Determine whether the linear transformation T is invertible by considering its matrix with respect to the standard bases. T : P_2 → P_2 defined by

T(p(x)) = p(x) + p'(x)

If T is invertible, use the theorem below to find the inverse of T (attached).

Which is a reasonable estimate of the amount of water in a small, inflatable pool used by children?

Which number completes the inequality? 2/3 < _ < 7/9

Every weekday, mr. jones bikes from his home to his job. sometimes he rides along two roads, the long route that is shown by the solid lines. other times, he takes the shortcut shown by the dashed line. how many fewer kilometers does mr. jones bike when he takes the shortcut instead of the long route?