Mathematics: 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

The number of teams who entered in a 3-on-3 charity

Ответ:

vlout

13.01.2022

Mathematics

Option A:

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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