A construction crew built 9 3/4 miles of road in 4 1/2 days. What is the unit rate in miles per day
2 answers:
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Answer:
2n - 11
Step-by-step explanation:
Note there is a common difference d between consecutive terms of the sequence, that is
d = - 7 - (- 9) = - 5 - (- 7) = - 7 + 9 = - 5 + 7 = 2
This indicates the sequence is arithmetic with n th term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 9 and d = 2, thus
= - 9 + 2(n - 1) = - 9 + 2n - 2 = 2n - 11
Let be the dimensions of the rectangle. We know the equations for both area and perimeter:
So, we have the following system:
From the second equation, we can deduce
Plug this in the first equation to get
Refactor as
And solve with the usual quadratic formula to get
Both solutions are feasible, because they're both positive.
If we chose the positive solution, we have
If we choose the negative solution, we have
So, we're just swapping the role of and
. The two dimensions of the rectangle are
and