Can anyone please help I’ve been working on this one for awhile

x=8

<AQB= 40

<BQC=40

Therefore AQC = 40 + 40 = 80

Step-by-step explanation:

If QB is the angle Bisector of < AQC

Then, <AQB=<BQC (Reason: The angle bisector divides an angle in equal measurement)

So,

5x= 8x-24

24 = 8x - 5x

24= 3x

24 /3 = x

Therefore, x = 8

Then lets substitute

<AQB =5 x

5 ×8 = 40

--

<BCQ = 8x - 24

8×8-24

64-24= 40

(the angle AQB and angle BQC are equal)

Then <AQC= 40 +40 = 80

--

FINISH

---

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

17 1/3

step-by-step explanation: