You are at Market Place Mall searching for a new cell phone. You have identified two plans that will work for you. The first plan is through Vextel Communications. The second plan is though Perizon Wireless. Vextel charges a monthly fee of $20 for text messaging, call waiting, and caller ID. Vextel also charges you 6 cents per minute to use the phone. Perizon charges a monthly fee of $10 for text messaging, call waiting, and caller ID. Perizon Wireless charges you 8 cents per minute to use the phone. How many minutes per month do you need to use for the Vextel plan to be the better choice

Step-by-step explanation:

Vextel Communications

monthly fee= $20

charges per minute=$6

let the number of minutes be x

and the total charges for x minutes be y

The total charges is expressed by the linear function below

y=6x+201

Step two:

Perizon

monthly fee= $10

charges per minute=$8

let the number of minutes be x

and the total charges for x minutes be y

The total charges is expressed by the linear function below

y=8x+102

Step three:

Required is the number of minutes x

equating 1 and 2 we have

6x+20=8x+10

collect like terms

6x-8x=10-20

-2x=-10

divide boths sides by -2

x=-10/-2

x=5 mintues

For Vextel plan to be the better choice it must be use for 5minute

rectangle: 9 1/8 x 4 1/9 = 37 37/72in

parallelogram: b times h= 10.3 x 6.2 = 63.86

trapezoid: a+b/2 times h= 42.5

volume of prism: l times w times h= 36

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!