show that the points (1 ,7) ,(4, 2), (-1, -1) and (-4, 4) taken in order are the vertics of a square. Also find its area

Answers

Answer 1

Answer:

Step-by-step explanation:

A (1 ,7) ,   B(4, 2),  C(-1, -1) and D(-4, 4)

Find the distance of sides using distance formula.

Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

A (1 ,7) ,   B(4, 2)

[tex]AB = \sqrt{(4-1)^{2}+(2-7)^{2}}\\\\ =\sqrt{3^{2}+(-5)^{2}}\\\\ \\ = \sqrt{9+25}=\sqrt{34} units\\\\\\\\BC = \sqrt{(-1-4)^{2}+(-1-2)^{2}}\\\\ =\sqrt{(-5)^{2}+(-3)^{2}} = \sqrt{25+9}=\sqrt{34} units\\\\\\CD = \sqrt{(-4-[-1])^{2}+(4-[-1])^{2}}\\\\=\sqrt{(-4+1)^{2}+(4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(5)^{2}}\\\\=\sqrt{9+25} = \sqrt{34} units\\\\\\AD = \sqrt{(-4-1)^{2}+(4-7)^{2}}\\\\=\sqrt{(-5)^{2}+(-3)^{2}} =\sqrt{25+9} = \sqrt{34} units[/tex]

AB = BC = CD = AD = √34 units. so , ABCD is  a square.

Area of square = side * side

                          = √34 * √34

                          = 34 square units


Related Questions

Which algebraic expression matches the transformation

Answers

Answer:

A

Step-by-step explanation:

In the last ten years, the population of Brazil has grown at an
exponential rate of 0.8% per year to 205,813,615. If this rate continues,
what will be the population in 10 more years? (Simplify your answer
completely. Round your answer to the nearest whole number.)

Answers

Answer:

just look at the 10 years in the past then we produce more people then we lose so times it by 3

The population of Brazil in the next 10 years would be 444336158

What is an exponential function?

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

The population of Brazil has grown at an exponential rate of 0.8% per year to 205,813,615. Hence, in the next 10 years:

Population = 205813615(1.08)¹⁰ = 444336158

The population of Brazil in the next 10 years would be 444336158

Find out  more on exponential function at: https://brainly.com/question/12940982

g(x)= 33/x −x^2at x=a+b,

Answers

Answer:

33/x - x^2 where x = a + b

33/(a + b) - (a + b)^2

d/da(33/(a + b) - (a + b)^2) = -2 (a + b) - 33/(a + b)^2

Step-by-step explanation:

;-;

question one

which statement explains why the numerical pattern below is a linear progression

1 4, 7 , 10


A)THE PATTERN IS POSITIVE

B) THE PATTERN START WITH 1

C) THE PATTERN CONTINUES INFINITELY

D) THE PATTERN HAS A CONSTANT RATE OF CHANGE ​

Answers

The answer would be d since your pattern above has a constant change of three.

Plzzzz answer fast......​

Answers

The answer to the question is 112

5th grade math. correct answer will be marked brainliest

Answers

Answer c
Well I think

Which is the better definition of line of best fit?

Answers

The line of best fit , also called a trendline or a linear regression, is a straight line that best illustrates the overall picture of what the collected data is showing. It helps us to see if there is a relationship or correlation between the two factors being studied. This trendline helps us to predict future events relating to the data being studied. Hope this helped!

A line of best fit guides a line through a scatter plot of data points that best describes the association between those points.

What is  line of best fit?

A line of best fit guides a line through a scatter plot of data points that best describes the association between those points. Statisticians typically utilize the least squares approach to arrive at the geometric equation for the line, either through manual computations or regression analysis software.

A line of best fit can be approximately specified utilizing an eyeball the method by marking a straight line on a scatter plot so that the numeral of points above the line and below the line stands about equal (and the line passes via as many points as possible).

To learn more about line of best fit refer to;

https://brainly.com/question/1518824

#SPJ2

Find the 2nd and 3rd term of the sequence 1, ___, ___, –11, –15, ...

Answers

Answer:

Step-by-step explanation:

-4 and - 7 are the second and third term

Answer:

-3, -7

Step-by-step explanation:

It's an arithmetic sequence subtracting four each time

-3, -7

A woman decides to have children until she has her first girl or until she has five children; whichever happens first. Find the expected value and standard deviation of X. Let X represent the number of children she has. Assume that she is equally likely to give birth to a boy or a girl on each child, and that gender is independent between children.
(a) Write out and sketch the complete probability distribution function for X.
(b) Write out and sketch the complete cumulative distribution function for X.
(c) Find the expected value and standard deviation of X.

Answers

Answer:

E(X) = 1.9375

SD(X) = 1.20

Step-by-step explanation:

Let :

G = girl ; B = Boy

P(G) = 0.5 ; P(B) = 0.5

Sample space :

G, BG, BBG, BBBG, BBBBG, BBBBB

Using the multiplication rule of independence :

P(G) = 0.5

P(BG) = 0.5 * 0.5 = 0.25

P(BBG) = 0.5 * 0.5 * 0.5 = 0.125

P(BBBG) = 0.5 * 0.5 * 0.5 * 0.5 = 0.0625

P(BBBBG) = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.03125

P(BBBBB) = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.03125

Creating a probability distribution table :

X = 1, 2, 3, 4, 5

For X = 5 ;

P(BBBBG) + P(BBBBB) = 0.03125 + 0.03125 = 0.0625

X :___ 1 ____ 2 ____ 3 _____ 4 _____ 5

P(X) : 0.5 __ 0.25 _ 0.125 _0.0625 _0.0625

The expected value E(X) :

√(ΣX * P(X)) = (1*0.5)+(2*0.25)+(3*0.125)+(4*0.0625)+(5*0.0625) = 1.9375

The standard deviation SD(x) :

√(ΣX²*p(x) - E(X)²

√((1^2*0.5)+(2^2*0.25)+(3^2*0.125)+(4^2*0.0625)+(5^2*0.0625) - 1.9375^2)

√(5.1875 - 3.75390625)

√1.43359375

SD(X) = 1.197

SD(X) = 1.20

Melvin bought a life insurance policy from Martin, and if Melvin dies, the
insurance company has to pay Monica, whose daughter is Mary. Who is the
beneficiary of the life insurance policy?
A. Martin
B. Mary
O C. Monica
O D. Melvin
IN

Answers

Answer:

monica

Step-by-step explanation:

Find the y-intercept of the line: 4x−2y+7=0

Answers

Answer:

= (0, 7/2)

Step-by-step explanation:



In 2010, $1 was worth 45.65 Indian rupees. That same year, $1 was worth 31.7
Thailand bahts. How many more rupees than bahts was $1 worth in 2010?
77.35
14.58
13.95
48.82

Answers

31.7 is 31.70 then add 13.95 then it equals 45.65.


Answer:13.95

Help asap !! Giving out brainliest answer !! Answer has to be correct

Answers

Answer:

33 ft

Step-by-step explanation:

hey, hope this helps and right.

Four more than twice Kai’s age does not equal Kara’s age. If Kara is 15 years old, find Kai’s age. Let k = Kai's age.



2k + 4 ? 15

Answers

Just -4 to 15 and the divide
Kais 3 years old I think not sure

Dylan bought 3 identical shirts online for a total cost of $71.83 including a flat rate (one time fee) of $7.99 for shipping. What equation can be used to determine the cost, s, of one shirt?

3s + 7.99 = 71.83
3 - 7.99s = 71.83
3 + 7.99s = 71.83
3s - 7.99 = 71.83

Answers

Answer:

The first option

Step-by-step explanation:

The second and third options are just wrong.

Good Luck!!!

Yoshi made a scale drawing of his yard. The scale drawing is 1 centimeter = 0.5 meter. The length of the patio is 4.5 centimeters in the drawing. Find the actual length.

Answers

here's your answer

hope it helps you

Can't manage to figure out this question. Can anyone help?

Answers

Answer:

Z=20

Y=16

X= 12

Step-by-step explanation:

Hope it helps


[tex] {4 }^{2} \times 25 \div \sqrt{25 - 15} [/tex]

Answers

The answer is 126.58
You first double the 4 which is 16, then you multiply the 16 by 25 to get 400. Next, you have to subtract 25 from 15 to get 10. Then, you square root the 10, becoming 3.16
Finally, you divide the 400 by 3.16 to have the final answer: 126.58

Dave buys a baseball for $15 plus an 8% tax. Mel buys a football for $20 plus an 8% tax. How much more did Mel pay than Dave? show your work and answer in complete sentence. Round your answer to the nearest cent.

Answers

Answer:

4.6, or 4.60

Don't forget the dollar signs.

Step-by-step explanation:

8 percent of 15 = 1.2.

15-1.2=13.8

8 percent of 20 = 1.6

20-1.6=18.4

18.4-13.8=4.6

Answer:

4.6

Step-by-step explanation:


HELP PLSS ILL GIVE BRAINLESS

Answers

Answer:

Green = 26.86 or 26.855

Yellow = 50.28 or 50.275

Blue = 36.85

Step-by-step explanation:

Use the formulas for perimeter

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Yellow is the answer

Ms. Taylor has 25 students in her class. Only 7 of her students ride the bus to and from school. What percent of Ms. Taylor’s class does NOT ride the bus? The percent of students in Ms. Taylor's class that do not ride the bus is %.

Answers

Answer:

75

Step-by-step explanation:

Please I need this asap, my answer is wrong

Answers

Answer: [tex]512\pi[/tex]

Step-by-step explanation:

Given

Equation of curve is [tex]x=\sqrt{8+y}[/tex]

When this curve is rotated about the y-axis, then volume generated is given by

[tex]V=\int_{a}^{b}\pi x^2dy[/tex]

When [tex]x=0[/tex], [tex]y=-8[/tex]

Put the limits and solve the integral

[tex]\Rightarrow V=\int_{-8}^{24}\pi (8+y)dy\\\\\Rightarrow V=\pi\left ( 8y+\dfrac{y^2}{2}\right )_{-8}^{24}\\\\\Rightarrow V=\pi \left ( 8\times 32+\dfrac{24^2-8^2}{2}\right )\\\\\Rightarrow V=512\pi[/tex]

From a point on a circle, two perpendicular chords are drawn. One is 6 cm from the center and the other is 3 cm from the center. Find the lengths of these chords.

Answers

Answer

the lengths of the chords are 12 cm and 6 cm

Answer:

The lengths of the chords are 12 cm and 6 cm

Step-by-step explanation:

See attached image

Hope this helps! :D

Monica hizo galletas de dos tamaños como se muestra en la imagen. ¿Cuánto mide el lado Z de la galleta más grande?

Answers

¡Hola! No he visto a dos mejores amigos. ✨

please help i will marl you brainless tha thangkyou​

Answers

Answer:

5

Step-by-step explanation:

The faces are 5

And the Name is rectangle prism

What is the value of the expression below when
x
=
5
x=5
x=5 and
y
=
2
y=2
y=2?
x
+
6
y
x+6y
x+6y

Answers

Answer:

17

Step-by-step explanation:

if x=5 and y=2 then

x+6y = 5+6x2

so 6x2= 12

12+5=17 sooooooo thats ur anwere plz thank meeeee

Adrian is putting streamers across the ceiling of his dining room to decorate for his nephews birthday party. The ceiling is rectangular. Its area is 122,5 square feet, and its
width is 7 feet. How long should Adrian cut a streamer that will run the length of the ceiling?

Answers

Answer: 17.5 feet long.

Hae Suk flips a penny, a nickel, and a dime. How many ways can she get at least two heads?

Answers

she can at least get 2 heads in: 3C3 + 3C2 = 4 ways

A bicycle has a listed price of $529.95 before tax. If the sales tax rate is 7.5%. Find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.

Answers

Answer:

569.95 dallars

Step-by-step explanation:

Consider this right triangle

Answers

Take out the x and the y and you will get your answer hope this help man haven’t done this a while
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