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Kirti has developed formulas to help her determine the size of her rectangular flower garden each spring. If she wants to plant 
n varieties of flowers, she determines the length, 
L, and the width, 
W, of her garden, in feet, according to the following formulas:

L(n)=n+2

W(n)=0.5 n+1
Let 
A be the area of Kirti's flower garden if she plants 
n types of flowers.
Write a formula for 
A(n) in terms of 
L(n) and 
W(n).

A(n)=
Write a formula for 
A(n) in terms of 
n.

A(n)=

Kirti has developed formulas to help her determine the size of her rectangular flower garden each spring. If she wants to plant n n varieties of flowers, she determines the length, L L , and the width, W W , of her garden, in feet, according to the following formulas:\newlineL(n)=n+2 L(n)=n+2 \newlineW(n)=0.5n+1 W(n)=0.5 n+1 \newlineLet A A be the area of Kirti's flower garden if she plants n n types of flowers.\newlineWrite a formula for A(n) A(n) in terms of L(n) L(n) and W(n) W(n) .\newlineA(n)= A(n)= \newlineWrite a formula for A(n) A(n) in terms of n n .\newlineA(n)= A(n)=

Full solution

Q. Kirti has developed formulas to help her determine the size of her rectangular flower garden each spring. If she wants to plant n n varieties of flowers, she determines the length, L L , and the width, W W , of her garden, in feet, according to the following formulas:\newlineL(n)=n+2 L(n)=n+2 \newlineW(n)=0.5n+1 W(n)=0.5 n+1 \newlineLet A A be the area of Kirti's flower garden if she plants n n types of flowers.\newlineWrite a formula for A(n) A(n) in terms of L(n) L(n) and W(n) W(n) .\newlineA(n)= A(n)= \newlineWrite a formula for A(n) A(n) in terms of n n .\newlineA(n)= A(n)=
  1. Area Formula: To find the area AA of a rectangle, we use the formula A=L×WA = L \times W, where LL is the length and WW is the width of the rectangle.
  2. Given Formulas: We are given the formulas for the length and width in terms of nn: L(n)=n+2L(n) = n + 2 and W(n)=0.5n+1W(n) = 0.5n + 1.
  3. Substitute into Area Formula: Substitute L(n)L(n) and W(n)W(n) into the area formula to get A(n)A(n) in terms of L(n)L(n) and W(n)W(n): A(n)=L(n)×W(n)A(n) = L(n) \times W(n).
  4. Perform Substitution: Now, perform the substitution using the given formulas: A(n)=(n+2)×(0.5n+1)A(n) = (n + 2) \times (0.5n + 1).
  5. Multiply Expressions: To find A(n)A(n) in terms of nn, we need to multiply the expressions for L(n)L(n) and W(n)W(n): A(n)=(n+2)×(0.5n+1)=0.5n2+n+1n+2A(n) = (n + 2) \times (0.5n + 1) = 0.5n^2 + n + 1n + 2.
  6. Simplify Expression: Simplify the expression by combining like terms: A(n)=0.5n2+2n+2A(n) = 0.5n^2 + 2n + 2.

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