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Mrac [35]
2 years ago
9

The sum or product of a non-zero rational number and an irrational number is always

Mathematics
2 answers:
vazorg [7]2 years ago
8 0
The product of a non-zero rational and an irrational number is always irrational (2)
frosja888 [35]2 years ago
8 0

Answer:

Option 2 - Irrational              

Step-by-step explanation:

To find :  The sum or product of a non-zero rational number and an irrational number is always  

Solution :

By the statement,

→ "The sum of a rational number and an irrational number is irrational."

Example : Let a rational number 3 and irrational number \sqrt{5}

Sum of rational and irrational number

3+\sqrt{5}= 3+2.236067977.....=5.236067977....

5.236067977.... is a irrational number as if you add a non-repeating and non-terminating decimal to a repeating decimal, you will have a repeating decimal.

→ "The product of a non-zero rational number and an irrational number is irrational."

Example : Let a rational number 3 and irrational number \sqrt{5}

Sum of rational and irrational number

3\times\sqrt{5}= 3\times2.236067977.....=6.708203931.....

6.708203931...... is a irrational number as If you multiply any irrational number by the rational number it gives you irrational except zero which is rational.

Therefore, Option 2 is correct.

The sum or product of a non-zero rational number and an irrational number is always  irrational.

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Please i need help quick thank you
Veronika [31]

Answer:

I got positive for both. But I’m not sure

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Evaluate and solve <br> f(3)+f(0) when f (x) = 10x – 5
Monica [59]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

f(x) = 10x - 5

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f(3) = 10(3) - 5

f(3) = 30 - 5

f(3) = 25

_________________________________

f(0) = 10(0) - 5

f(0) =  - 5

##############################

f(3) + f(0) = 25 - 5

f(3) + f(0) = 20

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6 0
2 years ago
Use the identity tan(theta) = sin(theta) / cos(theta) to show that tan(???? + ????) = tan(????)+tan(????) / 1−tan(????) tan(????
VMariaS [17]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following indentity:

tan(x+y) = \frac{tan (x) + tan(y)}{1- tan(x) tan(y)}

So we need to begin with the definition of tangent, we know that tan (x) =\frac{sin(x)}{cos(x)} and we can do this:

tan (x+y) = \frac{sin (x+y)}{cos(x+y)}   (1)

We also have the following identities:

sin (a+b) = sin (a) cos(b) + sin (b) cos(a)

cos(a+b)= cos(a) cos(b) - sin(a) sin(b)

Now we can apply those identities into equation (1) like this:

tan (x+y) =\frac{sin (x) cos(y) + sin (y) cos(x)}{cos(x) cos(y) - sin(x) sin(y)}   (2)

We can divide numerator and denominator from expression (2) by \frac{1}{cos(x) cos(y)} we got this:

tan (x+y) = \frac{\frac{sin (x) cos(y)}{cos (x) cos(y)} + \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{cos(x) cos(y)}{cos(x) cos(y)} -\frac{sin(x)sin(y)}{cos(x) cos(y)}}

And simplifying we got:

tan (x+y) = \frac{tan(x) + tan(y)}{1-tan(x) tan(y)}

And that complete the proof.

8 0
3 years ago
Write the equation of the line in slope-intercept form using y=mx+b​
Ierofanga [76]

Answer:

y= -5x + 2

Step-by-step explanation:

the slope is heading downwards, and down five units for each one across (hence m=5) and the y-intercept is 2 (hence the 2)

3 0
2 years ago
This 7-digit number is 8,920,000 when rounded to the nearest ten thousand. the digits to the tens and hundreds places are the le
Aliun [14]
The 7-digit number we are looking for is 8,92a,bcd



"The value of the thousands digit is double that of the ten thousands digit."

The value of the ten thousands digit is 2. Thus the value of the thousands digit is 4.



The 7-digit number we are looking for is 8,924,bcd



"The sum of all its digits is 24."

8+9+2+4+b+c+d = 23 + b+ c+ d

Thus b+c+d = 1



The digits to the tens and hundreds places are the least and same value.

These two digits (b and c) must be 0, because b+c+d = 1

That means that the digit "d" must be equal to 1.



The 7-digit number we are looking for is 8,924,001



This number is the only number that satisfies all the conditions stated in the question.
3 0
3 years ago
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