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umka21 [38]
3 years ago
14

Find the value of x for which ABCD must be a parallelogram.

Mathematics
1 answer:
Musya8 [376]3 years ago
5 0

The value of x is 13°.

Solution:

Given ABCD is a parallelogram.

⇒ AD || BC and AC is a transversal line.

<u>Property of parallel lines:</u>

<em>If two parallel lines cut by a transversal, then the alternate interior angles are equal.</em>

∠DAC = ∠CAB

(4x - 1)° = (x + 38)°

4x° - 1° = x° + 38°

Add 1° on both sides.

4x° - 1° + 1° = x° + 38° + 1°

4x° = x° + 39°

Subtract x° from both sides.

4x° - x° = x° + 39° - x°

3x° = 39°

Divide by 3° on both sides.

x = 13°

The value of x is 13°.

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Let K and T be the current ages of two siblings Katie and Thomas Katie is currently twice the age of Thomas. In 6 years Katie wi
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Answer:

Here, K represents the current age of Katie and T represents the current age of Thomas.

(a)

As per the statement:

Katie is currently twice the age of Thomas.

⇒K = 2T                ......[1]

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K+6 = 4T

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A system of equations that describe the situation is:

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(b)

To find the solution:

equate [1] and [2] we have;

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3 years ago
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According to a survey conducted by Netpop Research, 65% of new car buyers use online search engines as part of their car-buying
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(b) 0.46

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Let's first list the probabilities of each event:

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Buyers that use search engines AND skip test drives = 0.65 * 0.11 = 0.07

(a) To find this probability, we simply need to add the probabilities of the above conditions that meet the criteria of the question. Since all of the above conditions meet the criteria set by the question, we have:

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(b) The probability of buyers that do not use search engines = 1 - 0.65 = 0.35

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(c) Probability of buyers buyers that do not skip test drive = 1 - 0.11 = 0.89

Probability of buyers using online search engine AND not skipping the test drive = 0.65 * 0.89 = 0.58

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5 0
3 years ago
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