"If you have 2 pieces of spaghetti that have lengths 4 cm and 10 cm, what could be the possible length of a third piece of spaghetti to complete the triangle?" and it has to have "cm < x <"

   6  <   third side    <   14

Third side must be greater than 6 and less than 14

Step-by-step explanation:

A triangle can be formed from 2 sides of any length.

The third side must be longer than the difference of the other 2 sides and

 the third side must be less than the sum of the other 2 sides.

I had a quiz with the same question and got an A

Hope this helps! :)

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

i think the amount would be $140.62