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12 votes
12 votes
point k is between j and l. if jk = x^2 - 4x , kl = 3x - 2 and jl = 28 write and solve an equation to find the lengths of jk and kl

User PVermeer
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1 Answer

23 votes
23 votes

Answer:

JK=12

KI=16

Explanation:


K\in\ [JI]\ \Rightarrow\ |JK|+| KI |=|KI|\\\\x^2-4x+3x-2=28\\\\\Longleftrightarrow\ x^2-x-30=0\\\\\\\Longleftrightarrow\ x^2+5x-6x-30=0\\\\\\\Longleftrightarrow\ x(x+5)-6(x+5)=0\\\\\\\Longleftrightarrow\ (x+5)(x-6)=0\\\\x=-5\ (excluded)\ or\x=6\\\\\\\Longleftrightarrow\ \\|JK|=x^2-4x=6^2-4*6=36-24=12\\|KI|=3x-2=3*6-2=18-2=16\\\\Proof: 12+16=28\\

User CrBruno
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