A student received a coupon for 19​% off the total purchase price at a clothing . Let be the original price of the purchase. Use the expression below for the new price of the purchase. Write an equivalent expression by combining like terms. b-0.19b

the equivalent expression is 0.81b

Step-by-step explanation:

The equivalent expression is shown below:

Let us assume the original price of the purchase be b

Given that

b - 0.19b

= (1 - 0.19)b

= 0.81b

hence, the equivalent expression is 0.81b

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

this is answer of 144 cubic meters