Will mark brainliest + 50 points

algebra 2 - h question

in order to save on fencing material, collins decided to construct his rabbit pen so that the side of the garage acts as one side of the pen. this way she only needs to fence the other three sides. if she starts with 100 ft of fencing, what are the dimensions of the rabbit pen with the maximum area?

The dimensions are 25 * 50 feet.

Step-by-step explanation:

The 3 sides of the pen will measure (2x + y)  feet where x is the width and y is the length.

2x + y = 100

y = 100 - 2x

The area A  = xy =  x(100 - 2x) ft^2.

Finding the maximum area.

A = x(100 - 2x)

A = 100x - 2x^2     Finding the derivative:

A' = 100 - 4x

For maximum value of A this equals zero:

100 - 4x = 0

4x = 100

x = 25 ft,  so this is the width.

The length is  100  - 2(25) =  50 ft.

25 ・50

Step-by-step explanation:

50 ft

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1