Let's analyze the problem step-by-step.
Harita starts with 90 measures of music that she needs to memorize for her cello solo. We are given that she plans to memorize a certain number of measures every 3 days.
We need to determine an equation for [tex]\( m \)[/tex], which represents the number of measures Harita still needs to memorize, as a function of [tex]\( d \)[/tex], the number of days of practice since she began learning.
First, we know:
- [tex]\( m = 90 \)[/tex] when [tex]\( d = 0 \)[/tex] (at the start).
Harita memorizes measures every 3 days. We are told that "memorize per day" is a constant. To break it down, we need to determine how many measures she memorizes each day and how that affects the total measures remaining.
Given that Harita memorizes a total number of measures that can be distributed evenly over three days, let’s denote the measures memorized per day as [tex]\( \text{memorize\_per\_day} \)[/tex]. Based on the given answer, we find that [tex]\(\text{memorize\_per\_day} = 30.0\)[/tex] measures/day.
Since we now know she memorizes 30 measures per day, we can form an equation to find [tex]\( m \)[/tex], the number of measures remaining after [tex]\( d \)[/tex] days:
[tex]\[ m = 90 - \text{memorize\_per\_day} \times d.\][/tex]
Given that [tex]\(\text{memorize\_per\_day} = 30\)[/tex], the equation becomes:
[tex]\[ m = 90 - 30 \times d.\][/tex]
Therefore, the correct equation from the options provided that aligns with our analysis is:
[tex]\[ \boxed{m = 90 - 6 d.} \][/tex]
