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user100 [1]
3 years ago
9

Given: m∠A = m∠C = 90° AB ║ DC Prove: ∆ABD ≅ ∆CBD

Mathematics
1 answer:
Genrish500 [490]3 years ago
4 0

Answer:

Angle-Angle-Side (AAS)

Step-by-step explanation:

Given triangles; ΔABD and ΔCBD

  <A = <C = 90^{0} (right angle property)

   AB ║ DC (given)

Then,

    DA ║ CB

   <B ≅ <D (congruent property)

    DB ≅ BD (similarity property)

    <D + <B = <B + <D (complementary angles, and property of triangles)

Therefore by Angle-Angle-Side (AAS),

                 ∆ABD ≅ ∆CBD

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Calculate the expected value E(X) of the given random variable X. X is the higher number when two dice are rolled, or the common
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Answer:

4.4722

Step-by-step explanation:

The following table shows the 36 elements of the sample space of the experiment

\left[\begin{array}{cccccccc}&1&2&3&4&5&6\\--&--&--&--&--&--&--\\1\;|&1&2&3&4&5&6\\2\;|&2&2&3&4&5&6\\3\;|&3&3&3&4&5&6\\4\;|&4&4&4&4&5&6\\5\;|&5&5&5&5&5&6\\6\;|&6&6&6&6&6&6\end{array}\right]

From this table we can compute the probabilities :

P(X = 1) = 1/36

P(X = 2) = 3/36

P(X = 3) = 5/36

P(X = 4) = 7/36

P(X = 5) = 9/36

P(X = 6) = 11/36

So the expected value equals

1P(X=1)+2P(X=2)+3P(X=3)+4P(X=4)+5P(X=5)+6P(X=6) =

= 1/36 + 6/36 + 15/36 + 28/36 + 45/36 + 66/36 = 161/36 =  

4.4722

7 0
3 years ago
If x + y = 5 and at the same time 2x - y = 7. find the value of x
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x = 2y − 2

Step-by-step explanation:

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5 0
2 years ago
A school district signs a contract to purchase 50 of the electric typewriters (normally selling for $129.95) from ABC at a quant
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Total purchase price of the typewriters after the discount = (100 - 18) x 6,497.50

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To learn more about how to calculate discounts, please check: brainly.com/question/26061308

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