The teacher does not have to spend all $36. Write an inequality relating 36 and 9 (7 - x) representing this situation. (Copy/paste as needed: ≤ ﹤ ≥ ﹥)

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

The graph of a hyperbola is shown. what are the coordinates of a vertex of the hyperbola? (0, −4) (−3, 0) (0, 0) (0, 5)

Rewrite the following quadratic functions in intercept or factored form. show your work. f(t) = 20t^2 + 14t - 12