In order to make a box, James cut out four small 2 by 2 squares from each corner of a square piece of cardboard. If the volume of the box he made is 50 inches cubed, what is the length of a side of the original square?

Please help, thanks.

9 inches.

Step-by-step explanation:

Let the length of the square cardboard =x inches

If James cut out four small 2 by 2 squares from each corner of a square piece of cardboard.

In the attached diagram, the box is folded along the green dotted line.

Therefore:

Volume of a rectangular prism=LWH

Volume =50 inches cubed

Therefore:

2(x-4)(x-4)=50

Divide both sides by 2

Therefore, the length of the original square is 9 inches.

there is no grid

step-by-step explanation:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.