Julianne opens a dance studio. her start-up costs for the building, advertising, and supplies $52,000. each day, she spends $650 on operating costs (like utilities and wages). she earns $960 per day from her students' lesson fees. part a: write an equation or inequality to represent this situation. let d be the number of days. part b: when will julianne begin making a profit? show all the work you did to arrive at your answer.

Answer-

The equation is and Julianne will begin making a profit after 168 days.

Solution-

Julianne's start-up cost = $52,000,

Each day, she spends = $650,

and she earns = $960 per day,

If 'd' is the number of days to overcome the start-up and daily operation cost, then  

total operation cost of d days = $650d and  

total student lesson fees earned in d days = $960d

∴ The equation to represent the situation is,

∴ Julianne will begin making a profit,

she will most likely have 33  

step-by-step explanation:

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.