Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at lea
st 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft. The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.
Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?
The given constraints are (a) y ≥ 24 ft (b ) x ≤ 10 ft (c) y ≥ 3x (d) y ≤ 33 ft The acceptable region is shown shaded.
A (0, 33) satisfies all conditions B (4, 36) fails condition (d) C (4.8, 30.5) satisfies all conditions D (9, 26) fails condition (c) E (2, 22) fails condition (a)
The inequality is still true! If you add a number, say 5 to both sides of the following inequality, does anything change?
3 < 6
3 + 5 < 6 + 5
8 < 11
The inequality is still true. We know the statement holds for subtracting the same number because, in a way, addition and subtraction are pretty much the same operation. If I subtract 5 from both sides, I can think of it like "I add negative 5 to both sides" or something along those lines. It's kind of backwards thinking.