• Is this a parallelogram? • Defend your answer.
1 answer:
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Answer:
C. (see the attachment)
Step-by-step explanation:
Both inequalities include the "or equal to" case, so both boundary lines will be solid. That excludes choices A and D.
The first inequality is plotted the same way in all graphs, so we must look at the second inequality. The relationship of y and the comparison symbol is ...
-y ≥ (something)
If we multiply by -1, we get ...
y ≤ (something else)
This means the solution space will be <em>on or below (less than or equal to) the boundary line</em>. This is the shaded area in graph C. (Graph B shows shading <em>above</em> the line.)
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<em>Further comment</em>
Since the boundary for the second inequality is fairly steep, "above" and "below" the line can be difficult to see. Rather, you can consider the relationship of x to the comparison symbol. For the second inequality, that is ...
x ≥ (something)
indicating the solution space is <em>on or to the right of the boundary line</em>.
Answer:
The room dimensions for a minimum cost are: sides of 10 feet and height of 8.75 feet.
Step-by-step explanation:
We have a rectangular room with sides x and height y.
The volume of the room is 875 cubic feet, and can be expressed as:
With this equation we can define y in function of x as:
The cost of wall paint is $0.08 per square foot. We have 4 walls which have an area Aw:
The cost of ceiling paint is $0.14 per square foot. We have only one ceiling with an area:
We can express the total cost of painting as:
To calculate the minimum cost, we derive this function C and equal to zero:
The sides of the room have to be x=10 feet.
The height can be calculated as:
The room will have sides of 10 feet and a height of 8.75 feet.