Rational numbers are numbers that can be expressed as a fraction (ratio). Irrational numbers can not be expressed like that (like sqrt(2)).
To prove your statement, assume the opposite until you have a contradiction.
If the result of adding them would be rational, then your irrational number can be expressed as the difference of two rational numbers, which itself is also a rational number. That cannot be, because it should be an irrational number. This contradiction forces that rational + irrational = irrational.
You can reason the same way for multiplication. Suppose rational * irrational = rational, you find that your irrational can be expressed as the fration of two rationals, which is a contradiction.
Answer: B, 64
Step-by-step explanation:
To simplify this, first simplify all the parenthesis and multiply.
When an entire expression is raised to another exponent, everything in the parentheses is raised to that degree.
As such:
![(2w^{-2}})^3 = 8 * w^{-6](https://tex.z-dn.net/?f=%282w%5E%7B-2%7D%7D%29%5E3%20%3D%208%20%2A%20w%5E%7B-6)
You can then multiply this and the other expression:
![8w^{-6} * 8w^6 = 8 * 8 * w^6 * w^{-6} = 64 * w^0](https://tex.z-dn.net/?f=8w%5E%7B-6%7D%20%2A%208w%5E6%20%3D%208%20%2A%208%20%2A%20w%5E6%20%2A%20w%5E%7B-6%7D%20%3D%2064%20%2A%20w%5E0)
As such, the correct choice is B. The 'w's cancel each other out.
Answer:
Hi there!
Your answer is:
88,000
Step-by-step explanation:
88457
The bolded is the thousands place
8<u>8</u>457
457 is <u>less</u><u> </u><u>than</u> 500, so it's rounded down
88,000
Hope this helps
We have the following function
![f(x)=\frac{3}{x+2}-\sqrt{x-3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B3%7D%7Bx%2B2%7D-%5Csqrt%7Bx-3%7D)
We want to know what is the value of f(x) when x is 19
![f(19)=\frac{3}{19+2}-\sqrt{19-3}=1/7-4=\boxed{-27/7}](https://tex.z-dn.net/?f=f%2819%29%3D%5Cfrac%7B3%7D%7B19%2B2%7D-%5Csqrt%7B19-3%7D%3D1%2F7-4%3D%5Cboxed%7B-27%2F7%7D)
If you have additional questions feel free to ask.
Hope this helps.