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3 years ago

Why is the product of a rational number and an irrational number Irrational?

Mathematics

2 answers:

Llana [10]3 years ago

5 0

Answer:

Because the product is always non-termination,non-repeating decimal.

Step-by-step explanation:

If we have $a$ is irrational; $b$ is rational such that $b \neq 0$ , then $a \cdot b$ is irrational.

A way to represent this is:

$a\in\mathbb{R}\setminus\mathbb{Q}, b\in\mathbb{Q},ab\in\mathbb{Q}\implies a\in\mathbb{Q}\implies\text{Contradiction}\therefore ab\not\in\mathbb{Q}.$

Note that we have a contradiction, because $a$ is not a rational number, as I stated in the beginning. Therefore, ab is irrational.

Marta_Voda [28]3 years ago

5 0

Answer: A

Step-by-step explanation:

Multiplying an irrational number by a rational number will always be an irrational number because irrational numbers do not repeat and terminate.

So for example multiplying pi by a rational like two you will have an irrational number because pi is an irrational number.

$\pi * 2$ = 6.28318530718 as you could see that is an irrational number because there is no repetition or termination.

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Write a linear equation in standard form for the line that goes through (4,3) and (8,2).

notsponge [240]

Answer:

Ax + By = C

A, B and C can be any number--including negative numbers, zero and one! So examples of standard form can look like this:

3_x_ + 7_y_ = 10, where A = 3, B = 7 and C = 10.

Or they can look like this:

x + 5_y_ = 6. In this case, A = 1, B = 5 and C = 6.

Or this:

8_y_ = 9. In this case, A = 0, which is why x does not appear in the equation. B = 8 and C = 9, as you would expect.

And here's one more:

3_x_ − 5_y_ = 12. Here, A = 3, B = −5 and C = 12. Notice that in this case, B is negative five!

The standard form of a linear equation is Ax + By = C, where A, B and C can be any number.

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4 years ago

Show work and find the value of the area of the circle with a 10 cm diameter.

Akimi4 [234]

Answer:

A = 78.54cm²

Step-by-step explanation:

A = π r²

D = 2r

A = $\frac{1}{4}$ π × d² = $\frac{1}{4}$ × π × 10² = 78.53982cm² = 78.54cm²

I hope this helps. : )

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4 years ago

A group of roommates decide to split the cost of a new sofa. If s is the cost of the sofa and n is the number of roommates, the

tiny-mole [99]

B. $238.75 because $955 divided by 4 is $238.75

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4 years ago

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For a Geometric Series explain how you can tell if the series converges or diverges as you keep adding an infinite number of ter

Sav [38]

It will converge if the common factor r is between 0 and 1.
For example:-
A GS with first term a1 = 2 and d = 1/2, the terms are:-

2 , 1 , 1/2, 1/4, 1/8,1/16 and so on

Each term gets smaller and smaller and they will become very small - close to 0. The sum will converge to a certain value also.
In this case it will converge to 2 /( 1 - 1/2) = 4

If d > 1 the terms will increase without bounds and the sum gets bigger and bigger . The series diverges.

for example 2, 8, 32, 128, 512 .... where a1 = 2 and d = 4.

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4 years ago

Please hurry Solve the inequality. ∣ 3g−4∣ >2

Galina-37 [17]

Answer:

d. d<2/3 or g>2

Step-by-step explanation: I got it right on the test!

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3 years ago