Line segments can be divided into sub-segments.
The value of DF is 18
The given parameters are:
[tex]\mathbf{BE = 3x + 6}[/tex]
[tex]\mathbf{DF = 7x + 4}[/tex]
We have:
[tex]\mathbf{BE + DF = 30}[/tex]
So, we have:
[tex]\mathbf{3x + 6 + 7x + 4 = 30}[/tex]
[tex]\mathbf{10x + 10 = 30}[/tex]
Subtract 10 from both sides
[tex]\mathbf{10x = 20}[/tex]
Divide both sides by 10
[tex]\mathbf{x = 2}[/tex]
Substitute [tex]\mathbf{x = 2}[/tex] in [tex]\mathbf{DF = 7x + 4}[/tex]
[tex]\mathbf{DF = 7 \time 2 + 4}[/tex]
[tex]\mathbf{DF = 14 + 4}[/tex]
[tex]\mathbf{DF = 18}[/tex]
Hence, the value of DF is 18
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