3. a cell phone company offers two texting plans. people who use plan a pay 10 cents
for each text sent or received. people who use plan b pay 12 dollars per month, and
then pay an additional 2 cents for each text sent or received.
a. write an inequality to represent the fact that it is cheaper for someone to use
plan a than plan b. use x to represent the number of texts they send.
b. solve the inequality.

  a. 0.10x < 12 + 0.02x

  b. x < 150

Step-by-step explanation:

a. For sending x texts, the cost of Plan A in dollars is ...

  0.10x

For sending x texts, the cost of Plan B in dollars is ...

  12 + 0.02x . . . . . . where 12 is the monthly charge regardless of texts sent

We want the Plan A charge to be less than the Plan B charge, so the inequality is ...

  0.10x < 12 + 0.02x

__

b. Subtract 0.02x:

  0.08x < 12

Divide by 0.08

  x < 12/0.08

  x < 150 . . . . . the solution to the inequality

Plan A: 0.10x

Plan B: 12 + 0.02x

It greatly depends on how many texts they receive each month. If they send or receive only 50 text messages a month, plan A will be the plan to go with. They will pay $5.00 for plan A and they would pay $13 for plan B. If they send or receive 1000 text messages a month, plan B will be the plan to go with. They will pay $100.00 for plan A and they would pay $32 for plan B.

0.10x = 12 + 0.02x

-11.90x = 0.02x

x = 150

For you to want plan A, the inequality would be x < 150 and for you to want plan B, the inequality would be x > 150. In other words, you must send or receive less than 150 text messages to want plan A and you must send or receive over 150 text messages for you to want plan B.

Hope this helps!

true !

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240