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Ivanshal [37]
3 years ago
6

Marissa is an event organizer for a charity group. She is organizing a five-hour dinner event being held to raise funds for the

charity. The following list shows the costs for hosting the event.
Facility Rental: $150 per hour of event
Linens: $2 per attendee
Food: $20 per attendee
Table Decorations: $3 per attendee
Musical Entertainment: $1,800 (flat fee)
Cleaning Fee: $250 (flat fee)
The total cost of the event, with n attendees, is represented by the given expression.



Which statement best describes the constant in this expression?

A.
It is the cost per person for food, linens, and table decorations.
B.
It is the total cost for entertainment and cleaning.
C.
It is the total cost for entertainment, facility rental, and cleaning.
D.
It is the cost per hour for facility rental and cleaning.
Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
6 0

Answer: C.  

It is the total cost for entertainment, facility rental, and cleaning.

For a 5 hour event organized by Marissa, we have a list of cost from different categories that would add up to the total for hosting the event. It includes the facility rental which is paid $150 per hour so for 5 hours it would be $750.

Next we have linens, food and table decorations that are charged according to the number of attendees at the event. Since the number of attendees is unknown here, we are going to skip everything which is effected by the number of attendees. Furthermore, we have musical entertainment and cleaning fee at a flat rate of $1800 and $250 respectively. So there are 3 things that we are sure about that they will stay constant despite the number of attendees and they are facility rental, musical entertainment and cleaning fee.

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Given that the <span>straight line p(x) joins the ordered pairs (0, 2) and (1, -5), thus the equation of the line joining ordered pairs (0, 2) and (1, -5) is given by

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Thus, p(x) = -7x + 2

</span>Given that the <span>straight line f(x) joins the ordered pairs (4, 1) and (2, -3), thus the equation of the line joining ordered pairs (4, 1) and (2, -3) is given by

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The solution to the pair of equations represented by p(x) and f(x) is given by

p(x) = f(x)
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p(1) = -7(1) + 2 = -7 + 2 = -5

Therefore, the solution to the pair of equations represented by p(x) and f(x) is  (1, -5)



Part B:

From part A, we have that f(x) = 2x - 7

when x = -8

f(-8) = 2(-8) - 7 = -23

Thus, (-8, -23) is a solution to f(x).

When x = -10

f(-10) = 2(-10) - 7 = -27

Thus, (-10, -27) is a solution to f(x).

Therefore, two solutions of f(x) are (-8, -23) and (-10, -27).



Part C:

From part A, we have that p(x) = -7x + 2, given that g(x) = 1 + 1.5^x

From the graphs of p(x) and g(x), we can see that the two graphs intersected at the point (0, 2).

Therefore, the solution to the equation p(x) = g(x) is (0, 2).

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