33. Albert says that the two systems of equations shown below have the same solutions.
12x + 5y = 21
-8.5y = -51
Determine and state whether you agree with Albert. Justify your answer.
Solve the second system first. If -8.5y = -51, then divide and get y = 6. Then 8x + 9(6) = 48.
8x = -6
x = -0.75
Substitute these numbers into the first system: 12(-0.75) + 5(6) = 21 ?
21 = 21 (check)
Albert was correct.
Don't forget to say that Albert was correct even though there is NO CREDIT for saying he is correct without the justification.
34. The equation to determine the weekly earnings of an employee at the Hamburger Shack is given by w(x), where x is the number of hours worked.
Determine the difference in salary, in dollars, for an employee who works 52 hours versus one who works 38 hours.
Determine the number of hours an employee must work in order to earn $445. Explain how you arrived at this answer.
This is how overtime generally works in the real world.
The 38 hour employee earned $380. (38 * 10)
The 52 hour employee earned $400 + 12 * 15 = $580. The difference is $200.
In order to earn $445, they need to work 40 hours, earning $400, and then another $45, which at $15/hour is three more hours, for a total of 43 hours.
35. An online electronics store must sell at least $2500 worth of printers and computers per day. Each printer costs $50 and each computer costs $500. The store can ship a maximum of 15 items per day. On the set of axes below, graph a system of inequalities that models these constraints.
Determine a combination of printers and computers that would allow the electronics store to meet all the constraints. Explain how you obtained you answer.
First, the inequalities you need to graph are:
50p + 500c > 2500
The graph looks like this:
Possible combinations that would work would be, for example, 0 printers and 5 computers, or 10 printers and 4 computers.
36. An application developer released a new app to be downloaded. The table below gives the number of downloads for the first four weeks after the launch of the app.
Write an exponential equation that models these data.
Use this model to predict how many download the developer would expect in the 26th week if this trend continues. Round your answer to the nearest download.
Exponential regression, which can be done in the calculator.
Since I don't have one handy, I can see that it increases by 60, 90, 135 ... which increasing by half, so an equation could be
y = 120(1.5)^(w-1)
Using that formula, on the 26th week, there would be 3030140 downloads (rounded).
Using that formula, on the 52nd week, there would be 1.15 X 10^11 downloads, which is not a reasonable number because it is more than the number of people on the planet to begin with, all of whom, by this point, would have already downloaded it.
I'm curious if anyone is going to explain that apps die out after a few months and wouldn't keep growing.
This question is worth 6 credits.
37. A football player attempts to kick a football over a goal post. The path of the football can be modeled by the function h(x) = -1/225 x2 + 2/3 x, where x is the horizontal distance from the kick, and h(x) is the height of the football above the ground, when both are measured in feet.
On the set of axes below, graph the function y = h(x) over the interval 0 < x < 150.
Determine the vertex of y = h(x). Interpret the meaning of this vertex in the context of the problem.
The goal post is 10 feet high and 45 yards away from the kick. Will the ball be high enough to pass over the goal post? Justify your answer.
The graph looks like the one below. Put the equation in your calculator and check the Table of Values. Note that your graphing calculator defaults to showing from -10 to +10, not 1 to 150, so you won't see it unless you change the display settings. Also, be careful about entering the equation. I entered "255" instead of "225" the first time and you can see the erasures. I didn't realize my mistake until I noticed that 75 wasn't the vertex, which I reasoned it should be.
The vertex of y=h(x) is (75, 25), which means that at 75 feet away from the kicker, the ball will reach a maximum height of 25 feet and start descending.
At 45 yards, or 135 feet, the ball will be 9 feet of the ground (135, 9), so it will not pass over the goal post, which is 10 feet high.
That's it for this test. Finally complete. Except for some illustrations, which will be added when they are available.