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Fernando, an interior decorator, is designing an entryway for a client's new home. The entryway will include a set of double doors and hardwood moulding. The moulding will be an equal width around the sides and top of the double doors, which will be 6060 inches wide and 8080 inches tall. The total area of the double doors and moulding in square inches can be modeled by the expression (2x+60)(x+80)(2x + 60)(x + 80), where xx is the width of the moulding in inches. This expression can also be written in the form 2x2+220x+4,8002x^2 + 220x + 4,800. What does the quantity 2x2+220x2x^2 + 220x represent in the expression?\newline(A)the perimeter around the outside of the double doors and moulding in inches\newline(B)the area of the double doors in square inches\newline(C)the height of the double doors and moulding together in inches\newline(D)the area of the moulding in square inches

Full solution

Q. Fernando, an interior decorator, is designing an entryway for a client's new home. The entryway will include a set of double doors and hardwood moulding. The moulding will be an equal width around the sides and top of the double doors, which will be 6060 inches wide and 8080 inches tall. The total area of the double doors and moulding in square inches can be modeled by the expression (2x+60)(x+80)(2x + 60)(x + 80), where xx is the width of the moulding in inches. This expression can also be written in the form 2x2+220x+4,8002x^2 + 220x + 4,800. What does the quantity 2x2+220x2x^2 + 220x represent in the expression?\newline(A)the perimeter around the outside of the double doors and moulding in inches\newline(B)the area of the double doors in square inches\newline(C)the height of the double doors and moulding together in inches\newline(D)the area of the moulding in square inches
  1. Expand expression: The expression for the total area is (2x+60)(x+80)(2x + 60)(x + 80), which expands to 2x2+160x+60x+4,8002x^2 + 160x + 60x + 4,800.
  2. Combine like terms: Combine like terms in the expanded expression to get 2x2+220x+4,8002x^2 + 220x + 4,800.
  3. Identify moulding area: The term 2x2+220x2x^2 + 220x represents the area of the moulding because the 4,8004,800 represents the area of the double doors alone (6060 inches wide by 8080 inches tall).

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