Three consecutive vertices of a parallelogram are (– 2, 1); (1, 0) and (4, 3). Find the coordinate of the fourth vertex and find the area of the parallelogram.

Answers

Answer 1

Answer:

D(1,4) - the fourth vertex, the area is equal to 12

Step-by-step explanation:

A(2,-1), B(1,0),C(4,3), They are consecutive, we need to find the point D, find the midpoint of AC (O)

xo= (xA+xc)/2    x0= (-2+4)/2=1

y0=(yA+yC)/2    y0= (1+3)/2=2

0(1,2)

O is the midpoint of BD, so let's find the vertex D

X0= (xB+xD)/2     1= (1+xD)/2   xD=1

y0= (yB+yD)/2      2= (0+yD)/2    yD=4

D(1,4)

the vector DA is (-2-1, 1-4)= (-3,-3)

the vector DC is (4-1, 3-4)= (3,-1)

The modul of DC is sqrt ((-3)^2+(-3)^2)= 3*sqrt2(the length of the side Dc)

The modul of DA is sqrt (3^2+(-1)^2)= sqrt10(the length of the side DA)

cosD= (-3*3+(-3)(-1))/3*sqrt2*sqrt10=-6/3*2*sqrt5=-1/sqrt5

sinD= sqrt (1- 1/5)=2/ sqrt5

S=3sqrt2*sqrt10*2/sqrt5= 12


Related Questions

What was Veronica's speed if she drove 475 miles in 6 1/4 hours?

Answers

Answer: 76 mph

Step-by-step explanation: speed is distance divided by time so 475 : 6.25 = 76 (mph)

Answer:

76 mph

Step-by-step explanation:

To find the answer, you would divide the miles she drove: 475 by the amount of time it took to get there: 6 1/4 hours. Convert the fraction to a decimal: 1/4= .25 so your problem would look like this...

475 / 6.25 = 76

why are there three zeros in the product of 6 times 103

Answers

Answer:

There’s not

Step-by-step explanation:

It’s 618

WILL GIVE BRAINLIEST TO WHOEVER CAN EXPLAIN:
True or False-in scientific notation when you move the decimal point left is it positive.

Answers

Answer:

false.

Step-by-step explanation:

just cause you move a decimal point to the left dosent mean its positive.

What does x equal?
2x + 5x – 4= 17


Answers

Answer:

x = 3

Step-by-step explanation:

2x + 5x - 4 = 17

Combine like terms

7x - 4 = 17

Add 4 to both sides

7x = 21

Solve for x

x = 21/7

x = 3
___________________
Hope this helps!

Love you.

- doomdabomb

Answer:

x = 3

Step-by-step explanation:

2x + 5x - 4 = 17      (Given)

7x - 4 = 17              (Simplify)

7x - 4 + 4 = 17 + 4  (Add 4 on both sides)

7x = 21                   (Simplify)

7x/7 = 21/7             (Divide 7 on both sides)

x = 3                      (Simplify)

Find a polynomial f(x) of degree 4 that has the following zeros. 2, 5, 0, -7

Answers

Answer:

Step-by-step explanation:

f(x) = (x - 2)(x - 5)x(x+ 7)

f(x) = (x^2 - 7x + 10)*x * (x + 7)

f(x) = x(x^3 - 39x + 70)

f(x) = x^4 - 39x^2 + 70x

To show that this is correct, I've made a graph with these points labeled. The graph is just around the x axis. The local maximums and minimums are just too large a value.

8w-2=12w+6 both answers

Answers

Answer:

your answer is -2

I hope it's helps you

Answer:

[tex]8w - 2 = 12w + 6 \\ 8w - 12w = 6 + 2 \\ - 4w = 8 \\ w = \frac{8}{ - 4} \\ w = - 2[/tex]

I hope it helped U

stay safe stay happy


6.55743... is an irrational number because it is an
a terminating decimal
a repeating decimal
a non-terminating and non-repeating decimal
a non-repeating decimal
a non-terminating decimal

Answers

Answer:

#3. a non-terminating and non-repeating

Step-by-step explanation:

6.55743... never ends and it never repeats either

Answer:

Not terminating but doesn't repeat either

Step-by-step explanation:

-5x²-2x³-4x Write the polynomial in standard form. Then identify the polynomial by the number of terms.

Answers

-2x^3-5x^2-4x
Cubic Trinomial

Answer:

-2x³ - 5x² - 4x and cubic

Step-by-step explanation:

→ Rearrange the polynomial so the highest power is at the start

-2x³ - 5x² - 4x

→ Now look at the highest power and determine the type of polynomial

Cubic

V=s^2h/3
Find the volume of a square pyramid If ‘s’ is increased by 30% and ‘h’ remains constant

Answers

Answer:

1.69s^2h/3.

Step-by-step explanation:

New s = 1.3s

New volume = (1.3s)^2h /3

= 1.69s^2h/3.

The speed of a falling object increases at a constant rate as time increases since the object was dropped. Which graph could represent the relationship between t, time in seconds, and s, speed in meters per second? A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line increases from 0 to 10 seconds. A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line decreases from 0 to 4 seconds. A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line increases from 0 to 4.5 seconds. A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line decreases from 1 to 9 seconds.

Answers

Answer:

Since the guy on top was so difficult the answer is A

Step-by-step explanation:

Edge 2021

Answer: Option A if your doing Edge.

Step-by-step explanation:

none

A van moves with a constant speed of 116 km/h. How long will it take to travel a distance of 174 kilometers?

Answers

Answer:

1.5 hours / 90 minutes

Step-by-step explanation:

time = distance ÷ speed

if x and y are two overlapping subsets of a universal set U, write the relation between n(U),n(X U Y), and n(xūy).​

Answers

Answer:

the relation between them are

n(U) = n(X U Y) + n(xūy).

HELP ASAP!!!

The line (y-1)=(2/3)(x+1) contains point (a,-3).

What is the value of a? Show
your work.​

Answers

[tex]\\ \sf\Rrightarrow y-1=\dfrac{2}{3}(x+1)[/tex]

[tex]\\ \sf\Rrightarrow -3-1=\dfrac{2}{3}(a+1)[/tex]

[tex]\\ \sf\Rrightarrow -4=\dfrac{-2(a+1)}{3}[/tex]

[tex]\\ \sf\Rrightarrow -2(a+1)=-4(3)[/tex]

[tex]\\ \sf\Rrightarrow -2(a+1)=-12[/tex]

[tex]\\ \sf\Rrightarrow a+1=\dfrac{-12}{-2}[/tex]

[tex]\\ \sf\Rrightarrow a+1=6[/tex]

[tex]\\ \sf\Rrightarrow a=6-1[/tex]

[tex]\\ \sf\Rrightarrow a=5[/tex]

Jace has consumed 1,500 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily calorie total to 1,900 calories per day. How many calories does he have left to consume for the day? Is 1,100 a viable solution to this problem?

Yes; 1,100 is less than 1,500.
No; 1,100 is more than the 400 he burned off at the gym.
No; 1,100 will cause him to exceed 1,900.
Yes; 1,100 is less than 1,900.

Answers

Answer:

Option 3

Step-by-step explanation:

If he burned off 400 calories from 1500 consumed calories, he has 1100 consumed calories.  1900 - 1100 = 800 calories left to consume.

While option 2 also says no, it's not the right reason.  

The calories left to consume for the day is 800 calories.

No, 1,100 will cause him to exceed 1,900.

Given,

Jace has consumed 1,500 calories so far today.

He has also burned off 400 calories at the gym.

He would like to keep his daily calorie total to 1,900 calories per day.

We need to find how many calories he has left to consume for the day.

And see which option is the best choice.

We have,

Calories consumed in a day = 1500

Burned calories = 400

Calories to keep in a day = 1900

Find the Calories left

= 1500 - 400

= 1100

Find how many calories need to be consumed to keep 1900 calories.

= Calories needed to keep in a day - calories remaining after burned

= 1900 - 1100

= 800

We see that the calories left to consume is 800 calories.

So 1100 is not a viable solution. It will cause him to exceed 1,900.

Thus,

The calories left to consume for the day is 800 calories.

No, 1,100 will cause him to exceed 1,900.

Learn more about finding the calories needed to consumed to keep daily calories here:

https://brainly.com/question/12862654

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The following shapes are similar. AB : IJ is 5:1 and the length of FE is 30. What is the length of NM?

Answers

Answer:

6

Step-by-step explanation:

5:1

30:6

multiply by 6 so its 6

Let w 1-5 and z=2+ 4i, Find z+w

Answers

Step-by-step explanation:

w+z=1-5+2+4¡

w+z=-2+4¡

and if you mean w= 1-5¡ , z= 2+4¡

z+w= 1-5¡+2+4¡

z+w= 3-¡

A polygon which is regular has interior angles measuring 150°. This polygon is called a:​

Answers

Answer:

Step-by-step explanation:

equilateral triangle

Answer:

Dodecagon (12 - sided polygon)

Step-by-step explanation:

Let it be n- sided polygon.

Sum of interior angles is 150n.

On the other hand we know the sum of interior angles of a regular n - sided polygon is calculated using the following formula:

S = 180(n - 2)

Compare the sums and solve for n:

180(n - 2) = 150n180n - 360 = 150n180n - 150n = 36030n = 360n = 360/30n = 12

12-sided polygon is called dodecagon

Solve for x and z (and find the total or a fraction or root of the equation)

4+x-3z*(7+3+6)=?

Answers

Answer:

Step-by-step explanation:

4+x-3*z(7+3+6)

4+x-3*z*16

4+x-3*16z

4+x-48z

x-48z+4

Four times the sum of three and a number

Answers

Answer:

4*3+X

IGNORE THIS JWINFWONDIWJFIENFIWKQPXK

16 The cost for parking at a city airport is shown in the table.
Price for first day
$16.60
For every
2
day afterwards
$9
Yuri pays $124.60 to park his car.
How many days does he park his car for?
Show your working.

Answers

Answer:

He paid $9 twelve times

12× 2= 24 days

Step-by-step explanation:

1st day = $16.60

3rd day=$ 9 (i.e for every 2days afterwards)

5th day=$ 9

Yuri pays : 124.60

124.60-16.60

= $108.00

After paying the first day he paid 108.00

108.00÷ 9 = 12

He paid $9 twelve times

12× 2= 24 days

What is the value of X?​

Answers

Answer:

5 * sqrt(3)

Step-by-step explanation:

The sine of 60 degrees is equal to x/10 because x is opposite to it and 10 is the hypotenuse. Since the sine of 60 degrees is equal to sqrt(3)/2, sqrt(3)/2 = x/10. Because 5sqrt(3)/10 = sqrt(3)/2, 5sqrt(3)/10 = x/10 and therefore 5sqrt(3) = x.

The answer would be 5 and something to help you when doing these questions is using sin tan cos. If you search it up it shows which one to use when it comes to equations like this. And when you find it you enter it in your calculator. Since you need the opposite your gonna use COS. Cos(60) = 10 and then your gonna put an x under cos(60) as if it was a fraction and do cross multiply. And that’s how you will get 5.

Compare negative square root of 7 and -3.12345

Answers

Answer: Square root of negative 7 is greater than -3.12345

Step-by-step explanation: Since the square root of -7= 2.64575131 i (A positive number) Then it's greater, since the positive number is always greater than the negative numbers, because the negative numbers are further below zero than the positive number, if there is a number below the zero and a number above the zero, the one above the zero is greater,  because it's a positive number, the one below 0 is negative.

express rational number in standard form: -216/144​

Answers

Answer:

[tex] \frac{ - 3}{2} [/tex]

Step-by-step explanation:

[tex] \frac{ - 216}{144} \\ \\ = \frac{ - 3}{2} [/tex]

Hope it is helpful....

0.582 times 10 what is value of the 2​

Answers

Answer:

5.82

Step-by-step explanation:

0.582 x 10

=> Shift the decimal place by 1

=> 5.82

The required simplified value of the product is 5.82 and the value of 2 in the expression is 0.01 times.

To determine the value of 2 in the product of 0.582 times 10.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
According to the question,
Product = 10 * 0.582
Product = 5.82,
Where 2 is located at the thousandth place,
So, the value of 2 in 5.82 is 0.01 times of 2.

Thus, the required simplified value of the product is 5.82 and the value of 2 in the expression is 0.01 times.

Learn more about simplification here: https://brainly.com/question/12501526

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Which numbers are a distance of 3.5 units from −4 on a number line?

A number line with increments of .5 with a range of 0 to negative 7.5

Select the two correct answers.


−7

−7.5

−6.5

−4.5

−3.5

−0.5

(help)

Answers

To be 3.5 units from -4, you either need to add or subtract 3.5 from -4.

-4 - 3.5 = -7.5

-4 + 3.5 = -0.5

In the diagram below BD is parellel to XY what is the value of y ?

Answers

Answer:

C

Step-by-step explanation:

y and 67 are alternate exterior angles and are congruent , then

y = 67° → C

Please help me with this question:)

Answers

Answer:

Ada is correct.

Step-by-step explanation:

Problems with Naman:

Naman is supposed to follow PEMDAS, which is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Division

Addition

Subtraction

~

The mistake: Naman moved +6 to the left and added it to the 2 located on the left side of the expression. You cannot do that, as it breaks the law of PEMDAS. On the other hand, Ada did the correct thing, which was to distribute 2 to all terms within the parenthesis (as one term in the parenthesis has a variable, and the other is a constant, meaning that they cannot be combined). This leads to Naman not doing the rest of the question correct.

Next, Ada correctly combined the two constants, which resulted in 0. 0 means nothing, therefore the placeholder is not needed. Therefore, 8x is the final answer.

Step by step please (variable expression)

Answers

Answer:

139

Step-by-step explanation:

Substitute x for 15.

9(15)+4

Then multiply:

135+4

And then add:

139

solve the system of equations by substitution y=1-x; -2x+y=4

Answers

Answer:

[tex]\displaystyle [-1, 2][/tex]

Step-by-step explanation:

[tex]\displaystyle -2x + [1 - x] = 4 → 4 = 1 - 3x → \frac{3}{3} = \frac{-3x}{3}; -1 = x, 2 = y \\ \\ [-1, 2][/tex]

I am joyous to assist you at any time.

PLEASE HELP I WIL, GIVE BRAINLIST

Answers

I believe the answer is b.

Answer:

B There should be lines drawn through the inner vertices as well

Step-by-step explanation:

The answer is B There should be lines drawn throu the inner verticesas well Because

those red lines are from inner vertices

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