Question

6 multiple choice 2 points what is the decimal form of 2.16×10^(-4)? 2,160 0.000216 21,600 0.0000216 7 multiple choice 2 points an example of an irrational number is -11/6 0 √5 5.3 8 multiple choice 2 points what is the value of x in the equation 5 - 3x = -7? -4 2/3 4 -2/3

Explanation:

Step1: Recall scientific - notation rule

For a number in scientific notation $a\times10^{-n}$ ($1\leqslant a<10$, $n$ is a positive integer), we move the decimal point $n$ places to the left. For $2.16\times10^{-4}$, we move the decimal point 4 places to the left.
$2.16\times10^{-4}=0.000216$

Step2: Recall the definition of irrational numbers

A rational number can be written as a fraction $\frac{p}{q}$ where $p,q\in\mathbb{Z}$ and $q
eq0$. $-\frac{11}{6}$ is a fraction, 0 is an integer (and can be written as $\frac{0}{1}$), $5.\overline{3}=\frac{16}{3}$ is a repeating - decimal (rational). $\sqrt{5}$ cannot be written as a fraction of two integers, so it is irrational.

Step3: Solve the linear equation

Given $5 - 3x=-7$. First, subtract 5 from both sides:
$5-3x - 5=-7 - 5$
$-3x=-12$. Then divide both sides by - 3:
$x = 4$

Answer:

1. B. 0.000216
2. C. $\sqrt{5}$
3. C. 4