Math Problem Statement
Solve and explains the answers to both A and B
Solution
Let's solve the problems step by step for both parts A and B based on the image.
Part (a):
You have a segment with point in between. From the image, it seems:
- Segment
- Segment
- The whole segment
Since lies on the segment , we can use the segment addition postulate:
Substitute the given expressions into this equation:
Now, simplify:
Subtract 16 from both sides:
Now, divide by 3:
This is the value of . To find and , substitute into the expressions for and :
Thus:
Part (b):
Again, you have a segment with point in between. The details are:
- Segment
- Segment
- The whole segment
By the segment addition postulate:
Substitute the given expressions:
Simplify:
Subtract 27 from both sides:
Now divide by 6:
This is the value of . To find and , substitute into the expressions for and :
Thus:
Summary of Results:
- (a) , , and
- (b) , , and
Would you like further details on any part of this solution, or do you have any questions?
Related Questions:
- How do we calculate segment lengths when multiple variables are involved?
- What does the segment addition postulate imply in geometry?
- How do we solve equations with fractions and integers combined?
- Can we always determine the position of points on a line given algebraic expressions?
- What would happen if the total length was less than the sum of the segments in part (a)?
Tip: Always simplify both sides of an equation before isolating the variable to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Segment Addition Postulate
Formulas
Segment Addition Postulate: AB + BC = AC
Linear Equation Solution: Combine like terms, isolate variable
Theorems
Segment Addition Postulate
Suitable Grade Level
Grades 8-10