Without simplifying, select all the expressions that represent a rational number. Group of answer choices LaTeX: 4\frac{2}{3}+\frac{\sqrt{3}}{9} 4 2 3 + 3 9 4 2 3 + 3 9 4 2 3 + 3 9 LaTeX: 4\frac{2}{3}\times\frac{8}{\sqrt{3} } 4 2 3 × 8 3 4 2 3 × 8 3 4 2 3 × 8 3 LaTeX: 4\frac{2}{3}-\frac{\sqrt{4}}{8} 4 2 3 − 4 8 4 2 3 − 4 8 4 2 3 − 4 8 LaTeX: 4\frac{2}{3}\times\frac{\sqrt{3}}{9 } 4 2 3 × 3 9 4 2 3 × 3 9 4 2 3 × 3 9 LaTeX: 4\frac{2}{3}\div\frac{\sqrt{4}}{8}

Option C.

Step-by-step explanation:

We know the following properties,

1. Product of an irrational number and a non-zero rational number is always an irrational number.

2. Sum of a rational and an irrational number is always an irrational number.

3. Sum or products of rational numbers are always a rational number.

In option A,

Here, is an irrational number.

is an irrational number using property 1.

is an irrational number using property 2.

So, using the above properties we can say that this expression represents an irrational number.

Similarly,

In option B,

Here, is an irrational number. So, using the above properties we can say that this expression represents an irrational number.

In option C,

Here, , which is a rational number.

So, this expression represents a rational number using property 3.

In option D,

Here, is an irrational number. So, using the above properties we can say that this expression represents an irrational number.

Therefore, the correct option is C.

a - base

b - exponent

so,

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.