Question

Can someone explain this?

Answer 1

Hello!

The answer is:

The missing step is the step shown in the last option:

D. $324=0.042x+16$

Why?

To find which is the missing step, we need to remember that to cancel a square root, we need to elevate it, so:

Starting from the last step before the missing step, we have:

$-18=-\sqrt{0.042x+16}$

In order to calculate the value of the variable (x) we need to square both sides of the equation, since squaring a root will cancel the root.

We must remember the following properties:

$\sqrt{a^{m} }=a^{\frac{m}{2}}\\\\(a^{b})^{c}=a^{b*c}$

Now, finding the missing step, we need to find what to do in order to get the expression of the following step.

So, squaring both sides of the equation in order to cancel the square root and isolate the variable, we have:

$-18=-\sqrt{0.042x+16}\\\\(-18)^{2} =(-\sqrt{0.042x+16})^{2} \\324=0.042x+16\\324-16=0.042x\\\\x=\frac{304}{0.042}=7333$

Hence, we found the the missing step is:

D. $324=0.042x+16$

Have a nice day!