1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lesya [120]
2 years ago
13

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.
Mathematics
1 answer:
antiseptic1488 [7]2 years ago
6 0

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

You might be interested in
Write the first 4 multiples of 3/8
sesenic [268]

Multiples of 3

: 3, 6, 9, 12, 15, 18, 21, 24, ...

Multiples of 4

: 4, 8, 12, 16, 20, 24, ...

Multiples of 8

: 8, 16, 24, ..

2

Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 2424

Method 2: By Prime Factors

1

List the prime factors of each number.

Prime Factors of 3

: 3

Prime Factors of 4

: 2, 2

Prime Factors of 8

: 2, 2, 2

2

Find the union of these primes.

2,2,2,32,2,2,3

3

Multiply these numbers: 2\times 2\times 2\times 3=242×2×2×3=24. This is the LCM.

LCM = 2424

3 0
2 years ago
If liquids can be separated into layers of density, could gases also be separated? Explain your reasoning.​
Scilla [17]

Hey there! I'll try to provide you with my best answer.  

Answer: The main reason why it probably wouldn't be seperated is because the molecules in gas are much farther away from each other. This created a huge gap within the two states so sometimes it's likely to be not seperated. But it solely depends on the sort of gas is being used. If they have higher density difference then it is possible to be seperated.  

If air is included as gas then yes, because there is heavy and light air. The heavy air is the cold air which you feel at night. Meanwhile the light air the warm air which rises in the sky during day light. Both of them are seperated because of their densities. Or atleast they are seperated into layers themselves. For example: this slightly cold and hot air is felt when your nearby a camp fire.  

Hope it made sense.

3 0
2 years ago
Read 2 more answers
A store sells televisions for $360 and video cassette recorders for $270. At the beginning of the week its entire stock is worth
kaheart [24]

Answer:

The number of Television at the beginning was 90

The number of video cassette recorders at the beginning was 89

Step-by-step explanation:

Selling Price of 1 Television =$360.

Selling Price of 1 video cassette recorders for $270.

Let the number of Television at the beginning=x

Let the number of video cassette recorders at the beginning =y

Opening Stock =$56,430.

Therefore:

  • 360x+270y=$56,430.

It sells three quarters of the televisions and one third of the video cassette recorders for a total of $32,310.

\frac{3}{4}(360)x+\frac{1}{3}(270)y= \$32,310

270x+90y=32310

We then solve the two equations to obtain x and y.

  • 360x+270y=$56,430. (Multiply by 270)
  • 270x+90y=32310          (Multiply by 360)

97200x+72900y=15236100

97200x+32400y=11631600

Subtract

40500y=3604500

y=89

Substitute y=89 into 270x+90y=32310 to obtain x

270x+90(89)=32310

270x=32310-8010=24300

x=90

Therefore:

The number of Television at the beginning was 90

The number of video cassette recorders at the beginning was 89

8 0
3 years ago
Read 2 more answers
.36 (6 repeating) as a fraction in simplest form?
Blizzard [7]
Yeah Im pretty sure it is
8 0
2 years ago
Write an equivalent expression for 10x + 2 using the distributive property.:D
oksian1 [2.3K]
2(5x+1)

I think that's right?
5 0
3 years ago
Read 2 more answers
Other questions:
  • If one letter is chosen at random from the word substitute, what is the probability that the letter chosen will be a "t"?
    15·1 answer
  • Lindsey made 4 lunches out of 1\2 of a leftover casserole she put the same amount in each lunch.how much of a casserole did she
    15·2 answers
  • Describe the transformation. 
    12·2 answers
  • The shipping department must send out 50 cases of phones. Five stores will receive ten cases each. How many cases are left?
    6·2 answers
  • All in standard Notation please :/ 2.09 x 10^5
    15·1 answer
  • Can someone please help me
    5·1 answer
  • If a/b-d=2c/b find the value of c when a=3, b=4 and d=-5
    9·2 answers
  • Where do you get .28 from ?
    14·2 answers
  • Tell whether the angles are adjacent or vertical. Then find the value of x.​
    14·1 answer
  • X + 4 = x2? Assume x greater-than 0
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!