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x=21

Step-by-step explanation:

61+34 = 95  

360( a circle) - 95 = 265

265 +7 +22 = 294

9x+5x=14x

294=14x (divide both by 14 to get x)

X=21

x = 21

Step-by-step explanation:

A circle makes a 360 degree turn

So the measure of the arcs should add up to equal 360

That being said we create an equation to solve for x

360 = 61 + 5x - 7 + 34 + 9x - 22

Now we solve for x using basic algebra

Step 1 combine like terms

61 - 7 + 34 - 22 = 66

5x + 9x = 14x

now we have 360 = 14x + 66

step 2 subtract 66 from each side

66 - 66 cancels out

360 - 66 = 294

now we have 294 = 14x

step 3 divide each side by 14

294/14=21

14x/14=x

we're left with x = 21

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

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step-by-step explanation: