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.

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.