Let's analyze the given expression step-by-step to determine the coefficients of each variable. The expression provided is:
[tex]\[ 6a - \frac{3}{4} + 7.5 - \frac{b}{3} \][/tex]
First, let's remember that in algebra, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic term.
1. Identify the coefficients for each variable:
- For the variable [tex]\( a \)[/tex]: Look at the term that contains [tex]\( a \)[/tex]. The coefficient for [tex]\( a \)[/tex] is the number in front of [tex]\( a \)[/tex]. Here, it is [tex]\( 6 \)[/tex].
- For the variable [tex]\( b \)[/tex]: Look at the term that contains [tex]\( b \)[/tex]. The term is [tex]\( -\frac{b}{3} \)[/tex]. This can be rewritten as [tex]\( -\frac{1}{3}b \)[/tex]. Hence, the coefficient for [tex]\( b \)[/tex] is [tex]\( -\frac{1}{3} \)[/tex].
2. Identify the constant terms:
- The constant term [tex]\(-\frac{3}{4}\)[/tex] is just a constant and has no variable associated with it.
- The constant term [tex]\( 7.5 \)[/tex] is also just a constant and has no variable associated with it.
- These constants do not affect the coefficients of the variable terms.
3. Conclusion:
- The coefficient of [tex]\( a \)[/tex] is [tex]\( 6 \)[/tex].
- The coefficient of [tex]\( b \)[/tex] is [tex]\( -\frac{1}{3} \)[/tex].
Thus, the correct coefficients for the variables in the expression are:
[tex]\[
6 \quad \text{and} \quad -\frac{1}{3}
\][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{6 \text{ and } -\frac{1}{3}} \][/tex]
