Question

Given: HJ = 5x - 3, JK = 8x - 9, and KH = 13. Find 2, HJ, and JK.

Option 1: 2 =
Option 2: HJ =
Option 3: JK =
Option 4: None of the above

Answer 1

To find the values of HJ and JK, we solve the equation (5x - 3) + (8x - 9) = 13 for x, and then substitute this value back into the expressions for HJ and JK to obtain their lengths.

Step-by-step explanation:

To solve the problem, we need to find the values of HJ and JK given that JK = 8x - 9, HJ = 5x - 3, and KH = 13. Given the segments are parts of a continuous line, we can deduce that HJ + JK = KH. Substituting the expressions for HJ and JK into the equation, we can solve for x:

1. Write the equation for the continuous line: (5x - 3) + (8x - 9) = 13.
   
2. Simplify the equation: 13x - 12 = 13.
   
3. Add 12 to both sides: 13x = 25.
   
4. Divide both sides by 13: x = 25 / 13.
   
5. Substitute x back into the expressions for HJ and JK:

• HJ = 5x - 3 = 5(25/13) - 3,
• JK = 8x - 9 = 8(25/13) - 9.
  

Simplify the expressions to find the lengths of HJ and JK.

The correct answer is HJ and JK, given by the above expressions after simplifying.