true proportion of customers who file a warranty claim to be 0.15 to 0.28. Which of the following can be accounted for by the margin of error of this interval?

response bias
nonresponse bias
sampling variation
undercoverage bias

Answers

Answer: sampling variation

Step-by-step explanation: took the quiz

The margin of error is given by the sampling variation of the proportion of customers

What is simple random sampling ( SRS )?

The most accurate type of probability sampling is random sampling. Each person in a population has an equal probability of getting selected for the sample thanks to this method of sampling.

This kind of sampling is perfect for highly controlled investigations where it is unacceptable to have human bias in the selection of the sample.

Each sampling unit in a population has an equal probability of being included in the sample when using simple random sampling (SRS). As a result, each potential sample has an equal probability of being chosen.

Given data ,

Let the margin of error be represented as A

where the value of A is

The confident interval is = 96 %

And , the value of sample is of 200 customers

where the warranty claims from 0.15 to 0.28

So , the cell phone screen protector maker can be 96% confident that the interval from 0.15 to 0.28 captures true proportion of customers who file a warranty claim

Therefore , it is a sampling variation

Hence , the situation is a sample variation

To learn more about simple random sampling click :

https://brainly.com/question/30759604

#SPJ7

Find the surface area of this rectangular prism .

thanks!!!!!!! ​

Answers

Answer

Step-by-step explanation:

Answer:

solution given;

length [l]=9cm

breadth [b]=7cm

height[h]=3cm

we have

the surface area of this rectangular prism =2[lb×bh×lh]=2[9×7+7×3+9×3]=222cm²

is your answer

Hey can you help me fast!!

Answers

Answer: 12

Step-by-step explanation:

2.93/.25=11.72 round up to 12

19 1/2 is 3/4 of what number?

Answers

Answer:

19.5 = 0.75x

x = 26

I hope this finds you well and have a great day.

3.5333 (repeated 3)as a fraction

Answers

Answer:

3  3/5

Step-by-step explanation:

Answer:

3 5333/10,000

Step-by-step explanation:

Find the angle measures

Answers

Answer:

m<1 = 140º

m<2 = 40º

Step-by-step explanation:

5x + x + 12 = 180

6x + 12 = 180

6x = 180 - 12

6x = 168

x = 28

<1 = 28 x 5 = 140º

<2 = 28 + 12 = 40º

Hope that helps! :)

-Aphrodite

Need a clear answer ASAP please
If $1205 is borrowed for 11 years at an annual simple insterest rate of 11.3%, what is the total amount that must be repaid rounded to the nearest cent?

Answers

Answer:

If the interest is yearly $2702.87 will be owed

Step-by-step explanation:

first you would need to find out how much 11.3% of $1205 is which is $136.17. And since the interest is yearly you would multiply the $136.17 by the 11 years which would be $1497.87. Then you would add the amount that they borrowed to the interest that they would owe after 11 years which would be $1497.87 + $1205 = $2702.87. So after 11 years the total amount that must be repaid is $2702.87

help please//////////////

Answers

20 x 11.4 x 3.5=

use a calculator to multiply

this dot plot is not symmetric the data has two extreme values
what is the best measure of center for this dot plot

Answers

Answer: I believe your answer is the median.

Step-by-step explanation:

Answer:

C: median

hope this helps

HELP ME ILL GIVE BRANLIEST IF UR RIGHT!!!

Answers

Answer: 62

hope this helps :)

given m||n,find the value of x ​

Answers

Answer:

8x+5 + 2x+5 = 180

10x+10=180

10x =170 = x = 17

Step-by-step explanation:

Answer:

answer: x = 17 Hope this helps!

2 x 17 + 5 = 39 8 x 17 + 5 = 141

Straight angles are 180 degrees

39 + 141 = 180

So x = 17

Megan has $45.12 in her purse. She spends $7.89 for lunch and $21.25 for a pair of sunglasses.
Which is the best estimate for the amount of money Megan has left?

Answers

Answer:

Hello Love!

A good estimate would be 15 or 16 dollars left

Hope this helps!

Answer:

$15.98

Step-by-step explanation:

45.12-7.89=37.23

37.23-21.25=15.98

A man drove his car a distance of 315 miles in 5 hours. If continuing at this rate is possible, he will travel ____ miles in 9 hours.

Numerical Answers Expected!

Answer for Blank 1:

Answers

Answer:

567 miles

Step-by-step explanation:

we break down how many miles he went in 1 hour

315/5

he went 63 miles in 1 hour

times this by 9 is 567 miles in 9 hours

Answer:

567 milesStep-by-step:we break down how many miles he went in 1 hour 315/5 he went 63 miles in 1 hour times this by 9 is 567 miles in 9 hours

Step-by-step explanation:

The dot plot shows the heights of the players on two basketball teams.

Which statement is best supported by these data?

Answers

The dot plot is wrong as I am right

If the triangle is reflected over the y axis what coordinate pair would be contained within the triangle

Answers

Answer:

(-4,-4)

Step-by-step explanation:

The reflected triangle will be in the third quadrant. Option 2 is in the first quadrant, option 3 is in the first quadrant as well, and option 4 is in the second quadrant. That leaves option 1, which you can see is in the third quadrant. Option 1, (-4,-4), is the only plausible solution.

Important!!!!!!!
Can someone please help me with this question.
The answer choices are in the picture right along with the question.
I will mark the first person brainliest if they answer with an actual answer not a link.

Answers

Answer:

C has the lease value of 1/3

Step-by-step explanation:

A:  (2³)² ÷ 2^5 = 2

B:  4^0 = 1

C:  3^(4-5) = 3^-1 = 1/3

D: 5^0 = 1

PLEASE HELP ME ANSWER THIS:(

Answers

#1 is A

I hope this helps I don’t know the other ones

Answer:

#1y = x² - 8x - 20 y = (x - 10)(x + 2), zero's are (10, 0) and (- 2, 0)

Vertex is:

x = -8/-2 = 4, y = 4² - 8*4 - 20 = -36

Correct choice is A

#2x² + 1/3x = 4x² + 2*x*(1/6) + (1/6)² = 4 + 1/36(x + 1/6)² = 4 1/36

Correct choice is A

#3(-√-1) = -ii² = -1 ⇒ i²ⁿ = -1i²ⁿ⁺¹ = -i

Correct choice A or B

The correlation coefficient between two quantitative variables is approximately 0.02. What does the value of this correlation coefficient indicate about how well the model
fits the data?
O A. The correlation coefficient is not within the correct range.
O B. The model is a good fit.
OC. No conclusion can be drawn regarding how well the model fits the data.
The model is not a good fit.

Answers

Answer:

The model is not a good fit

Step-by-step explanation:

The correlation Coefficient is a metric used to evaluate the strength of the relationship between 2 variables, the correlation Coefficient ranges from - 1 to + 1 with values closer to either ±1 depicting the strongwr and better relationship. A value of 0 means no relationship exists and values close to zero means the relationship is weak. Wutb a correlation Coefficient value of 0.02, this value is very close to 0 and hence shows that the relationahip is extremely weak. Hence, the model is not a good fit.

How do you find the percentage of 70.9 of 100​

Answers

70.9/100=0.709=70.9%

Refer to the prism at the right. If all the
dimensions of the prism doubled, would the volume double? Explain your
reasoning


Pls help this is due tomorrow

Answers

if you were to double the dimensions of the prism, you create a similar prism with a scale factor of 2. The surface area of the similar prism will increase, as well as doubling the volume :) hope this helps!!

-7 2/3 + (-5 1/2) + 8 3/4 = ??

Answers

Answer: -4 5/12
Add the negatives first. Then add the positive number to find your answer.
-4 5/12
You use GEMDAS to solve equations like this. :D

pls help thanks!! lol

Answers

i agree with the other person, scr.ew school!
The second one is 2/3 I think! The first one... my best guess is 4 but I’m not sure. Hopefully this helps

The number of boys and girls in a class are in the ratio 5:4. If the
number of boys is 9 more than the number of girls, then number of
boys is 9

Answers

Answer:

no.of boys is 45

Step-by-step explanation:

here, let the number of boys and girls be 5x and4x

ATQ,

5x=4x+9

or,5x-4x=9

or,x=9

then, the number of boys is 9×5=45

and the number of girls is 9×4=36..

The 4th ans pls anyone?

Answers

Answer:

associative property of multiplication

Step-by-step explanation:

I hope this helps you :)

Please help me with this
Thanks

Answers

So you make them the same common denominator
As you see, 2/10 = 8/40
2/4 = x/40, multiply by 10
2/4 = 20/40
Then add because same denominator
Now you would get:
8/40 + 20/40 = 28/40

Answer:

8/40 + 20/40 = 28/40

Step-by-step explanation:

It's about finding the common denominator for the fractions.

we can easily see that 40 is a common denominator for denominators 10 and 4. 20 would work too, but 40 is "instantly seen".

2/10 = (2*4) / (10*4) = 8/40

2/4 = (2*10) / (4*10) = 20/40

8/40 + 20/40 = (8+20) / 40 = 28/40

SOMEONE PLEASEEEE HELPPPP????!!!!

Answers

Answer:

x = 15

y = 25

Step-by-step explanation:

WV = NP

WX = NM

VX = PM

VX/PM = WV/NP

8/20 = 6/x

8x = 120

x = 15

WV/NP = WX/NM

6/15 = 10/y

6y = 150

y = 25

Mr. Smith wants to buy some new shirts to wear at work. He hears that button down shirts are 30% off at the mall. He paid $27 to buy 1 button down shirt. What was the original price of the shirt?

Answers

Answer:

Answer:

$90

Step-by-step explanation:

27/.3

Can u solve this puzzle?

Answers

Answer:

i dont think so sorry

(x+2)·2x + (x-1)^2= 2 ?

Answers

Answer:

x = 1/3, x = -1.

Step-by-step explanation:

2x(x + 2) + (x - 1)² = 2

Distribute the 2x into x + 2.

2x² + 4x + (x - 1)² = 2

Square (x - 1).

2x² + 4x + x² - x - x + 1 = 2

Combine terms.

2x² + x² + 4x - 2x + 1 = 2

Combine terms again.

3x² + 2x + 1 = 2

Subtract 2 from both sides.

3x² + 2x - 1 = 0

Factor.

(3x - 1)(x + 1) = 0.

Finding the x-values here is the same thing as finding the 0s, so set both of the expressions to 0.

3x - 1 = 0

Add 1 to both sides.

3x = 1

Divide by 3.

x = 1/3.

x + 1 = 0

Subtract 1 from both sides.

x = -1.

Answer:

3x^2+2x+1 primero lo multiplicas y lo que te de lo sumas y asi sacas 3x^2+2x+1

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