MATHEMATICS
COLLEGE

Write one example of a linear function and one example of a non-linear function in the format: y=mx +b

Answer:

Answer:

Step-by-step explanation:

Linear Function= y=3x-2

Non-linear function - y=x^2

A non linear function look like a curve when graphed, It has a variable slope value and The input and output of a non-linear system is not directly related

A linear Function A simple linear equation is of the form: y = mx + c

, A linear equation looks like a straight line when graphed., It has a constant slope value and The output of a linear system is directly proportional to its input.

COLLEGE

a theater has two screens and shows its movies continuously. a 30 minute documentary is shown on one. a 120 minute film is shown on the other. If both showings start at noon, how many minutes will pass before both movies begin again at the same time?

Answer:

120 minutes

Explanation:

The film starts at noon (12pm) and takes 120 minutes or 2 hours meaning it will stop and replay at 2:00pm. The documentary is 30 minuets meaning it will finish and replay again at 12:30, 1:00, 1:30 then at 2:00.

120 minutes

Explanation:

The film starts at noon (12pm) and takes 120 minutes or 2 hours meaning it will stop and replay at 2:00pm. The documentary is 30 minuets meaning it will finish and replay again at 12:30, 1:00, 1:30 then at 2:00.

MIDDLE SCHOOL

Leslie ran 4 1/2 laps around the park in 3/4 hour. Kayla ran 3 1/2 laps around the same park in the same amount of time. How many more laps around the park can Leslie run in one hour than Kayla at these rates?Explain! A.3/4

B.1

C.1_1/3

D.2

Leslie:

h= hours

3/4h=4 1/2 laps

divide both sides by 3/4 or .75

1 hour = 6 laps

Kayla:

3/4h= 3 1/2 laps

divide both sides by 3/4

1 hour = 4 2/3 laps

Leslie can do C

1_ 1/3 more laps in an hour than Kayla

h= hours

3/4h=4 1/2 laps

divide both sides by 3/4 or .75

1 hour = 6 laps

Kayla:

3/4h= 3 1/2 laps

divide both sides by 3/4

1 hour = 4 2/3 laps

Leslie can do C

1_ 1/3 more laps in an hour than Kayla

MIDDLE SCHOOL

A bus averages 8 miles per hour faster than a trolley. If the bus travels 60 miles in the same time it takes the trolley to travel 44 miles, then what is the speed of each

Answer:

Bus speed: 22 mph; Trolley speed: 14 mph

Step-by-step explanation:

Let rb represent the speed of the bus and rt the speed of the trolley. Then rb = rt + 8 (mph).

Recall that distance = rate times time. Two different distances and two different speeds are involved here, but only one time.

Thus,

60 mi 44 mi

--------------------- = time (same in both cases) = -------------

rt + 8 mi/hr rt

Cross-multiplying, we get 44rt + 8(44) = 60 rt, or

352 = 16rt.

Solving this for rt, we get rt = speed of bus = 352/16 = 22 mph

The speed at which the bus travels is 22 mph and that at which the trolley travels is (22 mph - 8 mph) = 14 mph

MIDDLE SCHOOL

Choose two of the following choices that can represent the nth term of the sequence: 54, 18, 6, 2, ...

Answer:

The nth term of the given sequence is .

Step-by-step explanation:

Here, the first term of the sequence = 54

Second term = 18

Third term = 6

Now,

and,

as

Hence, the terms of the given sequence are in GEOMETRIC PROGRESSION with common ratio = 1/3

Now, the nth term in GP is given as

So here,

Hence, nth term of the given sequence is .