Answer:
The value of x = 2
Step-by-step explanation:
Given the equation

- Expand 12(x-2) = 12x - 24
- Expand 1/2(x+6) = 1/2x + 3
so the equation becomes

simplifying


multiplying both sides by 2

subtracting x from both sides


divide both sides by 29

simplifying

Therefore, the value of x = 2
In both cases,

(as a consequence of the interesecting secant-tangent theorem)
So we have
10.





(omit the negative solution because that would make at least one of AB or AD have negative length)
11.




(again, omit the solutions that would give a negative length for either AB or AD)
X/2 >= -4
x >= -4 * 2
x >= -8
This most definitely has to be a rhombus since it is a form of a square with 4 congruent sides where a rectangle only has 4 right angles.
To clarify, a trapezoid only has one pair of parallel sides if you were wondering.