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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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If the area of an equilateral triangle is 9root3 cm square find its side

kobusy [5.1K]

Answer:

6 cms.

Step-by-step explanation:

If the side of an equilateral triangle is 2x cm then its height is √3x and its base is 2x.

Area = 1/2 * base * height

9√3 = 1/2 * 2x * √3x

9√3 = x * √3x

9 = x^2

x = 3

So length of each side = 2*3 = 6.

x = 9

7 0

3 years ago

20 POINTS! Please help

Marysya12 [62]

The complete square will be $(x-3)^{2}$ = 3

Step-by-step explanation:

Given,

$2x^{2} -12x+12=0$

or, $x^{2} -6x+6=0$ [ by eliminating 2 from both the sides]

To make it square

$x^{2} -6x+6=0$

or, $x^{2} -2xX3+9-9+6=0$ [ $(a+b)^{2}=a^{2} +2ab+b^{2}$

or, $(x-3)^{2}$ = 9-6

or, $(x-3)^{2}$ = 3

Hence the correct option is B

3 0

4 years ago

Which of the following expressions represents "no more than 5"?

777dan777 [17]

Answer:

Ox>5

x is less than 5

means nothing more than 5 but anything less than 5

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3 years ago

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agasfer [191]

Answer:

(0.5,0) , (-3,0) ,and (0,-1.5)

Step-by-step explanation:

Just look where the points touch the x- and y-axis.

It touches twice on the x- and once on the y-axis.

Hope that helps!

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3 years ago

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Afina-wow [57]

Answer:

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Step-by-step explanation:

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Hope this helps! :D

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3 years ago