Sinah bought some packs of gum. There were 8 sticks of gum in each pack. She gave 12 sticks of gum to manuela. This left sinah with 28 sticks of gum. Which equation can be used to represent this situation where g is the number of packs of gum that sinah bought?

8g = 12 + 28

g = 5 packs

Step-by-step explanation:

Share of the sticks of gum

Manuela = 12 sticks

Sinah = 28 sticks

There are 8 sticks in each pack

g = number of packs of gum that sinah bought?

g × 8 sticks = 12 sticks + 28 sticks

8g = 40

Divide both sides by 8

g = 40 / 8

g = 5 packs

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: