At fridays football game, 1,294 tickets were sold for a total amount of $8,816.00. if each student ticket cost $5.00, and each adult ticket costs $8.00 , how many student tickets were purchased?

512 student tickets were purchased.

Step-by-step explanation:

Represenation of the unknowns:  Let s be the number of student tickets and a the number of adult tickets.  Then s + a = 1294.

The dollar amounts are thus ($5/ticket)s + (8/ticket)a = $8816.

Goal: Find s; to do this, eliminate a.

Since s + a = 1294, a = 1294 - s

Then:  5s + 8(1294 - s) = 8816, or

5s - 8s + 8(1294) = 8816, or

-3s + 10352 = 8816

Isolating the 3s term, we get

-3s - 1536 = 0, or

3s = 1536, which yields s = 512

512 student tickets were purchased.

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

45

step-by-step explanation:

to find a percentage, add a decimal in front and multiply it by the other number.

.25 times 180= 45