Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $13 monthly fee
1 answer:
Answer:
With 250 minutes of calls the cost of the two plans is the same
Step-by-step explanation:
We must write an equation to represent the cost of each call plan.
<u>For the first plan</u>
Monthly fee
$ 13
Cost per minute
$ 0.17
If we call x the number of call minutes then the equation representing the cost c for this plan is:
<u>For the second plan</u>
monthly fee
$ 23
Cost per minute
$ 0.13
If we call x the number of call minutes then the equation representing the cost c for this plan is:
To know when the cost of both plans are equal, we equate the two equations and solve for x.
With 250 minutes of calls the cost of the two plans is the same: $55.5
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Answer:
There are NO real roots for this equation. The only roots have imaginary parts and therefore cannot be represented on the real x-axis.
Step-by-step explanation:
We notice that the expression on the left of the equation is a quadratic with leading term , which means that its graph is that of a parabola with branches going up.
Therefore, there can be three different situations:
1) if its vertex is ON the x axis, there would be one unique real solution (root) to the equation.
2) if its vertex is below the x-axis, the parabola's branches are forced to cross it at two locations, giving then two real solutions (roots) to the equation.
3) if its vertex is above the x-axis, it will have NO real solutions (roots) but only non-real ones.
So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently.
We recall that the x-position of the vertex for a quadratic function of the form is given by the expression:
Since in our case and
, we get that the x-position of the vertex is:
Now we can find the y-value of the vertex by evaluating this quadratic expression for x = 3/4:
This is a positive value for y, therefore we are in the situation where there is NO x-axis crossing of the parabola's graph, and therefore no real roots.
We can though estimate a few more points of the parabola's graph in order to complete the graph as requested in the problem. For such we select a couple of x-values to the right of the vertex, and a couple to the right so we can draw the branches. For example: x = 1, and x = 2 to the right; and x = 0 and x = -1 to the left of the vertex:
See the graph produced in the attached image.
