The sum of two numbers is 11, and their difference is 9. what are the two numbers?

  10 and 1

Step-by-step explanation:

Let x and y represent the two numbers. The problem statement lets us write two equations describing their relationships:

  x + y = 11

  x - y = 9

Adding these equations together, we have ...

  (x +y) +(x -y) = (11) +(9)

  2x = 20

  x = 10 . . . . . . . . . you will notice this is the average of the two given numbers

Then ...

  10 + y = 11 . . . . substitute for x in the first equation

  y = 1 . . . . . . . subtract 10

The two numbers are 10 and 1.

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

answer: 193

explanation:

200-7 = 193