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Anuta_ua [19.1K]
3 years ago
15

Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you c

an use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.
Mathematics
2 answers:
Black_prince [1.1K]3 years ago
8 0

Answer:

Step-by-step explanation:

We can use distance formula and find the length of AB , BC, CD and DA.

Then using this length we can prove that AB = CD and BC = DA

Mandarinka [93]3 years ago
4 0

Answer:

Step-by-step explanation:

hello :

that parallelogram ABCD is a rectangle means : vectorAD is prpoduclar for vector AB

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Find the midpoint of the line segment with the given endpoints: (- 9, 3)(7, - 8)
Luda [366]

Answer:

\boxed {\boxed {\sf (-1, -\frac{5}{2} )  \ or \ (-1, -2.5) }}

Step-by-step explanation:

We are asked to find the midpoint of a line segment. The midpoint bisects the line segment, or divides it into 2 equal parts. We find the midpoint by finding the average of the x-coordinates, then the y-coordinates.

( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})

The endpoints are (-9, 3) and (7, -8). Match the value and the corresponding variable.

  • x₁= -9
  • y₁ = 3
  • x₂ = 7
  • y₂ = -8

Substitute the values into the formula.

(\frac {-9+7}{2},  \frac{3 + -8}{2})

Solve the numerators.

  • -9+7 = -2
  • 3+ -8 = -5

( \frac{-2}{2}, \frac {-5}{2} )

Divide.

(-1, - \frac{5}{2} )

The fraction can be written as a decimal.

(-1,-2.5)

The midpoint of the line segment is (-1, -5/2) or (-1, -2.5)

4 0
3 years ago
ABC is a right triangle. If AC = 12 and BC = 13, find AB.
AysviL [449]
Since BC is the hypotenuse...

α = 12
c = 13

Hence..

13² = 12² + ß²
ß = √(13² - 12²)
= √(169 - 144)
= √25
= 5

Hence, AB = 5

I hope this helps!
3 0
3 years ago
Read 2 more answers
1/2(4x)=-20 plz help and show work
Bas_tet [7]
X=10 because........
the opposite of 1/2=times 2
20 times 2=40
40 divided by 4=10, so 
x=10
6 0
3 years ago
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Assume that there are an equal number of births in each month so that the probability is that a person chosen at random was born
NikAS [45]

Answer:

0.2773 = 27.73% probability that at the May celebration, exactly two members of the group have May birthdays

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have a birthday in May, or they do not. The probability of a person having a birthday in May is independent of any other person. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Probability of a person being in May:

May has 31 days in a year of 365. So

p = \frac{31}{365} = 0.0849

Group of 20 friends:

This means that n = 20

What is the probability that at the May celebration, exactly two members of the group have May birthdays?

This is P(X = 2).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{20,2}.(0.0849)^{2}.(0.9151)^{18} = 0.2773

0.2773 = 27.73% probability that at the May celebration, exactly two members of the group have May birthdays

3 0
3 years ago
What is the solución to this equation <br> X/5=30
Mama L [17]

Answer:

150

Step-by-step explanation:

x/5=30

x=30*5

x=150

Hoped this helped!

5 0
3 years ago
Read 2 more answers
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