Zontini the Amazing Hypnotist is hypnotizing a volunteer at a performance by

Response: it is S - D

Detailed explanation:

Answer: To remove fractions prior to solving, each term in the equation must be multiplied by .

Step-by-step explanation:

Consider the given expression:

It is essential to simplify this before attempting to solve it.

Since the denominators differ, identifying the Least Common Denominator (LCD) is necessary.

Break down the denominators into their prime components:

Select , as it possesses the greatest exponent. Thus:

Ultimately, to remove the fractions before solving, multiply both sides by 4:

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.

(a) 4 <span>(b) y = sqrt(9 - (9/16)x^2) </span>The most accurate assumption for the equation based on the general format for an ellipse is: [[TAG_3]]x^2/16 + y^2/9 = 1 [[TAG_4]](a). An ellipse is symmetrical along both its major and minor axes. Thus, if you can calculate the area of the ellipse in one quadrant, multiplying that area by 4 will yield the total area of the ellipse, confirming the factor of 4 is accurate. [[TAG_5]] (b). The standard equation for an ellipse doesn't adequately represent a general function as it results in two y values for each x value. However, if we constrain ourselves to the positive square root, that issue can be resolved easily. Here’s how: [[TAG_6]] x^2/16 + y^2/9 = 1 [[TAG_7]] x^2/16 + y^2/9 - 1 = 0 [[TAG_8]] x^2/16 - 1 = - y^2/9 [[TAG_9]] -(9/16)x^2 + 9 = y^2 [[TAG_10]] 9 - (9/16)x^2 = y^2 [[TAG_11]] sqrt(9 - (9/16)x^2) = y [[TAG_12]] y = sqrt(9 - (9/16)x^2)

A proportion maintains a consistent ratio m/d

If m = 0.75d, then the m/d ratio translates to (0.75d)/d = 0.75

In this case, the ratio can be expressed as (.75d-2)/d = 0.75 - (2/d).

Thus, it is not proportional.