The price of a train ticket consist of a eternal fee plus a constant fee per stop

We can make an equation

So we can make “x” the price PER stop

And we can make ”y” the initial fee

3x + y = 6.5

7x + y = 12.5

11x + y = 18.5

We’re trying to find price per stop.

So we can calculate the difference between Each.

So for 3 and 7 stops, theres 4 stops in between

12.5-6.5= 6

6 dollars difference.

4 stops in between

So we can do

6/4= 1.25

Each stop is $1.25

We can doublue check this…

So 1.25 for each stop fo for the first one

1.25*3= 3.75

ANd the initial fee (from subtraction) 2.75

SO using this

7*1.25= 8.75

Plus the initial fee which is 2.75

you’d get the same price.

Final

Each stop is $1.25

Initial fee is $2.75

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12