Question

Point T is on line segment S U. Given TU = 4x + 1, SU = 8, and ST = 3x, determine the numerical length of TU. a) 1 unit b) 2 units c) 3 units d) 4 units

Answer 1

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Explanation:

To determine the numerical length of TU, we need to find the value of x in the equation TU = 4x + 1.

Given that ST = 3x and SU = 8, we can use the information to set up an equation.

We know that the sum of ST and TU should be equal to SU, so we have:

ST + TU = SU

Substituting the given values:

3x + (4x + 1) = 8

Now, we can solve for x:

7x + 1 = 8

Subtracting 1 from both sides:

7x = 7

Dividing both sides by 7:

x = 1

Now that we have the value of x, we can substitute it back into the equation for TU:

TU = 4x + 1

TU = 4(1) + 1

TU = 4 + 1

TU = 5

Therefore, the numerical length of TU is 5 units. The correct answer is option d) 4 units.