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What is a cross section of a cube?
It depends on the angle of the plane of the cross section. If it is parallel to the cube's face (or equivalently, two adjacent edges) the cross section will be a square congruent to the face. If the plane is parallel to just one edge (and so angled to a face), the cross section will be a rectangle which will have a constant width. Its length will increase, remain at a maximum level and then decrease. If neither, it will be a hexagon-triangle-hexagon-triangle-hexagon (triangles when passing through a vertex).
Is it possible for a quadrilateral to have three lines of symmetry?
It can't have exactly three (it can be a square and have four). Reflecting about a line of symmetry swaps at least two corners of the quadrilateral: a corner has to be symmetric to a corner, and if all four were symmetric to themselves, they'd all have to be on a line, which is impossible. Moreover, different lines of symmetry swap different pairs of corners. Once you pick two corners, there is only one line of symmetry which could possibly swap them - the perpendicular bisector of a segment drawn between the two corners. If two different corners are symmetric, that means that their angles are equal. So three lines of symmetry means that there are three pairs of corners with equal angles. Since there are only four corners total, the only way for this to happen is for all four corners to have equal angles. Then it's either a rectangle (which doesn't work - only two lines of symmetry) or a square (which has four lines of symmetry). Neither possibility has exactly three.
Is the sequence 1 4 16 64 arithmetic geometric or neither?
neither
Is zero a positive or negative number?
Neither. It represents "nothing" Zero is neither a positive or negative number. It is just plain zero. So you don't have to stress on remembering if it's a plus or minus! :0) neither 0 is neither negative nor positive. Zero is neither positive nor negative.
What two numbers are neither prime nor composite?
0 and 1 are neither prime nor composite.
