1. solve for x. show each step of the solution.
4.5(8 - x) + 36 = 102 - 2.5(3x+24)

x= -10

Step-by-step explanation:

       4.5(8 - x) + 36 = 102 - 2.5(3x + 24)

4.5(8) - 4.5(x) + 36 = 102 - 2.5(3x) -2.5(24)

       36 - 4.5x + 36 = 102 - 7.5x - 60

                72 - 4.5x = 102 - 7.5x - 60

                      -4.5x = 102 - 7.5x - 60 - 72

           -4.5x + 7.5x = -30

                           3x =  -30

                             x = -30/3

                             x = -10

Sorry if its wrong, I try my best.

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

answer: the correct answer is -32

step-by-step explanation: