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Carson wants to frame his diploma, which has the dimensions 1414 inches by 1111 inches. He is considering putting a border around the diploma that has the same width all around.\newlineThe total area of the diploma and border in square inches can be modeled by the expression (11+2x)(14+2x)(11 + 2x)(14 + 2x), where xx is the width of the border in inches.\newlineWhat does the quantity 14+2x14 + 2x represent in the expression?\newlineChoices:\newline(A)the perimeter around the outside of the border in inches\newline(B)the area of the border in square inches\newline(C)the total area of the diploma and border in square inches\newline(D)the length of the diploma and border in inches

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Q. Carson wants to frame his diploma, which has the dimensions 1414 inches by 1111 inches. He is considering putting a border around the diploma that has the same width all around.\newlineThe total area of the diploma and border in square inches can be modeled by the expression (11+2x)(14+2x)(11 + 2x)(14 + 2x), where xx is the width of the border in inches.\newlineWhat does the quantity 14+2x14 + 2x represent in the expression?\newlineChoices:\newline(A)the perimeter around the outside of the border in inches\newline(B)the area of the border in square inches\newline(C)the total area of the diploma and border in square inches\newline(D)the length of the diploma and border in inches
  1. Total Area Expression: The expression for the total area is 11 + 2x)(14 + 2x)\. We know that \$11 inches is the width of the diploma and 1414 inches is the length of the diploma.
  2. Additional Length Calculation: The term 2x2x represents the additional length added to each side of the diploma due to the border. So, 14+2x14 + 2x is the total length of the diploma including the border.
  3. Matching with Choices: Now, we need to match this understanding with the choices given. The perimeter is the total distance around the border, which is not what 14+2x14 + 2x represents. So, (A) is incorrect.
  4. Area of Border Alone: The area of the border alone would not include the original length of the diploma, so (B)(B) is incorrect.
  5. Correct Representation: The total area of the diploma and border is represented by the entire expression (11+2x)(14+2x)(11 + 2x)(14 + 2x), not just by 14+2x14 + 2x. So, (C)(C) is incorrect.
  6. Correct Representation: The total area of the diploma and border is represented by the entire expression (11+2x)(14+2x)(11 + 2x)(14 + 2x), not just by 14+2x14 + 2x. So, (C)(C) is incorrect.The length of the diploma and border in inches is correctly represented by 14+2x14 + 2x. Therefore, (D)(D) is the correct choice.

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