12 Write a system of equations for the following: The sum of two numbers is 7. Four times the firstnumber is one more than five times the second.x + y = 74x = 5y + 1x + y = 74x + 1 = 5yA:B:x + y = 75x = 4y + 1x + y = 74x = 5y - 1C:D:
14 If a system is consistent dependent, what can be said about the graph of the system?A:They are parallel linesB:They will intersect in one pointC:The lines are coincidentalD:They consistently need each other.
16 Misha has a 2500 meter spool of rope that he must cut into 50 meter and 75 meter lengths for hisrock climbing class. Write an inequality that willexpress the possible numbers of each length he can cutfrom this spool of rope.50x + 75y 2500A:B:50x + 75y ≤ 2500C:2500/50x ≤ 75yD:50x ≥ y
18 A company produces windows and doors. A profit of $5 is realized on each window, an $3 on each door.The company has 18 hours available for manufacturing atplant A where it takes 3 hours for each window and 2 hoursfor each door. Plant B has 7.5 hours available for assembly where it takes 1.5 hoursfor each window, and .75 hours for each door.Write the constraints for this problem.X ≥ 0Y ≥ 03x y ≤ 182x + .75y ≤ 7.5X ≥ 0Y ≥ 03x + 2y ≤ 181.5x + .75y ≤ 7.5A:B:X ≥ 0Y ≥ 05x + 3 y ≤ 182x + 1.5y ≤ 7.5C:D:You must be kidding me.
26 Describes what transformations on y = x? A slide of 2 up, 3 left, and a vertical stretch by a factor of 5.A slide of 2 up, 3 right and a vertical stretch by a factor of 5A:B:A slide of 2 up, 3 right and a vertical compression by a factor of 1/5.A slide of 2 up, 3 right and a vertical stretch by a factor of 1/5C:D:
27 A slide of 2 up, 3 right and a vertical stretch by a factor of 5
28 If a feasible region has its vertices at ( -2, 0), (3, 3), (6, 2) and ( 5, 1), what is the maximum giventhis objective function.P = 3x + 2.5yThe maximum is 23The maximum is 25A:B:The maximum is 27The minimum is -6C:D:
30 A ticket office sells reserved tickets and general admission tickets to a rock concert. The auditorium normally holds no more than 5000 people. There can be no more than 3000reserved tickets and no more than 4000 general admission tickets sold.Write a system of inequalities to represent the possible combinations of reserved tickets andgeneral admission tickets that can be sold.X + y ≤ 5000X ≤ 3000Y ≤ 4000X ≥ 0Y ≥ 0A:B:X + y ≤ 5000X ≤ 3000Y ≤ 4000X + y ≥ 5000X ≥ 3000Y ≤ 4000X ≥ 0Y ≥ 0X + y ≤ 5000X ≤ 3000Y ≤ 4000X ≤ 0Y ≥ 0C:D: