Andreas has drilled a hole at the 30 cm mark in a metre stick (100 cm length). He then nails the metre stick onto a piece of plywood, through the hole. If he rotates the stick at a constant rate, then the distance from its long end to the top of the plywood can be modelled by the blue graph shown. The distance from its short end to the top of the plywood can be modelled by the pink graph. a) How far is the nail from the top of the plywood? How do you know? b) How many times does Andreas spin the ruler in 2 minutes? Show your calculations. c) If Andreas takes out the nail and puts a new hole at the 50 cm mark, how would the graphs change? Be specific. Assume the length of one cycle doesn't change, nor does the axis.

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step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

the answer to your question is c.)   volcanoes built the mountains and earthquakes tore them down.

step-by-step explanation: