Abox is to be constructed with a rectangular base and a height of 5 cm. if the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box?
v = lwh p = 2(l + w)
a. y = 5(28 – x)(x)
b. y = 5(28 – 2x)(x)
c. y = 5(14 – x)(x)
d. y = 5(14 – 2x)(x)

c. y = 5(14 – x)(x)

Step-by-step explanation:

Let x be the length of the rectangle base,  

Since, perimeter of a rectangle,

P = 2(l+w)

Where, l is the length and w is the width,

We have, P = 28 cm,

So, the width of the rectangular base = 14-x  

We know that,

The volume of a box having rectangular base is,

V = lwh

Where, l and w are the length and width of the base respectively and h is the height of the box,

Given,

h = 5 cm,

Here, y represents the volume of the box,

⇒ y = x(14-x)(5)

Or y = 5(14-x)(x)

Option C is correct.

Option C.

Step-by-step explanation:

Let the dimensions of the rectangular base are x by y.

Height of box = 5 cm

Perimeter of rectangular base = 28

The formula for base is

Divide both sides by 2.

Subtract x from both sides.

It means width of the rectangular base is 10-x.

Volume of a box is

Therefore, the correct option is C.

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

i think it would be 42cm