In the figure, d is a point on ab such that cd = bd. if ∠abc = 90° , prove that ad = bd.

Both the red and blue line segments stretch from the center of the circle to a point on the circle. the length of the blue segment is 5. how long is the red line segment?

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 (%).

What is x3+3x2−16x−48 divided by x−1?