The case of 12 bottles of shampoo holds a total of 126 ounces. If each bottle of shampoo contains the same amount, which represents the total volume of shampoo in ounces, y, of any number of bottles, x?

y(x)=10.5x

Step-by-step explanation:

Since all bottles contain equal volume and the total volume is given as 126 ounces then to find volume of each bottle, considering that the 126 ounces are in 12 bottles then each bottle will have 126/12=10.5 ounces.

The volume for x similar bottles will be x*10.5 ounces.

Therefore, the formula for volume will be

y(x)=10.5x

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

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step-by-step explanation: vsfdvsfvd