PLEASE HELP ASAP Which fact would help Kari prove that the measure of angle QMN is equal to the measure of angle SNL?

1. Interior angles MNR and PMN are congruent to each other, and vertical angles SNL and MNR are congruent to each other.
2. Alternate interior angles MNR and QMN are congruent to each other, and vertical angles SNL and MNR are congruent to each other.
3. Alternate interior angles MNS and PMN are supplementary and vertical angles SNK and RNL are congruent to each other.
4. Interior angles MNR and PMN are supplementary and consecutive angles SNL and MNS are congruent to each other.

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

50*10 is greater

step-by-step explanation:

if you add the zero from 10 to 50, it will give you a bigger number.

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: