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Murljashka [212]
3 years ago
6

The quotient of (x^3+3x^2-4x-12)/(x^2+5x+6)

Mathematics
2 answers:
Umnica [9.8K]3 years ago
8 0
X-2 ....................
Elis [28]3 years ago
6 0

Answer: The quotient is (x-2).

Step-by-step explanation:

Since we have given that

f(x)=(x^3+3x^2-4x-12)\\\\and\\\\g(x)=x^2+5x+6\\\\So,\ \frac{\left(x^3+3x^2-4x-12\right)}{\left(x^2+5x+6\right)}

Now, we have to find the quotient of the above expression.

So, here we go:

Factorise\ (x^3+3x^2-4x-12)\\\\=\left(x^3+3x^2\right)+\left(-4x-12\right)\\\\=-4\left(x+3\right)+x^2\left(x+3\right)\\\\=\left(x+3\right)\left(x^2-4\right)

Now, we will divide the above simplest form with g(x):

\frac{\left(x+3\right)\left(x^2-4\right)}{\left(x+2\right)\left(x+3\right)}\\\\=\frac{x^2-4}{x+2}\\\\=\frac{\left(x+2\right)\left(x-2\right)}{x+2}\ using\ (a^2-b^2)=(a+b)(a-b)\\\\=x-2

Hence, the quotient is (x-2).


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Answer:

2

Step-by-step explanation:

5y-2x

5(2)-2(4)

10-8=2

8 0
3 years ago
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There are 3 kites Each kite measures 6 inches across and 12 inches long. The wall is 12 feet across. How many square inches of t
marissa [1.9K]
18sq ft

Step by step explanation:

6x3=18
8 0
3 years ago
Find the value of the combination. From a committee consisting of 8 men and 5 women, a subcommittee is formed consisting of 4 me
Alex787 [66]

Out of 8 men, 4 can be selected and lined up in (8 x 7 x 6 x 5) = 1,680 ways.
But within that number, each group of 4 appears in (4 x 3 x 2) = 24 orders.
So there are (1,680 / 24) = 70 different groups of men.

Out of 5 women, 3 can be selected and lined up in (5 x 4 x 3) = 60 ways.
But within that number, each group of 3 appears in (3 x 2) = 6 orders.
So there are (60 / 6) = 10 different groups of women.

Each different group of 70 men can be joined by any of the 10 groups
of women. So the total number of possible subcommittees is (70 x 10) = 700 . 

5 0
3 years ago
String a is 35 centimeters long.string b is 5 times as long as string a .both are necessary to create a decorative bottle .find
yulyashka [42]
First you convert centimeters to meters which will be 35 centimeters-> 0.35 meters

Once you have that, you multiply String A's length (0.35 m) by 5 to find String B's length which will be 1.75 meters.

Now that you have the two lengths you multiply each by 17.
 
17 x 1.75 = 29.75 and 17 x 0.35 = 5.95

Now you just add 29.75 and 5.95 and you get your answer which is
 
35.7 meters 
4 0
3 years ago
Read 2 more answers
Aaron has a triathlon. Sunday he bikes 12 5/8 miles and swims 5 2/3 miles. Monday, he runs 6 3/8 miles. How many total miles Aar
Alla [95]
Let’s put these into one fraction each:

Biking:
= (12*5)/8 miles
= 60/8 miles
This can be reduced to,
= 15/2 miles

Swimming:
= (5*2)/3 miles
= 10/3 miles

Running:
= (6*3)/8 miles
= 18/8 miles
This can be reduced to,
= 9/4

Now we add all the distances up:
= (15/2) + (10/3) + (9/4)

Now we just can add the numerators and the denominators. We must find the lowest common factor (LCF) for our 3 denominators (2,3,4). Our LCF turns out to be 12. *Remember what we do to the denominator we must do to the numerator. So:
= (15/2) + (10/3) + (9/4)
= [(15*6)/12] + [(10*4)/12] + [(9*3)/12]
= (90/12) + (40/12) + (27/12)
= (157/12)
Therefore Aaron Ran 157/12 miles or 13.08 miles.

Hope this helps!
4 0
3 years ago
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