Jae is constructing an open box from a piece of cardboard that is 9 in. Wide and 12 in. Long. Jae cuts squares of equal size from each corner of the cardboard, and then folds up the sides of the box. Write and simplify a polynomial function V for the volume of the box in terms of x.

The volume of the open box is .

Step-by-step explanation:

Geometrically speaking, the volume of the open box (), measured in cubic inches, is described by the volume of a right parellelepiped. That is:

(1)

Where , and are the width, length and height of the open box, respectively, measured in inches. Please notice that width of the open box is the width of the piece of cardboard (), measured in inches, minus two times the side of the cut squares (), measured in inches, length of the open box is the length of the piece of cardboard (), measured in inches, minus two times the side of the cut squares and the height of the open box is the side of the cut squares. That is:

(2)

(3)

(4)

By applying (2), (3), (4) in (1), we expand and simplify the volume function:

(5)

If we know that and , then the equation above is:

The volume of the open box is .

answer: answer

step-by-step explanation:

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500