Santosh spent $200, before tax, on a DVD player and DVDs. The player cost $120, new DVDs cost $15 and used DVDs cost $5. Santosh purchased the same number of new and uses DVDs. Write and solve an equation to find the number of each type of DVD Santosh purchased.

Santosh purchased 4 new and 4 used DVDs.

Step-by-step explanation:

From the information given, as you know that Santosh spent $200 and that the DVD player cost $120, you can say that the new and used DVDs cost $80, which can be expressed as:

15x+5y=80, where:

x refers to the number of new DVDs

y refers to the number of used DVDs

Now, as the statement indicates that Santosh purchased the same number of new and used DVDs, this means that x is equal to y and you can replace y with x and solve for x:

15x+5x=80

20x=80

x=80/20

x=4

According to this, the answer is that Santosh purchased 4 new and 4 used DVDs.

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