Suppose that there are two types of tickets to show: advance and same-daythe combined cost of one advance ticket and one same-day ticket is $55. for one performance, 25 advance tickets and 30 same-day tickets were sold. the total amount paid for the tickets was $1450 . what was the price of each kind of ticket?

the price of one advance ticket is $40

the price of one same day ticket is $15

Step-by-step explanation:

Let x represent the price of one advance ticket.

Let y represent the price of one same day ticket.

The combined cost of one advance ticket and one same-day ticket is $55. This means that

x + y = 55

For one performance, 25 advance tickets and 30 same-day tickets were sold. The total amount paid for the tickets was $1450. This means that

25x + 30y = 1450 - - - - - - - - -1

Substituting x = 55 - y into equation 1, it becomes

25(55 - y) + 30y = 1450

1375 - 25y + 30y = 1450

- 25y + 30y = 1450 - 1375

5y = 75

y = 75/5 = 15

Substituting y = 15 into x = 55 - y, it becomes,

x = 55 - 15

x = 40

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