The equation t^2 = a^3 shows the relationship between a planet’s orbital period, t, and the planet’s mean distance from the sun, a, in astronomical units, au. if planet y is twice the mean distance from the sun as planet x, by what factor is the orbital period increased?

If g(x) is an odd function, which function must be an even function?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.

The sum of 5consecutive even numbers is 100. what is the first number in this sequence?