Atrapezoid has an area of 20 cm2 and a height z cm. the lengths of the parallel sides are (2z + 3) cm and (6z – 1) cm. find the height, z, of the trapezoid. in your final answer, include all of the formulas and calculations necessary.

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.

What is the geometric mean of 3 and 7? a) square root of 21 b) 2 square root of 6 c) 2 square root of 7 d) 21