Geraldine solved a problem: 68.5 ÷ 0.01 = 6,850.
ralph said, "this is wrong because a quotient can’t be greater than the whole you start with. for example, 8 ÷ 2 = 4 and 250 ÷ 5 = 50." who is correct? explain your thinking.

Geraldine is Correct

Step-by-step explanation:

Topic: Dividing numers and fractions

the statement Ralph tells has a flaw, he is right for numbers greater than one, but what happens with number in between (0 , 1)?

lets check Geraldine example

remember how to transform decimals to fractions? look the image attached

you can express 0.01 as and by multiplying it by 100 the upper and down part of the fraction you have that

remember how to divide fractions?

by doing this you have that

so we found out that geraldine is right!

d

step-by-step explanation:

d

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