Question

A greenhouse that specializes in growing carnations is divided into sections. The number of plants in each section depends on the number of sprinklers in that section.

There are y(5y − 4) red carnation plants and (9 + y)2 white carnation plants in a section with y sprinklers.

Which simplified expression represents the total number of red and white carnation plants in a section with y sprinklers?

Answer 1

The required equation is
`T=6y^2+14y+81`

Explanation:

Given : A greenhouse that specializes in growing carnations is divided into sections. The number of plants in each section depends on the number of sprinklers in that section.

Red carnation plants =
`y(5y-4)`

White carnation plants =
`(9+y)^2`

with y sprinklers.

To find : Which simplified expression represents the total number of red and white carnation plants in a section with y sprinklers?

Solution :

Total number = Red carnation + White carnation plants

`T=y(5y-4)+(9+y)^2`

Now, we solve the equation

`T=5y^2-4y+9^2+y^2+2\cdot 9\cdot y`

`T=5y^2-4y+81+y^2+18y`

`T=6y^2+14y+81`

Therefore, The required equation is
`T=6y^2+14y+81`

Answer 2

The solution would be like this for this specific problem:

y(5y − 4) + (9 + y)²

Simplify the expression:

(5y² − 4y) + (81 + 18y + y²)

Combine the like terms:

6y² + 14y + 81

The simplified expression that represents the total number of red and white carnation plants in a section with y sprinklers is 6y² + 14y + 81. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.