A group of 5 people paid for general admission to the museum. Some of the people also bought movie tickets. The whole group spent a total of $108 for general admission tickets and movie tickets. Write and equation that can used to find x, the number of movie tickets purchased.

5 k + x m   = 108   is the needed equation.

k  : Cost of 1 general admission ticket

x  : Number of movie tickets purchased.

m : cost of 1 movie ticket.

Step-by-step explanation:

The number of people who visited the museum = 5

The total amount spent on general admission and movie tickets  = $108

x : the number of movie tickets purchased

Let us assume the cost of each ticket  = $ m

So, the cost of x tickets  = x ( cost of 1 ticket) = x ( $m) = m x  

Also, the general admission amount  for 1 person  = $ k

⇒ General admission amount for 5 people  = 5 x ( $k)  = 5 k

So, according to the question:

The general admission + Amount +  cost of x movie tickets  = $ 108

$ 5 k + x m   = 108

So, here: 5 k + x m   = 108

k: Cost of 1 general admission ticket

x: Number of movie tickets purchased.

m : cost p=of 1 movie ticket.

Hence, the needed  equation is  5 k + x m   = 108.

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