Quadrilateral abcd is inscribed in a circle with m< a = (x2)°, m< b = (7x - 10)°,
and
m< c = (3x)°.
what is m< d?

106°

Step-by-step explanation:

A quadrilateral inside a circle is a cyclic quadrilateral.

It means that the angles opposite are supplementary (add up to 180).

If we draw the quadrilateral ABCD, the angles A and C are supplementary and the angles B and D are supplementary.

Since we know A and C, we can write:

A + C = 180

x^2 + 3x = 180

x^2 +3x - 180 = 0

(x+15)(x-12) = 0

x= -15, or x = 12

Now, if we put x = -15, some angles become negative, so we disregard it and take x = 12.

Now finding B:

B = 7x - 10

B = 7(12) - 10

B = 74

We also know that B + D = 180, so:

B + D = 180

74 + D = 180

D = 180 - 74 = 106

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