A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which represents the situation, where x is the original cost of the item(s)?

0.6955x

Step-by-step explanation:

Given the following :

Promotional discount on items = 35%

Sales tax on items = 7%

Original cost of items = x

First we obtain the cost of item after the promotional discount is applied

Cost of item :

Original price - (original price * promotional discount)

x - (x * 0.35) = x - 0.35x

Cost of item = 0.65x

Then the sales tax is added :

Total amount after tax:

Cost of item + (cost of item × sales tax rate)

0.65x + (0.65x * 0.07)

0.65x + 0.0455x

= 0.6955x

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

step-by-step explanation: