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AlekseyPX
3 years ago
9

Find the lowest common denominator of p+3/p2+7p+10 and p5/p2+5p+6

Mathematics
2 answers:
NeTakaya3 years ago
6 0

Answer:  The required lowest common denominator of both the fractions is x^3+10x^2+31x+30.

Step-by-step explanation:  We are given to find the lowest common denominator of the following two fractions :

f_1=\dfrac{p+3}{p^2+7p+10},~~~f_2=\dfrac{p+5}{p^2+5p+6}.

After factorizing the denominators, the fractions become

f_1=\dfrac{p+3}{p^2+7p+10}=\dfrac{p+3}{p^2+5p+2p+10}=\dfrac{p+3}{(p+2)(p+5)},\\\\\\f_2=\dfrac{p+5}{p^2+5p+6}=\dfrac{p+5}{p^2+3p+2p+6}=\dfrac{p+5}{(p+2)(p+3)}.

Therefore, the lowest common denominator of both the fractions is

L.C.M.((x+2)(x+5),(x+2)(x+3))\\\\=(x+2)(x+3)(x+5)\\\\=(x^2+5x+6)(x+5)\\\\=x^3+5x^2+6x+5x^2+25x+30\\\\=x^3+10x^2+31x+30.

Thus, the required lowest common denominator of both the fractions is x^3+10x^2+31x+30.

Sunny_sXe [5.5K]3 years ago
4 0
(P+1)(p+2)(p+5) is LCM
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In the year 2002, the world population was estimated at 6 billion people. Based on research from the World Bank, about 20% lived
olga_2 [115]
In the given question all the information's are provided based on which the answer to the question can be easily deduced. It is already given that the population of the world in the year 2002 was estimated to about 6 billion. Among them 20% of the people lived on an an income of less that $1 per day.Firstly let us convert 6 billion from words to numbers.
6 billion = 6000000000
Now
Number of people earning less that $1 per day = (20/100) * 6000000000
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                                                                           = 1200000000
So the number of people earning less than $1 per day is 1200000000
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2 years ago
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Akimi4 [234]

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Hope this helped :)

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svetlana [45]

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Sauron [17]

Answer:

  • turning point: (0, -1)
  • domain, range: all real numbers
  • x-intercept: (1/27, 0)
  • y-intercept: (0, -1)
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Step-by-step explanation:

There are a couple of transformations that may be of interest:

  g(x) = k·f(x) . . . . vertical scaling by a factor of k

  g(x) = f(x) +k . . . vertical translation by k units (up)

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Unlike the square root function, which is undefined for negative values, the cube root function is defined for all real numbers. Its domain and range are all real numbers.

The turning point of a cube-root function is the origin. Here, that has been translated down 1 unit, so it is (0, -1). That is also the y-intercept.

The x-intercept is the value of x where g(x)=0:

  0 = 3∛x -1

  1 = 3∛x

  1/3 = ∛x

  (1/3)³ = x = 1/27

The x-intercept is (1/27, 0).

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<u>Transformations</u>

As we discussed above, the addition of -1 to the parent function causes it to be translated down 1 unit.

The multiplication of the parent function by 3 causes it to be vertically expanded by a factor of 3.

7 0
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makvit [3.9K]

Answer:

y≥5

Step-by-step explanation:

The range is the output values

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