Atree of height y meters has, on average, upper b branches, where upper b equals y minus 3. each branch has, on average, n leaves where n equals 2 upper b superscript 2 baseline minus upper b. find the average number of leaves on a tree as a function of height.

we are given

number of branches is

number of leaves on each branch

the average number of leaves = (number of branches)*(number of leaves on each branch)

so, we can plug values

we get

now, we can plug values

now, we can simplify it

............Answer

Area =  .

Step-by-step explanation:

Given : Vanessa uses the expressions (3x² + 5x + 10) and (x² – 3x – 1) to represent the length and width of her patio.

To find : Which expression represents the area (lw) of Vanessa’s patio?

Solution : We have given

Length =  (3x² + 5x + 10)

Width =  (x² – 3x – 1)

Area=  length *  width .

Area = (3x² + 5x + 10) *  (x² – 3x – 1).

Area = 3x²  (x² – 3x – 1) + 5x  (x² – 3x – 1) + 10  (x² – 3x – 1).

Area = .

Combine like terms

Area =  .

Area =  .

Area =  .

Therefore, Area =  .