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

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

y > 1/3x

y < = -x + 4

hope this : )