A moving company charges $40 plus point $.25 per mile to rent a van. Another company charges $25 plus point $.35 per mile to rent the same band. For what number of miles will the rental cost be the same for both companies?

150 miles

Step-by-step explanation:

m = mile

40 + 0.25m = 25 + 0.35m

0.25 * 150 = 37.5

37.5 + 40 = 77.5

0.35 * 150 = 52.5

52.5 + 25 = 77.5

77.5 = 77.5

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