help me pls

1) Mrs.Galicia sells online math and reading games. His 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. After how many days is the revenue for each game the same? Show your work and explain your answer.
Graph this system to show the solutions. Label each axis appropriately

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.
What are the two solutions to this system? Show your work.
Explain which solution is not reasonable in this situation.
After how many seconds do the rocket and the ball reach the same height.

Answer:

a) after 12.59 days the revenue will be equal

b) u just have to graph it

the second one is

a) the two solutions are x=4 and x=-4

b) x=-4 is not reasonable because time can’t be negative

c) after four seconds, the heights will be equal

Step-by-step explanation:

After 12.59 days the revenue for each game is the same. The two solutions of the system equation b(t) and p(t) are 4 and -4, and -4 is not a reasonable solution because time never be negative and after 4 seconds the rocket and the ball reach the same height.

1)

Given :

Math Game --   [tex]\rm M(d) = x^2-9x-10[/tex]

Reading Game --   R(d) = 2x + 10

It is given that after 'x' number of days the revenue for each game is the same, that is:

[tex]\rm x^2 -9x-10=2x+10[/tex]

[tex]\rm x^2 -11x-20=0[/tex]

Simplify the above quadratic equation.

[tex]\rm x = \dfrac{11\pm \sqrt{11^2-(4\times -20)} }{2}[/tex]

[tex]\rm x = \dfrac{11\pm \sqrt{201} }{2}[/tex]

x = 12.59 days

So, after 12.59 days the revenue for each game is the same.

The graph of both the revenue function is attached below.

2)

Given :

[tex]\rm b(t) =- t^2-2t+36[/tex]

p(t) = -2t + 20

The solution of this system can be determined by equating both the above function.

[tex]\rm -t^2 - 2t +36 = -2t +20[/tex]

Simplify the above equation.

[tex]\rm t^2 =16[/tex]

t = 4 and -4

a) The two solutions of the system are 4 and -4.

b) -4 is the solution is not a reasonable solution because time never be negative.

c) After 4 seconds the rocket and the ball reach the same height.

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