Ben drinks tea at an incredible rate. he drinks 3\dfrac123 2 1 3, start fraction, 1, divided by, 2, end fraction liters of tea every \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction of an hour. ben drinks tea at a constant rate.

liters per hour.

Step-by-step explanation:

Consider the question: Ben drinks tea at an incredible rate. He drinks liters of tea every of an hour. Ben drinks tea at a constant rate. How many liters of tea does he drink in one hour?

To find the liters of tea drank by Ben in one hour, we will divide amount of tea drank by time taken as:

Convert mixed fraction into improper fraction:

Convert division problem into multiplication problem by flipping the 2nd fraction:

Therefore, Ben drinks liters per hour.

He drinks 21/4, or 5 1/4, liters of tea in 1 hour

Step-by-step explanation:

The following question is missing: How much does he drink in one hour?

Given that he drinks 3 1/2 (= 7/2) liters of tea every 2/3 of an hour, and we want to know how much he drink in 1 hour, then the following proportion must be satisfied:

7/2 liters / x liters = 2/3 hour / 1 hour

x = (7/2)/(2/3) = 7/2 * 3/2

x = 21/4 = 5 1/4 liters

(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

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)