Lucy cuts 4 squares with side length x in. From the corners of a 6 in. By 9 in. Cardboard rectangle. She folds the remaining cardboard to make a tray that is x in. High. Write and simplify a function for the volume V of the tray in terms of x.

4x³ - 30x² + 54x

Step-by-step explanation:

Length of the rectangular cardboard = 9 inches

Width of the rectangular cardboard = 6 inches

if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, then we have

Length of the tray = length of cardboard - 2(side of square )

= 9 - 2x

Width of the tray = width of cardboard - 2( side of square)

= 6 - 2x

height of tray = sides of square

= x

volume of tray = Length × width × height

= (9 - 2x) (6 - 2x) (x)

Open the parenthesis

= (54 - 18x - 12x + 4x²)(x)

= 54x - 18x² - 12x² + 4x³

= 54x - 30x² +4x³

Re-arrange

4x³ - 30x² + 54x

Volume, V of the tray in terms of x = 4x³ - 30x² + 54x

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation:

3 3 6, because in every triangle the longer side is always shorter than the sum of the other two