Let's analyze the given problem step-by-step:
We have the following equalities:
[tex]\[ j = h \][/tex]
[tex]\[ k = m \][/tex]
We are provided with four possible expressions for [tex]\( g \)[/tex]:
1. [tex]\( g = \frac{f}{2} \)[/tex]
2. [tex]\( g = 2f \)[/tex]
3. [tex]\( g = \frac{j}{h} \)[/tex]
4. [tex]\( g = \frac{k}{m} \)[/tex]
To determine which expressions accurately represent the value of [tex]\( g \)[/tex], we need to evaluate each one in the context of the given equalities.
3. [tex]\( g = \frac{j}{h} \)[/tex]
Since [tex]\( j = h \)[/tex], substituting [tex]\( j \)[/tex] with [tex]\( h \)[/tex] in the expression results in:
[tex]\[ g = \frac{j}{h} = \frac{h}{h} \][/tex]
Simplifying this gives us:
[tex]\[ g = 1 \][/tex]
4. [tex]\( g = \frac{k}{m} \)[/tex]
Given [tex]\( k = m \)[/tex], substituting [tex]\( k \)[/tex] with [tex]\( m \)[/tex] in the expression yields:
[tex]\[ g = \frac{k}{m} = \frac{m}{m} \][/tex]
Simplifying this also gives:
[tex]\[ g = 1 \][/tex]
Having identified the equivalent expressions, it follows that both:
[tex]\[ g = \frac{j}{h} \][/tex]
and
[tex]\[ g = \frac{k}{m} \][/tex]
are valid given the equalities [tex]\( j = h \)[/tex] and [tex]\( k = m \)[/tex].
Thus, the expressions that correctly represent the value of [tex]\( g \)[/tex] are:
[tex]\[ g = \frac{j}{h} \][/tex]
and
[tex]\[ g = \frac{k}{m} \][/tex]
These expressions simplify to the value of 1.
