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4 years ago

Why is 5.432523421672389... considered an irrational number?

Mathematics

2 answers:

vlabodo [156]4 years ago

8 0

Answer:

This number is considered an irrational number because it cannot be expressed as a ratio between two numbers, meaning that it cannot be wriiten as a fraction as there is an infinite number of non repeating digits.

Step-by-step explanation:

Trava [24]4 years ago

4 0

Answer:

An irrational number is infinte and has no clear pattern. 3.33333 or .686868686868 would not be considered irrational because there is a clear pattern, but 5.432523421672389... would not be considered rational because the numbers it consists of are all random.

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For what values of x does<br> 25^x = 5^(x2-3?)

lidiya [134]

Answer:

Step-by-step explanation:

25^x = 5^(x^2 - 3)

<=> (5^2)^x = 5^(x^2 - 3)

<=> 5^(2x) = 5^(x^2 - 3)

<=> 2x = x^2 - 3

<=> x^2 - 2x - 3 = 0

<=> x^2 + x - 3x - 3 = 0

<=> x(x + 1) - 3(x + 1) = 0

<=> (x - 3)(x + 1) = 0

<=> x = 3 or x = -1

I hope this helps!

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3 years ago

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Answer:

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3 years ago

Read 2 more answers

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Dominik [7]

He spent $0.42 :)
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3 years ago

Graph abc and its image after a rotation of 180 about the origin

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3 years ago

In each diagram below, determine whether the triangles are congruent, similar, but not congruent, or not similar. If you claim t

Nadya [2.5K]

Part a

Angle ABC = angle CDA (given by the angle markers)

Angle BAC = angle DCA (alternate interior angles)

Segment AC = segment AC (reflexive property)

Through AAS (angle angle side) we can prove the two triangles are congruent. We have a pair of congruent angles, and we have a pair of congruent sides that are not between the previously mentioned angles.

If two triangles are congruent, they are always similar as well (scale factor = 1).

The same cannot be said the other way around. Not all similar triangles are congruent.

<h3>Answer: Congruent</h3>

======================================================

Part b

Angle FGH = angle JIH (both shown to be 50 degrees)

Angle FHG = angle JHI (vertical angles)

We have enough information to prove the triangles to be similar triangles. This is through the AA (angle angle) similarity rule. Since FG and JI are different lengths, this means the triangles are not congruent.

<h3>Answer: Similar but not congruent</h3>

======================================================

Part c

For each right triangle shown, divide the longer leg over the shorter leg

larger triangle: (long leg)/(short leg) = 6/3 = 2

smaller triangle: (long leg)/(short leg) = 3/2 = 1.5

The two results are different, so the sides are not in proportion to one another, therefore the triangles are not similar.

Any triangles that are not similar will also never be congruent.

<h3>Answer: Not similar</h3>

======================================================

Part d

Use the pythagorean theorem to find that PQ = 5 and KL = 12

We have two triangles with corresponding sides that are the same length

So we use the SSS (side side side) triangle congruence theorem to prove the triangles congruent. The triangles are also similar triangles (scale factor = 1)

<h3>Answer: Congruent</h3>

======================================================

<h3>Summary of the answers:</h3><h3>a. Congruent</h3><h3>b. Similar but not congruent</h3><h3>c. Not similar</h3><h3>d. Congruent </h3>

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3 years ago