1.)solve the absolute value equation.
2|3x -5| -8 =8
a. x= -1 5/6 or x= 5/6
b. x= -1 or x= 4 1/3
c. x= -1 5/6 or x= 4 1/3
d. x= -1 5/6 or x= -1

B.  x = -1 or x = 4 1/3.

Step-by-step explanation:

2|3x -5| -8 =8

2|3x -5| = 16

|3x -5|  =  8

The expression in the vertical lines can be positive or negative so we have 2 equations:

3x - 5 = 8 and 3x - 5 = -8

3x - 5 = 8

3x = 13

x = 13/3 or 4 1/3

3x - 5 = -8

3x = -8 + 5 = -3

x = -1.

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: y=4000x+14000

step-by-step explanation: