The revenue, in dollars, of a company that produces video game systems can be modeled by the expression 5x2 + 2x – 80. the cost, in dollars, of producing the video game systems can be modeled by 5x2 – x + 100, where x is the number of video game systems sold. if profit is the difference between the revenue and the cost, what expression represents the profit?

profit can be modeled by the polynomial expression

options:

x+20
x-180
3x+20
3x-180

if 1,000 video game systems are sold, the company’s profit is $

options:

820
1,020
2,820
3,020

How to choose the sign of the radical in the denominator of the formula for the distance from a point to a line.

The rectangle shown has a perimeter of 108 cm and the given area. its length is 6 more than five times its width. write and solve a system of equations to find the dimensions of the rectangle.

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).