Suppose that the sequence x0, x1, x2... is defined by x0 = 5, x1 = 6, and xk+2 = 5xk+1−6xk for k≥0. Find a general formula for xk. The right answer is: xk = −4(3k)+9(2k)

But how do we get that answer? Please show all your steps with explanation.

The figures below are made out of circles, semicircles, quarter circles, and a square. find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).

Given that abcd is a rhombus, what is the value of x?