You are choosing between two different cell phone plans. The first plan charges a rate of 23 cents per minute. The second plan charges a monthly fee of $49.95 plus 9 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

357 minutes

Step-by-step explanation:

I subtracted 9 cents/minute from the 23 cents/minute to get 14 cents to get the difference between the two per minute charges.  I then divided the monthly cost of $49.95 by .14 to get 356.79...  So if you used 357 minutes in a month, the second plan would be 3 cents cheaper at $82.08 (.09 x 357= 32.13 + 49.95), vs. the first plan costing $82.11 (.23 x 357).  At 356 minutes the first plan would still be cheaper.

answer: i believe the answer is e

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