Final answer:
The student's question involves calculating the remaining area to be mowed based on a linear equation. The results show 1326 acres left after 20 hours, 1230 acres left after 100 hours, and it would take 1125 hours to mow all 1345 acres by one person.
Step-by-step explanation:
The question is related to the mathematical concept of linear equations and graphing the relationship between work done, in this case, mowing lawns, and income earned. We'll address the exercises based on the given linear relation ŷ = 1350 - 1.2x.
Exercise Responses:
The question is related to the mathematical concept of linear equations and graphing the relationship between work done, in this case, mowing lawns, and income earned. We'll address the exercises based on the given linear relation ŷ = 1350 - 1.2x.
- To find the acres left after 20 hours of work, substitute x = 20 into the equation to get ŷ = 1350 - 1.2(20). This gives ŷ = 1350 - 24, which equals to 1326 acres remaining.
- To find the acres left after 100 hours of work, substitute x = 100 into the equation to get ŷ = 1350 - 1.2(100). This gives ŷ = 1350 - 120, which equals 1230 acres remaining.
- To find the number of hours to mow all lawns, set ŷ = 0 and solve for x. The equation becomes 0 = 1350 - 1.2x, thus x = 1350 / 1.2. Calculating this yields x = 1125 hours to mow all the lawns.
Note that these calculations are based on the assumption that there is only one person mowing the lawns.