The variable z is directly proportional to x. when x is 11, z has the value 44. what is the value of z when x = 21?

Directly proportional, both increase/decrease, Multiple k(constant you needed to solve for)..

Inversely --one increases as the other decreases, increase the denominator & fraction gets smaller So

Problem:

Dirextly to X (× by X)

Inversely to Y, (÷ by Y)

Z= k X/Y

Solve, working backwards: Z =5 becomes

5 = k (X) ÷ (Y). And

X=15 and Y =9 becomes

5= k(15)/(9). Undo ÷9, ×9 both sides

45= k(15). Now undo ×15 by ÷15 both sides

45/15 = 3. So k=3, (also called your constant of variation)and your Equation/Proportion becomes...

Z = 3X/Y

Use the new #s X=23, Y=14

Z= 3×23÷14 = 69/14. If they want spirochete answer divide and round to corresponding # if decimals

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reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.