Samantha and paula live in the same neighborhood, but her parents are always worried about them traveling to each other’s house. to put their minds at ease, paula decides to find the actual distance between their house. she finds a map of their neighborhood and overlays a coordinate grid. on her new map her house is located at (-1,-3) and samantha’s house is located at (2,2). if each box on the grid is 1/2 a mile, how far apart do they live?

4 miles

Step-by-step explanation:

to answer this problem I looked at a coordinate plane to get a visual. I marked (-1,-3) and then counted how many spaces it took me to get to (2,2) which was 8. then i divided that by 2, because each square is only 1/2 a mile

step-by-step explanation:

i hate black

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