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Write an expression that represents the length of line segment π΄π΅ in the given figure.

We first note that the length of the line segment is given by the sum of the mutually exclusive line segments that make up the entire line segment. Letβs call the following point πΆ. We can see that π΄π΅ is equal to π΄πΆ plus πΆπ΅. Since π΄πΆ is equal to seven π₯ and πΆπ΅ is equal to six π¦, we can add these expressions together to find an expression for π΄π΅. This gives us our final answer of seven π₯ plus six π¦.

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