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Find the number that we can place in the blank, so that the resulting expression can be factored as the product of two linear factors.
\[3mn - 6m + 5n + ___

-10

Step-by-step explanation: From the start of the equation, we know it must factor to something like (3m + x)(n+y), because the first term must be 3mn. Now, for the next term to be -6n, y must be -2, and for the third term to be 5n, x must be positive 5. So we end up with (3m+5)(n-2). If we factor this out, we get 3mn-6m+5n-10, meaning the final term is -10.

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.