Rewrite the following expression using the properties of logarithms. log2 z + 2 log2x + 4 log9 y + 12 log9 x - 2 log2 y

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Amachine part consists of a half sphere and a cylinder, as shown in the figure. the total volume of the part is π cubic inches.

Aladder that is 20ft long is leaning against the side of a building. if the angle formed between the ladder and the ground is 75 degrees how far is the bottom of the from the base of the building?

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?