Asked by Maddie McCorvey on Apr 24, 2024

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A closed rectangular box has dimensions of length n inches, width n+4 inches, and height n+5 inches. Write a polynomial function A(n) A ( n ) A(n) for the area of the largest side of the box if dimensions increase by 6 inches.

A) A(n) =n2+4n−116A ( n ) = n ^ { 2 } + 4 n - 116A(n) =n2+4n116
B) A(n) =n2−11n+110A ( n ) = n ^ { 2 } - 11 n + 110A(n) =n211n+110
C) A(n) =n2+4n+110A ( n ) = n ^ { 2 } + 4 n + 110A(n) =n2+4n+110
D) A(n) =n2+21n+110A ( n ) = n ^ { 2 } + 21 n + 110A(n) =n2+21n+110
E) A(n) =n2+11n+110A ( n ) = n ^ { 2 } + 11 n + 110A(n) =n2+11n+110

Closed Rectangular Box

A three-dimensional figure with six faces, all of which are rectangles, and all angles are right angles.

Polynomial Function

A mathematical expression involving a sum of powers in one or more variables, where the exponents are whole numbers and the coefficients are real numbers.

Area

The extent of a two-dimensional surface within a boundary.

  • Calculate the area or volume of geometric shapes by applying polynomial expressions.
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DO
D'Andrea Oliver7 days ago
Final Answer :
D
Explanation :
The largest side of the box initially is the side with dimensions n+4n+4n+4 and n+5n+5n+5 , so its area is (n+4)(n+5)(n+4)(n+5)(n+4)(n+5) . If dimensions increase by 6 inches, the new dimensions of this side will be n+4+6n+4+6n+4+6 and n+5+6n+5+6n+5+6 , or n+10n+10n+10 and n+11n+11n+11 . The area of the largest side after the increase is (n+10)(n+11)=n2+21n+110(n+10)(n+11) = n^2 + 21n + 110(n+10)(n+11)=n2+21n+110 .