Mathematics, 28.05.2020 21:59 gymer630

Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.

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Answer from: jay555538

f(g(x)) represents:

The amount of money Raul earns f, depends of number of tickets he sells g, and that depends on the number of hours he works x.

Step-by-step explanation:

Given that the function f(x) represents the amount of money Raul earns per ticket, and x is the number of tickets he sells.

The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works.

Now,

The amount of money Raul earns per ticket is a function of the number of ticket he sells.

Likewise, the number of tickets he sells is a function of the number of hours he works.

Finally, f(g(x)) a composite function.

Which means that f is a function of g which is a function of x.

The amount of money Raul earns f, depends of number of tickets he sells g, and that depends on the number of hours he works x.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

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Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticke...