(20 Points) Perform the indicated operations.
1 answer:
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Answer:
Check the attached graph for correct match.
Step-by-step explanation:
Graph of the given choices are not given but we can still solve this problem.
Given equation is 15x-12y=60.
Which is linear equation so we need at least two points to get the graph.
We are free to select any random number of x then plug that into given equation to find other variable.
Let's use x=0
15x-12y=60
15*0-12y=60
0-12y=60
-12y=60
divide both sides by -12
y=-5
Hence point is (0,-5)
Similarly plug y=0
15x-12y=60
15x-12*0=60
15x-0=60
15x=60
divide both sides by 15
x=4
Hence point is (4,0)
Now graph both points then join them by a straight line.
Any graph given in the choices which match with attached graph will be the answer.
Check the attached graph for correct match.
Answer:
First option:
Step-by-step explanation:
The missing options are:
We know that "x" represents the number of weeks Bess worked and "y" the number of weeks Gina worked.
According to the data given in the exercise, Gina and Bess earn $45 per week for delivering flowers, this is:
Since earned an additional total bonus of $20, then the total money in in dollars that Bess and Gina earned for delivering flowers can be shown with the following expression:
Notice that this expression matches with the one shown in the first option.
Answer:
168 trumpets for $1702
Step-by-step explanation:
Profit is the measure to be maximized. We are given revenue and cost relationships as a function of units, x (trumpets). Profit is the difference:
Profit = Revenue[R(x)] - Cost[C(x)]
Profit = (76x – 0.25x^2) - (-7.75x + 5,312.5)
Profit = 76x - 0.25x^2 + 7.75x - 5,312.5
Profit = 76x - 0.25x^2 + 7.75x - 5,312.5
Profit = - 0.25x^2 + 83.75x - 5312.5
At this point we can find the trumpets needed for maximum profit by either of two approaches: algebraic and graphing. I'll do both.
<u>Mathematically</u>
The first derivative will give us the slope of this function for any value of x. The maximum will have a slope of zero (the curve changes direction at that point). Take the first derivative and set that equal to 0 and solve for x.
First derivative:
d(Profit)/dx = - 2(0.25x) + 83.75
d(Profit)/dx = - 0.50x + 83.75
0 = - 0.50x + 83.75
0.50x = 83.75
x = 167.5 trumpets
<u>Graphically</u>
Plot the profit function and look for the maximum. The graph is attached. The maximum is 167.5 trumpets.
Round up or down to get a whole trumpet. I'll go up: 168 trumpets.
<u>Maximum Profit</u>
Solve the profit equation for 168 trumpets:
Profit = - 0.25x^2 + 83.75x - 5312.5
Profit = - 0.25(168)^2 + 83.75(168) - 5312.5
<u>Profit = $1702</u>
