The dimensions of a cube increase by a scale factor of 2. If the resulting cube has a volume of 64 cm3, then what was the length of one edge of the original cube?

The original length of the edges are equal to 2 cm.

Step-by-step explanation:

The volume of a cube is given by the following expression:

Where "a" is the length of each edge of the cube. Assuming that the original cube had a length of "x", then its volume would be:

Since the edges of the cube got scaled by a factor of 2, then the new edges are "2*x" and the volume is:

The original length of the edges are equal to 2 cm.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer