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PLEASE can anyone answer these questions? this is due tomorrow and still havent turned in anything URGENT

#1 Mrs. Galicia sells online math and reading games. Her revenue for each game (in dollars) is modeled by the given equations, where x is the number of days since the games went on sale.
Math game: M(d)=x^2-9x-10
Reading game: R(d)=2x+10
Solve the system algebraically.
a) what are the two solutions to this system? SHOW YOUR WORK.
b) after how many days is the revenue for each game the same?

#2 Mrs. Galicia dropped a ball from the top of a tower. At the same time, her son, Antonio, launches a rocket from a different level of the tower.
The height of the tennis ball in feet after t seconds can be represented by the quadratic function:
b(t)=-t^2-2t+36
The height of Antonio's rocket after t seconds can be represented by the linear function:
p(t)=-2t+20
a) what are the two solutions to this system? SHOW YOUR WORK.
b) explain which solution is not reasonable in this situation.
c) after how many seconds do the rocket and the ball reach the same height?

Respuesta :

lunathemoonchild13
1.
M(d) = x^2 - 9x - 10
R(d) = 2x + 10

A. Since M(d) and R(d) are technically the same term, we can substitute them for the other.

Substitute M(d) for R(d)’s expression

2x + 10 = x^2 - 9x - 10

x^2 - 11x - 20 = 0

Use this equation to put in the quadratic formula

x = (-(-11) +/- √((-11)^2 - 4(1)(-20)))/2(1)

x = (11 +/- √201)/2 or x = 12.5887… and -1.5887…

B. 12.6 days as there can’t be negative days

2.

Do the same substitution as the previous question

-t^2 - 2t + 36 = -2t + 20

Get all parts on the same side

t^2 - 16 = 0

Optional: quadratic formula

t = (-(0) +/- √((0)^2 - 4(1)(-16)))/2(1)

t = 4 and -4

b. -4 is not reasonable in this situation as time cannot be negative

c. 4 seconds


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