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3 years ago

Below is a proof showing that the sum of a rational number and an irrational number is an irrational number.

Mathematics

2 answers:

ankoles [38]3 years ago

4 0

Answer:

Step-by-step explanation:

To prove: The sum of a rational number and an irrational number is an irrational number.

Proof: Assume that a + b = x and that x is rational.

Then b = x – a = x + (–a).

Now, x + (–a) is rational because addition of two rational numbers is rational (Additivity property).

However, it was stated that b is an irrational number. This is a contradiction.

Therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number.

Hence, the sum of a rational number and an irrational number is irrational.

Goryan [66]3 years ago

4 0

Answer:

I believe the answer is B

Step-by-step explanation:

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-2n + 1.8 = 3.2
Subtract 1.8 from both sides
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Check your work:
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<h3>Further explanation</h3>

We will solve the problem of the measures of angles in the triangle.

Recall this condition:

The acute angle ⇒ an angle of less than 90°.
The right angle ⇒ an angle of exactly 90°.
A right triangle ⇒ a triangle in which one angle is a right angle.
The interior angles ⇒ the angles inside a triangle.
All the interior angles in a triangle , i.e., $\boxed{ \ \angle A + \angle B + \angle C = 180^0 \ }$

<u>Given that:</u>

The ratio of the measure of the acute angle in a right triangle is ¹/₂.

<u>Question:</u>

Find the measures of the two angles.

<u>The Process:</u>

We call it the triangle ABC. An interior angle inside is a right angle, e.g., ∠A = 90°.

From the ratio of two other acute angles, i.e., 1: 2, we call it ∠B = x and ∠C = 2x.

Let's arrange the three angles in ABC triangle as follows:

$\boxed{ \ 90^0 + x + 2x = 180^0 \ }$

Both sides subtracted by 90°.

$\boxed{ \ x + 2x = 180^0 - 90^0 \ }$

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Both sides divided by 3.

We get $\boxed{ \ x = 30^0 \ }$

We substitute the value of x back into B and C.

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We have succeeded in getting the measures of the two angles.

<h3>Learn more</h3>

Undefined terms needed to define angles brainly.com/question/3717797
What is 270° converted to radians brainly.com/question/3161884
A triangle is rotated 90° about the origin brainly.com/question/2992432

Keywords: the ratio, the measure, the acute angle, a right triangle, 1/2, 180°, 90°, 30°, 60°, the interior angles

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