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2 answers:

6 0

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

1) The given fractions to add are:

4p² + 6 2p - 2
------------ + ------------
 4p² 10p²

2) The statements to asses are:

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

E) The sum is a rational expression.

This is the result for each statement.


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

(2p - 2) × 2p = 4p² - 4p

10p × 2p = 20p²

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


 20p² + 30 4p² - 4p 24p² - 4p + 30
-------------- + --------------- = ----------------------
 20p² 20p² 20p²

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.

Gnoma [55]3 years ago

4 0

The 2nd, 4th, and 5th statements are correct. Let me know if you have questions on how to do the problem..

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y = x^2 +6x +8

Step-by-step explanation:

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y = (x +3)^2 -1 . . . . . . . . . vertex form; sometimes called standard form

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_____

Comment on standard form

There are different versions of "standard form" depending on what you're concerned with and where you are. Please consult your text or other reference material for the version of standard form you need. (The attachments show the conflict with respect to quadratic equations.)

___

Comment on the graph

The purpose of the graph attached is to show that the equation we propose produces the same curve as the one given.