Liz earns a salary of $2,100 per month, plus a commission of 3% of her sales. She wants to earn at least $2,400 this month. Enter an inequality to find amounts of sales that will meet her goal. Identify what your variable represents.

The inequality that represents her goals is "2100 + 0.03*x >= 2400" where 'x' is the amount she needs to sell. In oder for her to achieve her goals she needs to sell a value of x that is equal or greater than 10,000.

Step-by-step explanation:

Liz's salary is composed of a fixed part (2,100) and a variable part that depends on the amount she sells in a given month, so in order to calculate her salary we have to create an equation, for this equation we will use "y" as her salary and "x" as the amount she sold in that given month. So we have:

Liz's salary -> y

Liz's sales ->x

y = 2100 + (3%)*x

y = 2100 + (3/100)*x

y = 2100 + 0.03*x

We need to find an inequality that will represent her goal of earning at least 2,400 this month. So we have:

2100 + 0.03*x >= 2400

0.03*x >= 2400 - 2100

0.03*x >= 300

x >= 300/0.03

x >= 10,000

The inequality that represents her goals is "2100 + 0.03*x >= 2400" where 'x' is the amount she needs to sell. In oder for her to achieve her goals she needs to sell a value of x that is equal or greater than 10,000.

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