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Bingel [31]
3 years ago
5

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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Well, we just need to perform the operations:

  • Multiplication: 1\cdot 2 \cdot 3 \cdot 4 \cdot 5 = 120
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So, if you add all the numbers together you get

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See image for question.​
kotegsom [21]

Answer:

<h3>#7</h3>

(a)

<u>Sample space:</u>

  • 1*1, 1*2, 1*3, 1*4,
  • 2*1, 2*2, 2*3, 2*4,
  • 3*1, 3*2, 3*3, 3*4,
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(b)

  • (i) P(even) = 12/16 = 3/4
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  • (iii) P(perfect square) = 4/16 = 1/4
<h3>#8</h3>

(a) <u>Sample space:</u>

  • 1T, 1H, 2T, 2H, 3T, 3H, 4T, 4H

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(b)

(i) 1T, 3T

  • P(T and odd) = 2/8 = 1/4

(ii) 1H, 4H

  • P(H and square) = 2/8 = 1/4

(iii) 1H, 2H, 3H, 4H

  • P(H) = 4/8 = 1/2

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