Here is the graph of a function showing the amount of money remaining on a subway fare card as a function of the number of rides taken. please look at the picture to help answer the questions.

Step-by-step explanation:

This is a linear graph,

Let find the equation of the line

Equation of a line can be determine using

y = mx + c

Where m Is the slope of the graph and c is the intercept on y axis when x = 0

So,

Slope m can be calculated using

Let chose the two point on the x and y axis

P1 = (0,45) and , P2 = (18,0)

m = ∆y / ∆x  = y2 - y1 / x2 - x1

m = 0 - 45 / 18 - 0

m = -45 / 18

m = -2.5

So, the intercept on the y axis when x = 0 is 45. Then, c = 45

So,  the equation of the line becomes

y = -2.5x + 45

Multiply through by 2

2y = -5x + 90

Where

y is dollars on card, = output

x is the number of rides = input

A. So, we want to find the output when the input is 10, I.e when x = 10

Then,

y = -2.5x + 45

x = 10

y = -2.5 × 10 + 45

y = -25 + 45

y = 20

Then, the output is 20 dollars on card.

B. When the output is 5

I.e y = 5

Then,

y = -2.5x + 45

5 = -2.5x + 45

5-45 = -2.5x

-40 = -2.5x

x = -40 / -2.5

x = 16 rides

The input is 16 number of rides

C. Point P is (7,27.5)

This tells us that when the input is 7, I.e the number of rides is 7, then, the output is 27.5 I.e their are $27.5 dollars on card.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc