To solve the equation [tex]\( d = rt \)[/tex] for [tex]\( r \)[/tex], we need to isolate [tex]\( r \)[/tex] on one side of the equation. Here are the steps to do this:
1. Start with the given equation:
[tex]\[ d = rt \][/tex]
2. To isolate [tex]\( r \)[/tex], we need to get rid of [tex]\( t \)[/tex] on the right-hand side. We can do this by dividing both sides of the equation by [tex]\( t \)[/tex]:
[tex]\[ \frac{d}{t} = \frac{rt}{t} \][/tex]
3. When we divide [tex]\( rt \)[/tex] by [tex]\( t \)[/tex], the [tex]\( t \)[/tex] terms on the right-hand side cancel each other out, leaving:
[tex]\[ \frac{d}{t} = r \][/tex]
4. Therefore, the equation for [tex]\( r \)[/tex] in terms of [tex]\( d \)[/tex] and [tex]\( t \)[/tex] is:
[tex]\[ r = \frac{d}{t} \][/tex]
Given the options:
A. [tex]\( r = \frac{t}{d} \)[/tex]
B. [tex]\( r = d - t \)[/tex]
C. [tex]\( r = dt \)[/tex]
D. [tex]\( r = \frac{d}{t} \)[/tex]
The correct answer is:
D. [tex]\( r = \frac{d}{t} \)[/tex]
