What is true about the figure? In the figure, angles C and D are a
Therefore, angle C must measure
B = ?
C = ?
A = ?
D = 124°

<A = 56degrees

<B = 34degrees

<C = 56degrees

Step-by-step explanation:

From tyhe diagram, the sum of m<C and m<D is 180degrees. Hence;

<C + <D = 180

<C + 124 = 180

<C = 180 - 124

<C = 56degrees

Also;

<B + 90 + <C = 180

<B + 90 + 56 = 180

<B  + 146 = 180

<B = 180 - 146

<B = 34degrees

Similarly;

<A + <B = 90

<A + 34 = 90

<A = 90 - 34

<A = 56degrees

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