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Diano4ka-milaya [45]
3 years ago
11

What do you know about the slopes of lines that are parallel? Explain

Mathematics
1 answer:
Rudiy273 years ago
7 0

Parallel lines have to have the same slope.  The must stay the same distance apart at all times to be parallel and the only way to do that is to change in exactly the same manner as they move so slope is the change in x over the change in y.  it must be the same

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I have to rewrite the expressions because they look very confusing.

1) The given fractions to add are:

  4p² + 6        2p - 2
------------ +  ------------
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2) The statements to asses are:

<span>A) The least common denominator is 20p
.
B) The first fraction rewritten with the LCD is (20p² +30) / 20p²

C) The second fraction rewritten with the LCD is (4p - 4) / 20p

D) The sum is (24p² -4p +30 ) / 20p² = (12p-2p+15) / 10p^2

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This is the result for each statement.

</span>
<span>A) The least common denominator is 20p

FALSE: THE LCD IS 20p², because it the least expression that contains all the prime factors of both denominators: 4p² and 10p.

See that you cannot divide 20p by 4p² but you can divide 20p² by 4p² and 10 p. So, 20p is not a common denominator.
.
B) The first fraction rewritten with the LCD is (20p² +30) / 20p²

TRUE: you get this expression from the first fraction by multiplying both numerator and denominator by  20p² / 4p² = 5:

(4p² + 6)×5 = 20p² + 30

(4p²)×5 = 20p²

=>

  20p² + 30
--------------
      20p²

C) The second fraction rewritten with the LCD is (4p - 4) / 20p

FALSE: you have to multiply both numerator an denominator by 20p² / 10p = 2p

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So, the second fraction rewritten with the LCD is:

 4p² - 4p
-----------
    20p²

D) The sum is (24p² - 4p +30 ) / 20p² = (12p-2p+15) / 10p²

TRUE

</span>
<span><span>  20p² + 30        4p² - 4p         24p² - 4p + 30
-------------- +   --------------- = ----------------------
      20p²              20p²                    20p²</span>


And when you simplify the last fraction dividing by 2 you get:

  12p² - 2p + 15
-----------------------
          10p²

E) The sum is a rational expression.

TRUE:

The sum of rational number has the closure property which means that by adding rational expression you will always ge a rational expression.
</span>
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