Answer:

1. x = 14.5
2. x = 3 or -7

Step-by-step explanation:

1. To find the value of x, we need to equate the two expressions:

FU = 38

RQ = 2x + 9

So, 38 = 2x + 9

Subtracting 9 from both sides gives:

29 = 2x

Dividing both sides by 2 gives:

14.5 = x

2. To find the value of x, we can use the measures of angle CUA and angle CTA:

x^2 - 3x = 2x + 14

Expanding and rearranging the equation gives:

x^2 - 5x - 14 = 0

This is a quadratic equation, which can be solved using the quadratic formula or by factoring.

The value of x can be found to be 3 or -7.

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