To determine which expression correctly represents the value of [tex]\( g \)[/tex] given that [tex]\( j = h \)[/tex] and [tex]\( k = m \)[/tex], let's evaluate each of the expressions one by one:
1. Expression 1: [tex]\( g = \frac{f}{2} \)[/tex]
- In this expression, there is no information provided that directly relates [tex]\( g \)[/tex] to [tex]\( f \)[/tex].
- Without any specific relationship between [tex]\( g \)[/tex] and [tex]\( f \)[/tex], we cannot determine if this expression is correct based on the given conditions ([tex]\( j = h \)[/tex] and [tex]\( k = m \)[/tex]).
2. Expression 2: [tex]\( g = 2t \)[/tex]
- Similar to the first expression, there is no information given that connects [tex]\( g \)[/tex] to [tex]\( t \)[/tex].
- Therefore, we cannot validate this expression as correct with the available information.
3. Expression 3: [tex]\( g = \frac{J}{h} \)[/tex]
- This expression involves [tex]\( J \)[/tex] and [tex]\( h \)[/tex]. Although we know [tex]\( j = h \)[/tex], we do not have any information that relates [tex]\( J \)[/tex] to [tex]\( j \)[/tex] or [tex]\( h \)[/tex].
- So, we cannot confirm if this expression correctly represents [tex]\( g \)[/tex].
4. Expression 4: [tex]\( g = \frac{k}{m} \)[/tex]
- Given that [tex]\( k = m \)[/tex], we can substitute [tex]\( m \)[/tex] for [tex]\( k \)[/tex] in the expression:
[tex]\[
g = \frac{k}{m} \Rightarrow g = \frac{m}{m} = 1
\][/tex]
- This simplifies to [tex]\( g = 1 \)[/tex].
Given our evaluation above, the fourth expression [tex]\( g = \frac{k}{m} \)[/tex] correctly represents the value of [tex]\( g \)[/tex] based on the given conditions [tex]\( j = h \)[/tex] and [tex]\( k = m \)[/tex]. Hence, the correct expression is:
Expression 4: [tex]\( g = \frac{k}{m} \)[/tex]
