If it takes one person 4 hours to paint a room and another person 12 hours to
paint the same room, working together they could paint the room even quicker, it
turns out they would paint the room in 3 hours together. This can be reasoned by
the following logic, if the first person paints the room in 4 hours, she paints 14 of
the room each hour. If the second person takes 12 hours to paint the room, he
paints 1 of the room each hour. So together, each hour they paint 1 + 1 of the 12 4 12
room. Using a common denominator of 12 gives: 3 + 1 = 4 = 1. This means 12 12 12 3
each hour, working together they complete 13 of the room. If 13 is completed each hour, it follows that it will take 3 hours to complete the entire room.
This pattern is used to solve teamwork problems. If the first person does a job in A, a second person does a job in B, and together they can do a job in T (total). We can use the team work equation.
Teamwork Equation: A1 + B1 = T1
Often these problems will involve fractions. Rather than thinking of the first frac-
tion as A1 , it may be better to think of it as the reciprocal of A’s time.
World View Note: When the Egyptians, who were the first to work with frac- tions, wrote fractions, they were all unit fractions (numerator of one). They only used these type of fractions for about 2000 years! Some believe that this cumber- some style of using fractions was used for so long out of tradition, others believe the Egyptians had a way of thinking about and working with fractions that has been completely lost in history.
The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²
The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³
<h3>Writing Polynomials </h3>
From the question, we are to write a polynomial that has a GCF of 7m
That is,
We are to write a polynomial that has a greatest common factor of 7m
<em>Writing the polynomial</em>
14mn - 21m + 49m²n + 7mn²
The polynomial above has a greatest common factor of 7m. That is, 7m is the greatest factor that can divide each of the terms
We are to write a polynomial with a GCF of 2ab²
<em />
<em>Writing the polynomial</em>
6a²b² - 8ab³ + 4a³b² + 2a³b³
The polynomial above has a greatest common factor of 2ab². That is, 2ab² is the greatest factor that can divide each of the terms
Hence,
The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²
The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³
Learn more on Writing polynomials here: brainly.com/question/4525973
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Answer: the old price for 1 liter is $0.3
Step-by-step explanation:
Let x represent the old price for 1 liter of petrol.
Last week a man bought 20 liters at the old price. This means that the total amount that the man paid for 20 liters is 20x.
The cost of petrol rises by 2 cents a liter. This means that the new price per liter is x + 2/100 = x + 0.02
This week he bought 10 liters at the new price. This means that the total amount that the man paid for 10 liters is
10(x + 0.02)
= 10x + 0.2
Altogether, the petrol costs $9.20. This means that
20x + 10x + 0.2 = 9.2
30x + 0.2 = 9.2
30x = 9.2 - 0.2
30x = 9
x = 9/30
x = 0.3
