We have been given that an open box is made from an 8 by ten-inch rectangular piece of cardboard by cutting squares from each corner and folding up the sides. We are asked to find the volume of the box.

The side of box will be $8-x-x=8-2x$ and $10-x-x=10-2x$ .

The height of the box will be $x$ .

The volume of box will be area of base times height.

$\text{Volume of box}=(8-2x)(10-2x)\cdot x$

Now we will use FOIL to simplify our expression.

$\text{Volume of box}=(80-16x-20x+4x^2)\cdot x$

$\text{Volume of box}=(80-36x+4x^2)\cdot x$

Now we will distribute x.

$\text{Volume of box}=80x-36x^2+4x^3$

$V(x)=80x-36x^2+4x^3$

Therefore, the volume of the box would be $V(x)=80x-36x^2+4x^3$ .

6 0

3 years ago

Which equation represents a line that passes through (-9, -3) and has a slope of -6?

eimsori [14]

Answer:

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 6 and (a, b) = (- 9, - 3), so

y - (- 3) = - 6(x - (- 9)), that is

y + 3 = - 6(x + 9)

8 0

3 years ago

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Robert is purchasing some packs of chicken from the supermarket. The first pack weighs 45 ounces. The second pack weighs 3 pound

Dmitry [639]

Answer: 3 pounds

Step-by-step explanation:

6 0

3 years ago

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If a 25 ft rope is cut into two sections with one section 4 times as long as the other section, how long is the shorter piece?

DaniilM [7]

X = short section of rope
4x = longer section of rope

x + 4x = 25
5x = 25
x = 5

…or in other words the shorter piece of rope is 5 feet long

7 0

3 years ago