Megan constructed triangle ABC. In Megan’s triangle, m∠A is represented by x°, m∠B is 4 times greater than m∠A, and m∠C is 30° l

Response:

$54

Detailed steps to explanation:

Initially

45 multiplied by.05 equals 2.25

Next

45 added to 2.25

Following that

45 multiplied by.15 equals 6.75

Finally

45 plus 2.25 plus 6.75

Answer:

2.CE lies on line m.

4.Ray AD is identical to ray AC.

6.Angle ECB is formed by CE and CB.

Step-by-step explanation:

A diagram has been provided.

Our task is to identify the valid statements regarding the diagram.

1.CB is found on line n.

CB does not align with line n since points C and B do not lie on that line.

Thus, this statement is false.

2.CE is situated on line m.

CE is indeed positioned on line m because points C and E are both on this line.

This statement is accurate.

3.Ray BC is equivalent to ray CB.

A ray begins at a single point and continues indefinitely without a terminal point.

Ray CB starts at point C and stretches out from point B.

However, ray BC does not exist.

This statement is therefore false.

4.Ray AD is equivalent to ray AC.

Both AD and AC are rays.

They are equivalent since both originate from point A and extend in the same direction.

5.Angle EAD is formed from AE and DA.

This is false because angle EAD is created by ray AE and ray AD, not by ray DA.

6.Angle ECB is generated by CE and CB.

This is true as angle ECB is made by ray EC and ray BC.

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.