In 4th grade, Richard read 37 books. In 5th grade, he read
9 more books than the year before. This
year, in 6th grade, Richard plans to read at
least 12 more books than the total number
of books read in both 4th and 5th grades.
Richard writes the inequality b Ú 180 to
show the total number of books he will
have read in the 4th, 5th, and 6th grades. Is his
inequality correct? Why or why not?

Answer is in the photo. I can't attach it here, but I've uploaded it to a file hosting. link below! Good Luck!

cutt.ly/Kzv78uJ

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