Question

Determine the value of x.

A) 2 squareroot of 3.
B) 12
C) 6 squareroot of 3.
D)12 squareroot of 3.

Answer 1

Upon simplifying the equation ((2x)² = 4.0 (1 − x)²) by taking the square root of both sides and rearranging, we determined that x = 0.5, which is not listed among the provided options.

Step-by-step explanation:

The initial equation given is (2x)² = 4.0 (1 − x)². Taking the square root of both sides, we obtain 2x = 2(1 − x), since the square root of 4.0 is 2. Now, we rearrange the equation to 2x = 2 − 2x. By adding 2x to both sides, we get 4x = 2, and after dividing both sides by 4, we find that x = 0.5. Hence, x is not equal to any of the provided options A), B), C), or D).

Answer 2

Answer:
`6√(3)`

Reason:

For any 30-60-90 triangle, the long leg is exactly
`√(3)` times as long compared to the short leg.

In other words,

`\text{long leg} = (\text{short leg})*√(3)`

In this case, the short leg is 6 units long. The short leg is always opposite the smallest angle 30 degrees. Once again, this only applies to 30-60-90 triangles.