Point K is on line segment JL―. Given JK=2x−2,KL=x−9, and JL=2x+8, determine the numerical length of KL―.

Question

Point K is on line segment JL―. Given JK=2x−2,KL=x−9, and JL=2x+8, determine the numerical length of KL―.

Alix Ortiz · Accepted Answer

By Angle Addition Postulate, JL=JK+KL Substitute given expressions: 2x+8=(2x−2)+(x−9) Solve for x: 2x+8=3x−11 −x+8=−11 −x=−19 x=19 Hence, KL=19−9 KL=10

Jeffrey Jordon · Accepted Answer

Explanation

RizerMix · Accepted Answer

Let&#039;s assume the length of KL― is denoted by d.We are given:JK=2x−2KL=x−9JL=2x+8Since point K lies on line segment JL―, the sum of the lengths of JK― and KL― should be equal to the length of JL―.We can express this mathematically as:JK+KL=JL2x−2+x−9=2x+83x−11=2x+83x−2x=8+11x=19Now that we have found the value of x, we can substitute it back into the equation for KL― to find its length:KL=x−9KL=19−9KL=10Therefore, the numerical length of KL― is 10.

Don Sumner · Accepted Answer

To solve the problem, we&#039;ll start by applying the segment addition postulate. According to this postulate, the length of the entire segment JL― can be obtained by adding the lengths of its two parts, JK― and KL―. Therefore, we can set up the following equation:JK―+KL―=JL―Now, let&#039;s substitute the given lengths into the equation:2x−2+(x−9)=2x+8Simplifying the equation:3x−11=2x+8Moving the variables to one side and the constants to the other side:3x−2x=8+11x=19Now that we have found the value of x, we can substitute it back into the expression for KL―:KL―=x−9=19−9=10Hence, the numerical length of KL― is 10.

Vasquez · Accepted Answer

Answer:10Explanation:Let&#039;s solve for the numerical length of KL, denoted as KL―.Given:JK=2x−2KL=x−9JL=2x+8We know that JL=JK+KL. Substituting the given values, we have:2x+8=(2x−2)+(x−9)Now we can solve this equation for x:2x+8=2x−2+x−9Combine like terms:2x+8=3x−11Subtract 2x from both sides:8=x−11Add 11 to both sides:19=xNow that we have the value of x, we can find the length of KL by substituting x back into the equation for KL:KL―=x−9=19−9=10Therefore, the numerical length of KL― is 10.

Point K is on line segment ‾JL. Given JK = 2x - 2, KL = x - 9, and JL = 2x + 8, determine the numerical length of ‾KL.

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