The tangent, cotangent, and cosecant functions are odd , so the graphs of these functions have symmetry with respect to the:

Answer:

Part a) Your budget is $40.

Part b) The price for one gallon of gasoline is $3.55, while a car wash costs $8.

Part c)

Part d) Refer to the explanation below.

Step-by-step explanation:

Please see the complete question in the attached image.

Part a) The budget is expressed by the equation

y = 40

therefore,

Your budget amounts to $40.

Part b) In terms of costs, how much is a gallon of gasoline and what is the car wash price?

Let

y ------> denote the total cost for a gallon of gasoline along with a car wash

x -----> define the volume of gasoline in gallons

We can express the relationship as

y = 3.55x + 8

For calculations, when x = 0, we have:

y = 3.55(0) + 8 = 8

The y-intercept signifies the cost of the car wash, being $8.

Now, to identify the price of one gallon of gasoline:

We know the slope of the linear function is

m = $3.55 per gallon

This confirms that a gallon of gasoline costs $3.55.

Part c) Formulate an inequality representing the potential quantity of gasoline you can purchase:

We have:

Now, solve for x:

Part d) Utilize the graph to determine the solution of the inequality from part c)

We can set up the system:

y = 40

y = 3.55x + 8

The solution lies at the intersection of both graphs. By observing the graph, the intersection appears to be around (9, 40).

This indicates that the maximum volume of gasoline purchasable within your budget is approximately 9 gallons.

Answer:

Comprehensive explanation:

Let's denote

x -----> the number of days

and

y ----> the remaining minutes for Yuson

We know that

The linear equation in slope-intercept form can be represented as

here

m indicates the slope

b represents the y-coordinate of the y-intercept (starting value)

In this scenario, we have

The slope is defined as

----> negative, as it indicates a decreasing function

----> initial value

substituting the values

C. -31m⁴n - 8m²Step-by-step explanation:Given:(9mn - 19m⁴n) - (8m² + 12m⁴n + 9mn)Required:Identify an equivalent expression for itSolution:Distributing the negative sign across the parentheses results in:9mn - 19m⁴n - 8m² - 12m⁴n - 9mnNext, we combine like terms:9mn - 9mn - 19m⁴n - 12m⁴n - 8m²This simplifies to -31m⁴n - 8m²Thus, -31m⁴n - 8m² is the equivalent expression for (9mn - 19m⁴n) - (8m² + 12m⁴n + 9mn).