In the diagram below, the expression in each circle is the result of the sum of two rectangles connected to it. complete the diagram, writing the expressions in their simplified form.

The expression in each circle is the result of the sum of two rectangles is 2x.

Given the,

in the diagram below, the expression in each circle is the result of the sum of two rectangles connected to it.

We have to determine,

the expressions in their simplified form.

According to the question,

Expression; 5x + 2y and x + y

On solving the expression in the left rectangle.

Adding both the expression,

Expression; 5x + 4y and 4x + 5y

On solving the equation on the right rectangle,

On subtract both the expression,

Therefore,

The expression in each circle is the result of the sum of two rectangles is,

Hence, The expression in each circle is the result of the sum of two rectangles is 2x.

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Given:

Each circle is the result of the sum of two rectangles connected to it.

To find:

The missing expression in their simplified form.

Solution:

Left side circle:

Left circle = (5x + 2y) + (x + y)

                = 5x + 2y + x + y

                = 6x + 7y

The expression in left side circle is 6x + 7y.

Right side rectangle:

5x + 4y = (4x + 5y) + Right rectangle

Subtract 4x + 5y from both sides.

5x + 4y - (4x + 5y) = Right rectangle

5x + 4y - 4x - 5y = Right rectangle

x - y = Right rectangle

The expression in right side rectangle is x - y.

Bottom circle:

Bottom circle = (x + y) + (x - y)

                      = x + y + x - y

                      = 2x

The expression in left side circle is 2x.

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