The graph shows the relationship between the hours a soccer team practiced after the season started and their total practice time for the year.
A. How many hours did the soccer team practice before the season began?
B. What are the two quantities in this situation?
C. What are the two Dependant and independent variables?
D. Is the relationship between the variables additive or multiplicative.

A. the total practice time before the season began is 6 hours

B. See explanation

C. See explanation

D. Additive relationship

Step-by-step explanation:

The graph in the attached figure.

A. How many hours did the soccer team practice before the season began?

As the graph represents the relationship between the hours a soccer team practiced after the season started and their total practice time for the year.

and it is required to find the practice hours before the season began

We can deduce that, as the line begin at the point (0,6) which represent the intersection with the y-axis and consequently represents the total practice time before the season began as x = 0.

So, the  total practice time before the season began is 6 hours

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B. What are the two quantities in this situation?

There are two quantities, let the quantities x and y

x ⇒ The hours a soccer team practiced after the season started

y ⇒ The total practice time for the year in hours.

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C. What are the two dependent and independent variables?

The independent variable is x and the dependent is y

because The total practice time for the year in hours (y) depending on the hours a soccer team practiced after the season started (x)

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D. Is the relationship between the variables additive or multiplicative?

To find the relationship between the variables, we will find the equation between x and y

As shown the graph represents a line between x and y.

The general form of the line is ⇒ y = mx + c

where m is the slope and c is y-intercept

so, as x = 0 , y = 6 ⇒ c = 6

Choose another point to find m, say we choose (2,8)

so, as x= 2 ⇒ y = 8

Substitute at the general form with x= 2 ,  y = 8  and c = 6

8 = 2m + 6

Solve for m

2m = 8 - 6 = 2

m = 2/2 = 1

∴ y = x + 2

The last relation is  Additive relationship

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Note:

Additive relationships ⇒ you add the same number to any x-value to get the corresponding y-value for example y = x + c

Multiplicative relationships ⇒ you multiply any  x-value times the SAME number to get the corresponding y-value for example y = cx

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet

d≈7.07in

step-by-step explanation: