The table shows the ratio between the number of books ordered and their cost: number of books cost (dollars) 7 21 8 24 9 27 find equivalent ratios when the number of books ordered is 1, 2, and 3. write them as ordered pairs in the form (x-coordinate, y-coordinate). starting from the origin, explain how to plot the three equivalent ratios on a coordinate grid. (10 points)

The graph in the attached figure

Step-by-step explanation:

Let

x------->  the number of books ordered

y------> the cost in dollars

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have a proportional variation

so

Step 1

Find the value of k

For

------> substitute the values

For

------> substitute the values

For

------> substitute the values

The equation of the linear equation is equal to

Step 2

For -------> Find the value of y

substitute the value of x in the linear equation

The point is

Step 3

For -------> Find the value of y

substitute the value of x in the linear equation

The point is

Step 4

For -------> Find the value of y

substitute the value of x in the linear equation

The point is

Step 5

Using a graphing tool

Plot the three equivalent ratios on a coordinate grid

see the attached figure

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

1. perpendicular

2. parallel

3. perpendicular