Find the perimeter of quadrilateral ABCD with vertices A(0, 4), B(4, 1), C(1, -3), and D(-3, 0).

Answers

Answer 1

Given:

The vertices of a quadrilateral ABCD are A(0, 4), B(4, 1), C(1, -3), and D(-3, 0).

To find:

The perimeter of quadrilateral ABCD.

Solution:

Distance formula:

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

Using the distance formula, we get

[tex]AB=\sqrt{(4-0)^2+(1-4)^2}[/tex]

[tex]AB=\sqrt{(4)^2+(-3)^2}[/tex]

[tex]AB=\sqrt{16+9}[/tex]

[tex]AB=\sqrt{25}[/tex]

[tex]AB=5[/tex]

Similarly,

[tex]BC=\sqrt{(1-4)^2+(-3-1)^2}[/tex]

[tex]BC=5[/tex]

[tex]CD=\sqrt{(-3-1)^2+(0-(-3))^2}[/tex]

[tex]CD=5[/tex]

And,

[tex]AD=\sqrt{(-3-0)^2+(0-4)^2}[/tex]

[tex]AD=5[/tex]

Now, the perimeter of the quadrilateral ABCD is:

[tex]P=AB+BC+CD+AD[/tex]

[tex]P=5+5+5+5[/tex]

[tex]P=20[/tex]

Therefore, the perimeter of the quadrilateral ABCD is 20 units.


Related Questions

y = 2x + 3
y=2x-1
The system has how many solutions?

one solution
two solutions
no solution
an infinite number of solutions

Answers

The answer is no solutions

3(y+6)=30 solve equation

Answers

Answer:

3(y+6)=30

3y + 18 = 30

18 - 30 = 3y

12 = 3y

12/3 = y

4 = y

or

y = 4

Divide 3(y+6) by 3, and do the same to 30. You end up with y+6=10. Subtract both sides by six, and you end up with y=4.

A man is twice as old as his son. Five years ago, the ratio of their ages was 9:4. Find the son's present age

Answers

Answer:

Son's age is 25.

Step-by-step explanation:

Let the Father's age be 2x.

Let the son's age be x.

Five years ago:

Man's age will be = 2x - 5

Son's age will be = x - 5

If the ratio of their ages five years ago was 9:4, then:

2x - 5/x-5 = 9/4

⇒ 4(2x - 5) = 9(x - 5)

⇒ 8x - 20 = 9x - 45

⇒ -20 + 45 = 9x - 8x

⇒ 25 = x

∴ x = 25

Hence, the son's age = 25 years

If x = 25, the father's age (2x) will be 2 × 25 = 50 years

Select the two values of x that are roots of this equation.
x² + 3x-6=0
A. X=
-3+ /33
2
B. x=-3-83
c. x. -3-15
D. x. -3*4/15
please help

Answers

Answer:

[tex]x1 = \frac{ - 3 - \sqrt{33} }{2} \\ x2 = \frac{ - 3 + \sqrt{33} }{2} [/tex]

Step-by-step explanation:

[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 3 + - \sqrt{9 + 24} }{2} \\ x1 = \frac{ - 3 - \sqrt{33} }{2} \\ x2 = \frac{ - 3 + \sqrt{33} }{2} [/tex]

CAN SOMEONE PLEASE HELP ME!!

Answers

Answer:

29.8

Step-by-step explanation:

a^2+b^2=c^2

a^2+7^2=11^2

a = h = 8.5

A= 1/2*b*h

A= 1/2*8.5*7

A=29.8

Is the product of two prime numbers a prime number or a composite
number?

Answers

Step-by-step explanation:

No, the product of two (or more) prime numbers cannot result in another prime number. By definition, a prime number is a number that is divisible by 1 or itself - the act of multiplying two or more primes together will always yield a number divisible by 1, itself and the prime numbers multiplied together to achieve it.

Answer:

a composite one

Step-by-step explanation:

Why?

It is easy-peasy.

First, it is impossible to have a prime number. Because primes are only divisible by 1 and themselves.

For example, 3 is a prime. 7 is a prime. Multiply them and get 21.

I hope it helped:)

. Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. population mean math score parents college grads. population mean math score parents high school grads. _____ _____ b. What is the point estimate of the difference between the means for the two populations

Answers

Answer:

Following are the responses to the given question:

Step-by-step explanation:

For point a:

Following are the null and alternative hypotheses:

[tex]H_0 : \mu_1 \leq \mu_2\\\\H_1 : \mu_1 > \mu_2[/tex]

For point b:

By using the Excel we obtained the output of the 2 sample t-test that is defined in the attached file.  

These point estimately are the difference among the mean for the two populations:

[tex]\to \mu_{\bar{x_1}-\bar{x_2}} = \mu_{\bar{x_1}}-\mu{\bar{x_2}} ={\bar{x_1}-\bar{x_2}}=573-491=82[/tex]

help me solve the simultaneous linear inequalities

Answers

Answer:

The inequality form is -4<x<-2

The Interval Notation is (-4, -2]

I hope this helps!

How many solutions does the nonlinear system of equations graphed below
have?
• A. One
• B. Two
• C. Four
O D. Zero
SUBMIT

Answers

I’m not to sure but I think it’s 4 solutions

Find the measure of each numbered angle for each figure

Answers

Answer:

Angle 1 is 58. Angle 2 is 32.

Step-by-step explanation:

The measure of Angle ACB is 90 because C is on the circle and A and B connect to form a diameter of the circle. So, Angle 1 and Angle 2 add up to 90 (total degrees in triangle - 90). Now you can add the expressions the question gave for Angle 1 and Angle 2, and you get 7x + 6. So you have the equation 7x + 6 = 90. Solve the equation and you get x = 12. Now you can plug in that value for x into the expressions for Angles 1 and 2 to find their measures.

Pls help, I will give 50 points

Answers

I think this is the answer you are looking for

What is the mode of the set of numbers {55, 57, 59, 61, 62, 63, 64, 64, 65, 68, 69)

Answers

Answer:

64

Step-by-step explanation:

The mode of a data set is the number that occurs most frequently in the set.  So, just look for the number that appears the most.

I hope this helps!

You invest $4.000 in a savings account. The account pays 3% annual interest. How much money will be in the savings account after 9 years?

A) $4,938.29
B) $5,219.20
C) $5,124.33
D) $6,003.45​

Answers

Answer:

4000*0.03*9=1080

4000+1080=5080

umm but like thats not one of the answers sorry

Hope This Helps!!!

Step-by-step explanation:

4000*3% = 120

120*9= 1080

1080+4000=5080

What is the domain of the square root function graphed below

Answers

Answer:

Dominio de una Raíz cuadrada

Cuando tenemos una raíz, para estudiar su existencia debemos saber que una raíz existe si y solo sí el radicando (lo que está dentro de la raíz) sea mayor o igual a cero.

Por lo tanto deberemos estudiar el signo de lo que se encuentra dentro de la raíz; y determinar las zonas positivas y las raíces que son las zona de existencia de la función raíz o dominio de esta función.

Step-by-step explanation:

qsy

The probability distribution for a
random variable x is given in the table.
-5
-3
-2
0
2
3
Probability
.17
.113
.133
.16
.11
.10
Find the probability that -2

Answers

Note: The values in the table are not correct because the sum of the probability of all events is not equal to one. The should be 0.13 and 0.33 instead of 0.113 and 0.133 respectively.

Given:

The probability distribution for a random variable x is given in the table.

x     :    -5          -3            -2            0           2          3

P(x) :  0.17      0.13       0.33       0.16       0.11      0.10

To find:

The probability of -2.

Solution:

From the given probability distribution for a random variable x, it is clear that the value of the probability is 0.33 corresponding to -2.

[tex]P(-2)=0.33[/tex]

Therefore, the probability of -2 is 0.33.

The distance traveled (in meters) by a frog is modeled by the equation d=2t where d is the distance traveled in meters and t is the time in minutes. Find the distance traveled in 25 minutes.

Answers

Given,

d = 2t

here, t = 25

Therefore,

d = 2*25

= 50m

Evaluate: 4x3 - 7x2 for x = 3

Answers

Answer:

45

Step-by-step explanation:

4[tex]x^{3}[/tex] - 7[tex]x^{2}[/tex] for x = 3

Substitute 3 in for x

4([tex]3^{3}[/tex]) - 7([tex]3^{2}[/tex])

4(3·3·3) - 7(3·3)

4(27) - 7(9)

108 - 63

45

Answer:

45

Step-by-step explanation:

Hi there!

We are given 4x³-7x² and we need to evaluate the expression if x=3.

To do this, substitute 3 as x into the expression, and then use the order of operations to solve

so substitute 3 as x into the expression (remember: x² is x*x, or (x)²)  

4(3)³-7(3)²

now using the order of operations, start by evaluating the exponents

(3)³=3*3*3=9*3=27

(3)²=3*3=9

the expression then becomes:

4*27-7*9

multiply

108-63

subtract

45

Hope this helps! :)

does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?​

Answers

Answer:

Inside

Step-by-step explanation:

Given equation of the Circle is ,

[tex]\sf\implies x^2 + y^2 = 25 [/tex]

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]

Here we can see that the distance of poiñt from centre is less than the radius.

Hence the point lies within the circle

I need help with this, Im never good with these

Answers

Answer:

(a) basketball

(b) hat

(c) stuffed animal

explanation:

I'm not sure if got right but from what i see;

Chances from 1-23 you get a stuffed boi

Chances from 24-54 you get a hat (why)

Chances from 55-100 you get a basketball

Winner 5 got 90, which is between 55-100

Winner 6 got 35, which is between 24-54

winner 8 got a 7, which is between 1-23

Hope I didn't read it wrong

Find the domain of the following piecewise function.


Answers

Answer:

[tex](2,8][/tex]

Step-by-step explanation:

Given

The attached piece wise function

Required

The domain

To do this, we simply consider the inequalities that bound the values of x.

The inequalities are:

[tex]2 < x < 4[/tex]     [tex]4 < x < 8[/tex]   and   [tex]x \ge 8[/tex]

Combine the first two inequalities:

[tex]2 < x < 8[/tex]    and   [tex]x \ge 8[/tex]

For the inequality to be true, we must have:

[tex]2 < x \le 8[/tex]

In interval notation, the inequality is:

[tex](2,8][/tex]

Someone to give me the answer on the number line please

Answers

Answer:

Step-by-step explanation:

Equation for the total volume of the bucket has been given as,

V = 4 + 2t

Here V = Total volume

t = elapsed time

Table for the input-output values,

t        0         1         2        3        4

V       4         6        8        10      12

Therefore, line passing through the given points in the table will be the graph for the equation.

What is the interval of increase f(x)=3x^2-6x

Answers

Answer:

F(g(×)1=3(6+2)-5=18×+6-5=18×+1

Step-by-step explanation:

so correct answer is the last one pa brainliest plss

FG has a midpoint at M(5, 7). Point G is at (9,5). Find the coordinates of point F. Write the coordinates as decimals or integers. ​

Answers

i don’t know i need points though

The difference between two numbers is 12 and their sum is 26. Find the smallest number. A)9 B)7 C)-7 D)-9

Answers

Answer:

Step-by-step explanation:

We need a system of equations to solve for this. The first equation comes from "The difference between 2 numbers is 12". Difference means subtraction, the 2 numbers will be x and y, and the word "is" means equals:

x - y = 12

The second equation comes from "...their sum is 26". The numbers are still x and y but this time we have their sum, which is what they equal when they are added together. The word "is" means equals:

x + y = 26. So we will go back up to the first equation. If y taken away from x leaves a positive number, that means that y is smaller than x. We are looking for the value of the smaller number so we will find y. Solve the first equation for x to get it in terms of y:

x = 12 + y and we sub that into the second equation:

(12 + y) + y = 26 and

12 + 2y = 26 and

2y = 14 so

y = 7. Choice B is the one you want.

Can someone help me with this math homework please!

Answers

Answer:

See step by Step

Step-by-step explanation:

Both are correct. As long as we undo the operations that was given from the original term to both sides until we get the variable by itself., any way can be applied.

Both, Spencer and Jeremiah are correct. We can verify this by testing their methods.

Spencer's method:

[tex]6x - 2 = - 4x + 2[/tex]

[tex]6x - 2 + 4x= - 4x + 2 + 4x[/tex]

[tex]10x - 2 = 2[/tex]

[tex]10x = 2 + 2[/tex]

[tex]10x = 4[/tex]

[tex]x = \frac{4}{10} [/tex]

[tex]x = 0.4[/tex]

Jeremiah's method:

[tex]6x - 2 = - 4x + 2[/tex]

[tex]6x - 2 - 6x = - 4x + 2 - 6x[/tex]

[tex] - 2 = - 10x + 2[/tex]

[tex] - 2 - 2 = - 10x[/tex]

[tex] - 4 = - 10x[/tex]

[tex] \frac{ - 4}{ - 10} = x[/tex]

[tex]0.4 = x[/tex]

As seen, we get the correct answer by using Spencer's and Jeremiah's method. So, we can say that they both are correct.

Someone please help me ASAP please

Answers

246 degrees i think, 44+80= 124 then 360-124 which us 246. (i might have misunderstood the question)

Answer:

hey mate

plz mark it as brainliest

Find the missing side. Round to the nearest tenth.
A) 38.4
C) 33.9
B) 5.0
D) 27.6

Answers

Answer:

C)33.9. I hope it's help

What is the equation of the following line?
(-4, 8)
(0,0)

Answers

Answer

Step-by-step explanation:

y = -2x + 0

Therefore; y = -2x

solve it please please​

Answers

Answer:

D. 5 and 14

Explanation:

5,8,11,14

1 + 2= 6
1 +8= 16
Imma really smart right?

Evaluate x^-2 for x = -3 plsss i really need help on this thank you

Answers

Answer: -1/9

Step-by-step explanation:

Answer:

- 1/9 OR -0.111....

Step-by-step explanation:

Make x= -3

-3^-2= -1/9

Other Questions
Which one is the result of the output given by a compute I need help with this question. Pls give me an answer /steps and explanations. Da vo c im ca v qu v ht, loi qu no di y c xp cng nhm vi qu m ?A. Nho B. C chuaC. Chanh D. Xoi importance of hematology I need help with this I will appreciate if I get an answer for this problem Picture with the question is posted explain how data structures and algorithms are useful to the use of computer in data management Given = 1/(3), what is ((+)())/ ? 18 is 65% of what number A rectangles perimeter is equal to 27 plus its width. The length of the rectangle is four times its width. What is the width of the rectangle in units? f x equals 1 / x - 3 + 7 find the inverse of f x and its domain Match the following properties to the type of wave. 10. A moving van company charges a fee of 35.00 dollars for the truck rental and 25 cents for every mile the truck travels from the loading location. Let y be the cost in dollars for using the truck for x miles. Write the slope-intercept form of the equation. Plz help me with this question Drawing of water molecular formulas 1.Draw molecular structure of water Y+y+y+y rewrite in multiplication v sao cn hc thi ielts Una de las aplicaciones ms importa del electromagnetismo son A jar contains 30 red, 40 blue, and 50 white buttons. You pick one button at random , find the probability that it is blue. Psyllium is prescribed for the client diagnosed with a cardiac disorder to facilitate defecation and prevent straining with bowel movements. The nurse reinforces instructions to the client regarding administration of the medication. Which statement by the client indicates an understanding of the use of the medication Do the activity please it's trigonometry