Given the picture below, find x and both angles. X + 8
3x + 2
A.
X=
B. X+8=
C. 3x+2=

x =42.5

x+8 =50.5

3x+2 =  129.5

Step-by-step explanation:

The two angles shown are supplementary, so they add to 180

x+8   + 3x+2 = 180

Combine like terms

4x+10 = 180

Subtract 10

4x = 170

Divide by 4

x =42.5

x+8 = 42.5+8 = 50.5

3x+2 = 3*42.5 +2 = 127.5 +2 = 129.5

b.an increase in a causes b to decrease

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