Daniel expanded the expression as shown.

Negative 2 (Negative 8 x minus 4 y + three-fourths) = negative 10 x minus 8 y minus 1 and one-fourth

What errors did he make? Select three options.
The first term should be positive.
The second term should be positive.
The last term should be Negative 1 and one-half, not Negative 1 and one-fourth.
He divided Negative 8 by Negative 2 instead of multiplying Negative 8 by Negative 2.
He did not simplify the expression completely.

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19

a negative exponent is translated as follows:

so, we have

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