Three of these expressions are equal to the volume of the barn shown. which expression is not?

The statement that does not match the others is the one at lower right.

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The barn's volume can be decomposed into a rectangular prism and a triangular one. Thus the upper right expression is a true represenation of the barn's volume:

... Volume of triangular prism + Volume of rectangular prism

The volume of a rectangular prism is the product of its dimensions. The dimensions of the rectangular prism portion of the barn's volume are a, b, c, so the volume of that portion is ...

... Volume of rectangular prism = a·b·c

The volume of a triangular prism is the area of the triangular base multiplied by the length of the prism. Here, the triangular base has base dimension b and height (d-c), so its area is ...

... Area of triangular barn end = (1/2)b(d-c)

Since the length of the barn is "a", the volume of the triangular prism is ...

... Volume of triangular prism = (1/2)b(d-c)a = (1/2)·a·b·(d-c)

The total volume is the sum of the volumes of the parts ...

... a·b·c + (1/2)·a·b·(d-c) . . . . . . matches the upper right selection

This can be factored by removing a·b to outside parentheses:

... a·b·((1/2)·(d-c) + c) . . . . . . . . . matches the lower left selection

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Since the two left selections match the one at upper right, the odd one is the one at lower left.

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.

60 for the first and 130 for the second

step-by-step explanation: