Given that 
and 
, we can say the following:
Now, remember what happens if we have a negative square root: it becomes an imaginary number. We don't want this, so we want to make sure whatever is under a square root is greater than 0 (given we are talking about real numbers only).
Thus, let's set what is under both square roots to be greater than 0:
Since both of the square roots are in the same function, we want to take the union of the domains of the individual square roots to find the domain of the overall function.
Now, let's look back at the function entirely, which is:
Since 
is on the bottom of the fraction, we must say that 
, since the denominator can't equal 0. Thus, we must exclude 
from the domain.
Thus, our answer is Choice C, or 
.
<em>If you are wondering why the choices begin with the 
symbol, it is because this is a way of representing that 
lies within a particular set.</em>
140 pounds * 6 feet = 112 pounds * x feet
x feet = (140 * 6) / 112
x = 7.5 feet
Volume is length x width x height. It measures how much space it can hold inside of a shape.
The formula of an area of a rectangle:
A = wl
We have l = w - 4 and A = 21.
Substitute:
w(w - 4) = 21 <em>use distributive property</em>
(w)(w) + (w)(-4) = 21
w² - 4w = 21 <em>subtract 21 from both sides</em>
w² - 4w - 21 = 0
w² - 7w + 3w - 21 = 0
w(w - 7) + 3(w - 7) = 0
(w - 7)(w + 3) = 0 ↔ w - 7 = 0 ∨ w + 3 = 0
w = 7 ∨ w = -3 < 0
l = w - 4 → l = 7 - 4 = 3
<h3>Answer: the length = 3 u.</h3>
