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deff fn [24]
2 years ago
9

Prove ABCD is a parallelogram by showing both pairs of opposite sides are parallel. please Show All Work! Thanks!!

Mathematics
2 answers:
katrin [286]2 years ago
8 0

Answer:

Step-by-step explanation:

To prove this we should first make a little representation to get an idea of how will proceed to work .

To solve it we should use vectors so the first step is to identify this vectors :

  • we have four points : A/B/C/D
  1. A(-2,-4)
  2. B(1,2)
  3. C(2,10)
  4. D(-1,4)
  • VECTOR AB WITH VECTOR DC
  • VECTOR AD WITH VECTOR BC

NOW LET'S IDENTIFY THEIR COORDINATES :

  • VECTOR AB (1-(-2),2-(-4)) VECTOR DC (2-(-1),10-4)
  • VECTOR AD (-1-(-2),4-(-4)) VECTOR BC (2-1,10-2)

We get :

  • VECTOR AB (3,6) VECTOR DC (3,6)
  • VECTOR AD (1,8) VECTOR BC  (1,8)

We notice that the opposite ones have the same coordinates so the edges are parallel .

If we want to check more we can calculate the lenghts :

  • AB=\sqrt{3^{2}+6^{2}  }     DC=\sqrt{3^{2}+6^{2}  }

So AB=DC

  • AD=\sqrt{1^{2}+8^{2}  }     BC=\sqrt{1^{2}+8^{2}  }

So AD=BC

SO ABCD IS A PARALLELOGRAM

nadezda [96]2 years ago
7 0

Answer:

Here You Go! I'm not really sure about this one but i tried.

Step-by-step explanation:

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I need help bc I don’t have a calculator
kari74 [83]

Answer:

B is correct

Step-by-step explanation:

I think you don't need a calculator here. :) Try to figure out next time!

7 0
3 years ago
The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotation
a_sh-v [17]

The correct option is (c) h = 10sin(π15t)+35.

The equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds is  h = 10sin(π15t)+35.

<h3>How do windmills rotate?</h3>

The blades of a turbine, which resemble propellers and function much like an airplane wing, capture the wind's energy.

A pocket of low-pressure air develops on one side of the blade when the wind blows. The blade is subsequently drawn toward the low-pressure air pocket, which turns the rotor.

Calculation for the equation of the model height-

Let's now review each choice individually and select the best one.

The blade is horizontal at time t = 0. As a result, h = 35 at t = 0 is valid for all of the possibilities in this situation.

They accomplish two spins in a minute. The blades will so complete one rotation in 30 seconds. and they will complete a quarter rotation in 15/2 seconds. Because of this, the blade will be vertically up from time t = 0 to t = 15/2. Its height in this instance should be 35 + 10 = 45 ft. Let's now examine the available possibilities.

If we put t=15/2 in the options

Option (a) gives h = 25

Option (b) gives h = -10sin(15/2) + 35

Option (c) gives h = 45

Option (d) gives h = 10sin(15/2) + 35

Therefore, the correct equation is given in option c.

To know more about windmill, here

brainly.com/question/2031508

#SPJ4

The complete question is -

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

a) h = −10sin(π15t)+35  

b) h = −10sin(πt)+35

c) h = 10sin(π15t)+35

d) h = 10sin(πt)+35

6 0
2 years ago
The first term of an arithmetic sequence is 4 and the tenth term is 67.
serg [7]

Answer:

d = 7

Step-by-step explanation:

The nth term of an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Give a₁₀ = 67 and a₁ = 4 , then

a₁ + 9d = 67

4 + 9d = 67 ( subtract 4 from both sides )

9d = 63 ( divide both sides by 9 )

d = 7

8 0
2 years ago
What is the discount and sale price of a $300 item that has been discounted 10%?
Paha777 [63]
270 I think if not my bad
7 0
2 years ago
Read 2 more answers
Write three more expressions using exponents that evaluate to 216.
kow [346]
6^{3}
216^{1}
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3 years ago
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