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 polynomial function for the volume v of the tray in terms of x.

possible answers:
a. 4x ^ 3 – 30x ^ 2 + 54x
b. 4x ^ 3 – 12x ^ 2 + 54x
c. 4x ^ 2 – 30 ^ x + 54
d. 4x ^ 3 – 30x ^ 2 + 15 ^ x + 54

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

Step-by-step explanation:

From the question we are told that

Breath of cardboard h=6

Length of cardboard l=9

Let x be the height when fold

Generally the new rectangle is  mathematically given as

Breath

Length

Generally the Volume of tray is mathematically given as

The total nom of  code that can be used is equal to 5+3 = 8

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

The solution is in the following image

The answer is in the image 

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

The answer is in the image 

The solution is given in the image below

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.