What is the value of p?

p = 50°.

Step-by-step explanation:

To find the value of 'p', we will need to solve for the measure of the other angles of the triangle using the Supplementary Angles theorem.

Notice 140° at the top of the figure. This angle is supplementary to the top angle of the triangle. We can find this angle by:

180 - 140 = 40°.

Repeat this same step for the other angle.

180 - 90 = 90°.

Since the sum of all 3 sides = 180, we must subtract these from 180 to get the measure of 'p'.

180 - 90 - 40 = 50°.

Therefore, p = 50°.

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

70

step-by-step explanation:

2*5=10

4*15=60

60+10=

70