Laurie wants to put a portable cellular phone mini-tower in her roof. the tower cannot be placed higher than 30 feet. the slant of her roof can be represented by the equation r(x)=-1/4|x|+60. if her house is 40 feet wide, where could she place the tower? explain.

Nowhere on the roof

Step-by-step explanation:

The roof will never drop below 50 feet in height.  

The function is an absolute value function.  The graphs of absolute value functions consist of straight lines, so they either increase or decrease constantly in one direction.

We can use the domain of this function to solve it.  The house is 40 feet wide, so we could potentially place it anywhere on the roof from the beginning of the house (0 feet) to the end of the house (40 feet), so the domain is

D: [0, 40}

Now we want to determine the range of the function based on this domain.  Here the range will be the height of the roof.  At one side of the house (0 feet) we see that the roof height is...

r(0) = -(1/4)|0| + 60

  r(0) = 60         on one side of the house, the roof is 60 feet up.  

On the other side (40 feet) the roof height is...

r(40) = -(1/4)|40| + 60

    r(40) = -10 + 60

         r(40) = 50

So the roof is 50 feet high on the other side of the house.  Since the graph is a continuous line, there is no place between these points that could equal 30 feet, so the antennae can't go on the roof.

well what did you do it matters what you did : )

step-by-step explanation: