At lunch, Marc bought 2 quesadillas and 2 tacos for $10.16, and Jason paid $11.84 for 5 tacos and 1 quesadilla. What was the cost of each taco and quesadilla? Let the cost of a quesadilla be x and the cost of a taco be y.

X = 3.39 (Quesadilla)    Y= 1.69 (Tacos)

Step-by-step explanation:

You need to do systems of equations.

You take the quesadillas which is X and the Taco is Y and plug them into the equation with the total like this:

2x + 2y = $10.16

x + 5y = $11.84

solve and you get

(3.39, 1.69)

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