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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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Nookie1986 [14]

Answer: 80 cm

Step-by-step explanation:

2.4 divided by 3 is 0.8

To convert m to cm multiply by 100

100 x 0.8 = 80

8 0
3 years ago
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Find the minimum or maximum value of the function g(x)=−3x2−6x+5
polet [3.4K]

Step-by-step explanation:

g(x) = ax²+bx+c

g(x)=−3x²−6x+5

a = -3, b= -6, c = 5

since a <0 , the function has only maximum value.

=> g'(x) = 0

-6x -6 = 0

-6x = 6

x = -1

the maximum value => g(-1) =

-3(-1)²-6(-1)+5 = -3+6+5 = 9

the domain : {x | x € Real numbers}

the range : {y| y ≤ 9, y € Real numbers}

the function is increasing for x < -1

the function is decreasing for x > -1

4 0
3 years ago
. Find the inverse of the function below on the given interval and write it in the form yequalsf Superscript negative 1 Baseline
Elena L [17]

Answer:

The inverse of the function is f^{-1}(x)=\frac{x-5}{3}.

Step-by-step explanation:

The function provided is:

f (x)=3x+5

Let f(x)=y.

Then the value of <em>x</em> is:

y=3x+5\\\\3x=y-5\\\\x=\frac{y-5}{3}

For the inverse of the function, x\rightarrow y.

⇒ f^{-1}(x)=\frac{x-5}{3}

Compute the value of f[f^{-1}(x)] as follows:

f[f^{-1}(x)]=f[\frac{x-5}{3}]

               =3[\frac{x-5}{3}]+5\\\\=x-5+5\\\\=x

Hence proved that f[f^{-1}(x)]=x.

Compute the value of f^{-1}[f(x)] as follows:

f^{-1}[f(x)]=f^{-1}[3x+5]

               =\frac{(3x+5)-5}{3}\\\\=\frac{3x+5-5}{3}\\\\=x

Hence proved that f^{-1}[f(x)]=x.

8 0
2 years ago
12 one half times one nine
pshichka [43]

Answer:

1\frac{7}{18}  or one seven eighteenths

Step-by-step explanation:

we know that

12 one half times one nine is the same that multiply 12 one half by one nine

so

(12\frac{1}{2})(\frac{1}{9})

Convert mixed number to an improper fraction

12\frac{1}{2}=12+\frac{1}{2}=\frac{12*2+1}{2}=\frac{25}{2}

substitute

(\frac{25}{2})(\frac{1}{9})=\frac{25}{18}

Convert to mixed number

\frac{25}{18}=\frac{18}{18}+\frac{7}{18}=1\frac{7}{18}

therefore

12 one half times one nine is one seven eighteenths

6 0
3 years ago
Gabriela 30 in of ribbon to make bows each bow uses 5 in of ribbon how many ribbons dose Gabriela make
Shalnov [3]

Answer:

Gabriela Can Make 6 Bows.

Step-by-step explanation:

30 ÷ 5 = 6

So Gabriela Has Enough Ribbon To Make 6 Bows.

3 0
2 years ago
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