Question

Two more and im done i promise

Answer 1

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Answer:
`\textsf{8x + 11; 12x - 1; x = 3; TU = 35; UV = 35; TV = 70}`

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Given:
`\textsf{TU = 8x + 11, UV = 12x - 1}`

Find:
`\textsf{Determine the value of x, TU, UV, TV}`

Solution: In order to determine the value of TU and UV, we need to first create an equation using the given information. We know that TU is equal to 8x + 11 and UV is equal to 12x - 1. Since we know that U is the midpoint, we know that TU is equal to UV. Therefore, the equation would have the following format: TU = UV

Now that we have the format, we can plug in the expressions and then simplify the equation.

• 
  `\textsf{TU = UV}`
• 
  `\textsf{8x + 11 = 12x - 1}`

Now, we can solve for x by adding 1 to both sides and then subtracting 8x from both sides.

• 
  `\textsf{8x + 11 + 1 = 12x - 1 + 1}`
• 
  `\textsf{8x - 8x + 12 = 12x - 8x}`
• 
  `\textsf{12 = 12x - 8x}`
• 
  `\textsf{12 = 4x}`

We are now on the final step of solving for x. We just need to divide both sides by 4 to isolate the x variable and get the value of x.

• 
  `\textsf{12 / 4 = 4x / 4}`
• 
  `\textsf{3 = x}`

Now that we have the value of x, we can plug it into the TU and UV expressions to determine what the length of the segments are.

• 
  `\textsf{TU = 8(3) + 11}`
• 
  `\textsf{TU = 24 + 11}`
• 
  `\textsf{TU = 35}`

• 
  `\textsf{UV = 12(3) - 1}`
• 
  `\textsf{UV = 36 - 1}`
• 
  `\textsf{UV = 35}`

Now that we now both sides of the segment, we can add them together to determine the length of the total segment.

• 
  `\textsf{TU + UV = TV}`
• 
  `\textsf{35 + 35 = TV}`
• 
  `\textsf{70 = TV}`

Therefore, we know that the value of the variable x is equal to 3, the length of TU is 35, the length of UV is 35, the length of TV is 70.