Geometry Basics Homework 2: Segment Addition Postulate age document! ** 1. If LM= 22 and MN = 15, find LN. 2. If LN = 54 and LM = 31, find MN. 4. If DF = 9x – 39, find EF. 47 3x + 10
The Correct Answer and Explanation is:
Let’s work through these one by one.
Problem 1: If LM = 22 and MN = 15, find LN.
Using the Segment Addition Postulate, we know that the total length of a segment is the sum of the lengths of its parts. So, for this problem:LN=LM+MN=22+15=37LN = LM + MN = 22 + 15 = 37LN=LM+MN=22+15=37
Thus, LN = 37.
Problem 2: If LN = 54 and LM = 31, find MN.
Again, using the Segment Addition Postulate, we can rearrange the formula to solve for MN:MN=LN−LM=54−31=23MN = LN – LM = 54 – 31 = 23MN=LN−LM=54−31=23
Thus, MN = 23.
Problem 3: If DF = 9x – 39, find EF = 47 3x + 10.
This seems like there may be a typo or missing information in the question, but based on what’s given, we’re trying to find EF. The equation for DF is given as 9x−399x – 399x−39, and EF is written as 473x+1047 3x + 10473x+10. It seems like we should set DF equal to EF, assuming we’re dealing with an equation involving both segments:9x−39=47+3x+109x – 39 = 47 + 3x + 109x−39=47+3x+10
Now, let’s solve for x:9x−39=3x+579x – 39 = 3x + 579x−39=3x+57
Subtract 3x3x3x from both sides:6x−39=576x – 39 = 576x−39=57
Now add 393939 to both sides:6x=966x = 966x=96
Finally, divide by 6:x=16x = 16x=16
Now that we have x = 16, we can substitute it back into the expression for DF or EF to find the length of the segment. Using DF = 9x – 39:DF=9(16)−39=144−39=105DF = 9(16) – 39 = 144 – 39 = 105DF=9(16)−39=144−39=105
Thus, DF = 105.
If you meant to ask something else in the third problem, feel free to clarify!
