4 problems pls can you solve them with explanation i need to compare correct

n the summer time your friend wants to have a snow cone stand at a local grocery store parking lot. You want to make sure he actually makes money. The grocery store charges $300 per month. All products are calculated to be 25 cents per customer. Your plans are to sell each cone for $1.25.

a. Write a mathematical expression representing the cost of operation for a month.
b. Write a mathematical expression representing sales.
c. Create an equation that will represent overall profit of the operation for a month.
d. Simplify the equation into slope intercept form and standard form. What is the slope and explain its meaning in the context of selling snow cones? What is the intercept and what is its meaning?
e. Describe the method of graphing the slope intercept form and also the standard form of the equation.
f. What is the domain and range of the equation? Is the relation a function, why?
g. How many snow cones do you need to sell to break even in the first month?
h. How much is the profit if you sell 425, 550 or 700 snow cones in the first month of business?

2) Write a rational expression with at least one $footnotesize{x}$ in the denominator and then analyze it using the following questions:

a. Set your expression equal to 0. Does this expression have any solutions? Why, or why not?
b. Set your expression equal to $footnotesize{y}$ and graph the equation on a graphing utility or on your calculator. Are there any values that $footnotesize{x}$ cannot be? Explain.
c. How do the numbers and variables in your equation relate to the features of the graph?
d. Identify the denominator of your expression; add 6 to the denominator only. How does the graph change?

3) The following equations are given:

Equation #1: $footnotesize{3x + z + y = 8}$
Equation #2: $footnotesize{5y - x = -7}$
Equation #3: $footnotesize{3z +2x -2y = 15}$
Equation #4: $footnotesize{4x +5y - 2z = -3}$

a. Is it possible to solve for any of the variables using only Equation #1 and Equation #2? Explain your answer. If possible, solve for the variables using only equations #1 and #2.
b. Is it possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #3? Explain your answer. If possible, solve for the variables using only equations #1, #2, and #3.
c. If you found solutions in part b, do these solutions also hold for Equation #4?

4) Look at the following table then answer the questions below.

x      Equation 1  Equation 2   Equation 3  Equation 4   Equation 5   Equation 6      

0       0                 10                 -4                  2                 12                    12.31

1         0.06           9.5                -3.75            2.06            11.91             10.45

4           1                8                  -2.56            2.25            10.55            6.81

5           1.56           7.5                -1.95           2.31              9.73             6.05

7           3.06           6.5                -0.23           2.44              7.55            4.95

9           5.06            5.5                2.45            2.56                4.64           4.25

10          6.25            5                  4.31              2.66               2.91         4

11         7.56             4.5               6.64                2.69             1               3.8

12           9                4                    9.55               2.75             -1.09          3.64

15          14.06        2.5                 23.42               2.94            -8.45             3   

17          18.06          1.5                 39.41                3.06             -14.27           3.21

20          20                0                     81.74                3.25                 -24.36           3.11

a. Which of the functions in the table appear to be exponential?
b. What reasoning would you use to justify your answer?
c. Which function(s) would most likely model bacterial growth in a lab culture? Justify your reasoning.
d. Which values would most likely model the use of dial-up internet service? Justify your reasoning.

 
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