The area A of a rectangular garden is given by the expression2^2+ 2 − 12. The length L of the garden is given by the expression x2 - 9. Find an expression for the width W of the garden. (Recall that A = LW). What are the excluded values in this calculation and what do they represent in context?

Step-by-step explanation:

The correct question is

The area A of a rectangular garden is given by the expression 2x^2+2x− 12. The length L of the garden is given by the expression x^2 - 9. Find an expression for the width W of the garden. (Recall that A = LW). What are the excluded values in this calculation and what do they represent in context?

we know that

The area of a rectangular garden is given by the formula

we have

substitute

Solve for W

Find the roots of the quadratic equation of the numerator

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

so

The roots are x=2 and x=-3

The quadratic equation in factored form is equal to

substitute in the above expression of W

Rewrite the denominator as difference of squares

substitute

Remember that

In a quotient, the denominator cannot be equal to zero

so

x=-3 and x=3 are excluded values

x=3 represent a vertical asymptote

x=-3 is not included in the domain of the function because the length cannot be a negative number

Simplify

answer: 16

step-by-step explanation: first you would add 6+6 which equals 12 then add 2+2 which equals 4. then add 12 + 4 which is 16.

hope this ^_^

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺