What is the least possible integer value for which 40% of that integer is greater than 9.6?
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Answer:
Graph Y
Step-by-step explanation:
<u>Given information</u>:
- Initial production cost = $1,050
- Lowest production cost = $250 for 200 items
- Production cost increases after 200 items.
- The x-axis shows number of items in <u>hundreds</u>.
- The y-axis shows the cost in dollars.
The initial production cost is when the number of items is zero.
Therefore, the y-intercept of the graph will be (0, 1050).
The lowest production cost is the <u>minimum point</u> of the curve.
Therefore, the vertex of the graph will be (2, 250).
The only graph that satisfies these conditions is graph Y (attached).
Learn more about parabolas here:
<h2>Explanation:</h2><h3>Part A.</h3>
The boundary lines of both inequalities will be dashed, because neither includes the "or equal to" case.
The first inequality solution area is bounded by a line with slope +5 and y-intercept +5. The solution area is above the line (y is greater than ...). Since the line rises steeply, the solution area looks to be to the left of the line. (It is shaded red on the attached graph.)
The second inequality solution area is bounded by a line with slope -1/2 and y-intercept +1. The solution area for this inequality is also above the line.
The solution area is where the two solution spaces overlap, in the quadrant to the upper left of the point where the lines intersect.
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<h3>Part B.</h3>The graph shows the point (-2, 5) to be in the solution space.
We can show this point satisfies both inequalities.
- 5 > 5(-2)+5 ⇒ 5 > -5 . . . true
- 5 > (-1/2)(-2) +1 ⇒ 5 > 2 . . . true