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balandron [24]
3 years ago
12

The number of teams who entered in a 3-on-3 charity basketball tournament can be modeled by function T, where x is the number of

years since the tournament first started.
T(x)=4x+24

The entry fee paid by each team to enter the tournament can be modeled by function F, where x is the number of years since the tournament first started.

F(x)=5x+45

Which function, R, best represents the total entry fees collected in the xth year since the tournament first started?

A. r(x)=20x^2+300x+1,080

B. r(x)=9x+69

C. r(x)=9x^2+29x+69

D. r(x)=20x^2+1,080
Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
3 0

Answer:

<u>Option A:</u>

R(x)=20x^2+300x+1080

Explanation:

The revenue, R(x) is the product of the number of teams who entered the tournament, T(x), times the entry fee paid by each team, F(x); then you can write:

  • R(x)=T(x)\times F(x)

Thus you must multiply the two functions (polynomials):

  • R(x)=(4x+24)\times (5x+45)

Use distributive property:

R(x)=(4x+24)\times (5x+45)=(4x)(5x)+(4x)(45)+(24)(5x)+(24)(45)

Simplify:

R(x)=(4x)(5x)+(4x)(45)+(24)(5x)+(24)(45)=20x^2+180x+120x+1080

Add like terms:

R(x)=20x^2+180x+120x+1080=20x^2+300x+1080

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