An online furniture store sells chairs for $200 each and tables for $800 each. every day, the store can ship at most 19 pieces of furniture and must sell a minimum of $8000 worth of chairs and tables. if 7 chairs were sold, determine the minimum number of tables that the the store must sell in order to meet the requirements. if there are no possible solutions, submit an empty answer.

  9 tables (see below)

Step-by-step explanation:

Let t represent the number of table sales required to meet revenue requirements. The total of sales for the day must be ...

  7(200) +t(800) ≥ 8000

  800t ≥ 6600 . . . . . . . . . . subtract 1400

  t ≥ 8.25

If additional sales are limited to tables, the store must sell at least 9 tables. The revenue goal can also be met by selling 1 chair and 8 tables. (A chair brings in 0.25 times the revenue of a table.)

If the store sells 5 more chairs, it only needs to sell 7 tables. (This combination will result in 19 pieces being sold.)

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are

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