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.

-2

7 - 9 = -2

reversed:

-2 + 9 = 7

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.