Final answer:
To solve for n, given that m is the midpoint of JK and MK=5.45 while JK is expressed as 5n-1.1, we equate half of JK to MK and solve the resulting equation, which results in n being 2.4.
Step-by-step explanation:
To find the value of n when it is given that m is the midpoint of line segment JK, with JK having a length of (5n - 1.1) and MK having a length of 5.45, we use the property of the midpoint which tells us that the segment is divided into two equal parts. Therefore, the length of MK is equal to half the length of JK. Setting these two expressions equal to each other allows us to solve for n.
By substituting known values, we get:
5.45 = (5n - 1.1) / 2
Then, multiply both sides of the equation by 2 to clear the fraction:
2 * 5.45 = 5n - 1.1
Solving for n we have:
10.9 = 5n - 1.1
Add 1.1 to both sides:
10.9 + 1.1 = 5n
12.0 = 5n
Divide both sides by 5:
n = 12.0 / 5
Finally, we find that n = 2.4.