Pauline spent $7.50 every day for 3 days. which expression is the best choice to her determine the total amount of money she spent?

(7.50)(−3) = −22.50; she spent $22.50
(−7.50)(3) = −22.50; she spent $22.50
(−7.50)(−3) = 22.50; she spent $22.50
(7.50)(3) = 22.50; she spent $22.50

The correct option is 2.

Step-by-step explanation:

It is given that Pauline spent $7.50 every day for 3 days.

Amount spent on each day = $7.50

Number of days = 3

Spent amount and expenditure are always negative.

Total amount of money she spent is

On simplification we get

She spent $22.50 and required expression is (−7.50)(3) = −22.50. Therefore the correct option is 2.

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