What is the measure of angle x? enter your answer in the box. x = ° two perpendicular lines intersected by a third line, which goes from upper left to lower right. the angle formed on the left side of the figure by the diagonal line and the vertical line is labeled 42 degrees, and the angle formed on the right side of the figure by the diagonal line and the horizontal line is labeled x.

x = 48°

Step-by-step explanation:

The angle formed on the right side by the diagonal and the vertical lines is vertical to 42 , thus = 42

The angle between the axes is 90°, hence

x = 90° - 42° = 48°

there is no image or shapes attacted

step-by-step explanation:

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