To find the expression equivalent to \((3y-4)(2y+7)+11y-9\), we will follow these steps:
Step 1: Distribute the terms within the first parentheses \((3y-4)\) to the terms within the second parentheses \((2y+7)\):
Using the distributive property, we get:
\[3y \times 2y + 3y \times 7 - 4 \times 2y - 4 \times 7 + 11y - 9\]
Simplifying this gives:
\[6y^2 + 21y - 8y - 28 + 11y - 9\]
Step 2: Combine like terms:
Combine the terms with the same powers of \(y\) together. In this case, we have \(y^2\) terms, \(y\) terms, and the constant terms.
\[6y^2 + 21y - 8y + 11y - 28 - 9\]
Simplifying further:
\[6y^2 + 24y - 37\]
Therefore, the expression equivalent to \((3y-4)(2y+7)+11y-9\) is \(6y^2 + 24y - 37\).
The correct answer is option D: \(6y^2 + 24y - 37\).
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where m is the slope and 
is a point on the line.
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