Three different positions of the same dice are shown, the six faces of which are numbered from 1 to 6. Select the number that will be on the face opposite to the one showing`6'.
Let's examine the three given positions of the dice: - In the first position, the numbers shown on the visible faces are 4, 1, and 3. - In the second position, the numbers shown on the visible faces are 6, 2, and 1. - In the third position, the numbers shown on the visible faces are 3, 1, and 2. From these positions, we can see that the face with the number 6 is adjacent to faces with the numbers 1, 2, and 5. Since 1, 2, and 5 are adjacent to 6, the opposite face to 6 must be the number 3.
Thus, the correct answer is Option D.
If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are real and equal, then: