In a community center 15 bottles are evenly spaced 12 cm apart from each other in a row for a competition what is the distance from the fourth bottle to the tenth bottle?

72 cm

Step-by-step explanation:

Relative to the first bottle, there are n - 1 spaces between the first bottle and the nth bottle. Since, each bottle is placed relative to the first bottle.

Now, for the fourth bottle, that is, n = 4, there are 4 - 1 = 3 spaces between the first and fourth bottle.

Since each space is 12 cm, the distance between the first and fourth bottle is 12 cm × 3 = 36 cm.

Now, for the tenth bottle, that is, n = 10, there are 10 - 1 = 9 spaces between the first and fourth bottle.

Since each space is 12 cm, the distance between the first and fourth bottle is 12 cm × 9 = 108 cm.

So, the distance between the fourth bottle and tenth bottle is distance between tenth bottle to first bottle minus distance between fourth bottle to first bottle = 108 cm - 36 cm = 72 cm

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

y=mx+b

step-by-step explanation:

m slope, b y-intercept