The sum of two numbers is 37 and the difference is 9. What are the numbers
1 answer:
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Part A:
The first thing you should do is to graph both lines. Notice that one is of positive slope and another of negative slope.
The solution of the inequation system is given by the shaded region. That is, all the points that are in the shaded region satisfy the system of inequations.
Part B:
the point (-2, -2) is NOT included in the solution area (it is not in the shaded region.
Mathematically it is demonstrated by substituting inequalities and seeing that they are not satisfied
inequality 1
-2 <4 (-2) - 2
-2 <-10 (false)
inequality two
-2> = - (5/2) (- 2) - 2
-2> = 3 (false).
The first thing you should do is to graph both lines. Notice that one is of positive slope and another of negative slope.
The solution of the inequation system is given by the shaded region. That is, all the points that are in the shaded region satisfy the system of inequations.
Part B:
the point (-2, -2) is NOT included in the solution area (it is not in the shaded region.
Mathematically it is demonstrated by substituting inequalities and seeing that they are not satisfied
inequality 1
-2 <4 (-2) - 2
-2 <-10 (false)
inequality two
-2> = - (5/2) (- 2) - 2
-2> = 3 (false).
Note that 
in the given closed interval, so the area is exactly given by the definite integral
(no absolute values needed!)
Integrating gives
(no absolute values needed!)
Integrating gives