All categories

4 years ago

F(x)=x+9, g(x)=x^2-4x, h(x)=x^4+2x^3

Mathematics

1 answer:

11111nata11111 [884]4 years ago

7 0

Answer:

The degree of (f × g × h)(x) is 7.

i.e option a ) 7

Step-by-step explanation:

Given:

$f(x)=(x+9)\\\\g(x)=(x^{2} -4x)\\\\h(x)=(x^{4}+2 x^{3})$

To Find:

Degree of (f × g × h)(x) = ?

Solution:

For multiplication of given function we require

Law of indices:

$(x^{a} )(x^{b} )=x^{(a+b)}$

Distributive Property:

(A + B)(C + D) = A (C + D) + B(C +D)

= AC + AD + BC +BD

Now,

$(f\times g\times h)(x) = (x+9)(x^{2} -4x)(x^{4} +2x^{3})\\ \\ =(x(x^{2} -4x) + 9(x^{2} -4x))(x^{4} +2x^{3})\\\\=(x^{3}+5x^{2}-36x)(x^{4} +2x^{3})\\\\=x^{7}+5x^{6}-36x^{5}+2x^{6}+10x^{5}-72x^{4}\\\\=x^{7} +7x^{6}-26x^{5}-72x^{4} \\\\\therefore (f\times g\times h)(x) = x^{7} +7x^{6}-26x^{5}-72x^{4}$

Degree is highest power raised to the variable.

Therefore here highest power raised to the variable is 7

Therefore degree of (f × g × h)(x) is 7.

You might be interested in

Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7,2), and is parallel to the graph of x + 3y = -5

sukhopar [10]

Answer:

The found values are:

A = 1/3

B = -8/3

Step-by-step explanation:

We know that general equation is given by:

y = mx + c

where m is the slope and c is a constant.

x + 3y = -5

y = -(1/3)x - 1/3(5)

Slop of the equation is -(1/3). As parallel line have same slope substitute it in the first equation:

Ax + By = 3

By = -Ax - 3

By = (1/3)x - 3

Hence, A = 1/3

Substitute point (-7,2) into the equation:

B(2) = (1/3)(-7) -3

B(2) = -7/3 - 3

B(2) = -16/3

B = -16/6

B = -8/3

4 0

3 years ago

Please help me ASAP

e-lub [12.9K]

Answer:

x < 22/5, or in your case, D

Step-by-step explanation:

Hope it helps

8 0

3 years ago

which of the following is equivalent to 3 sqrt 32x^3y^6 / 3 sqrt 2x^9y^2 where x is greater than or equal to 0 and y is greater

Nutka1998 [239]

Answer:

$\frac{\sqrt[3]{16y^4}}{x^2}$

Step-by-step explanation:

The options are missing; However, I'll simplify the given expression.

Given

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$

Required

Write Equivalent Expression

To solve this expression, we'll make use of laws of indices throughout.

From laws of indices $\sqrt[n]{a} = a^{\frac{1}{n}}$

So,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ gives

$\frac{(32x^3y^6)^{\frac{1}{3}}}{(2x^9y^2)^\frac{1}{3}}$

Also from laws of indices

$(ab)^n = a^nb^n$

So, the above expression can be further simplified to

$\frac{(32^\frac{1}{3}x^{3*\frac{1}{3}}y^{6*\frac{1}{3}})}{(2^\frac{1}{3}x^{9*\frac{1}{3}}y^{2*\frac{1}{3}})}$

Multiply the exponents gives

$\frac{(32^\frac{1}{3}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

Substitute $2^5$ for 32

$\frac{(2^{5*\frac{1}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

From laws of indices

$\frac{a^m}{a^n} = a^{m-n}$

This law can be applied to the expression above;

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$ becomes

$2^{\frac{5}{3}-\frac{1}{3}}x^{1-3}*y^{2-\frac{2}{3}}$

Solve exponents

$2^{\frac{5-1}{3}}*x^{-2}*y^{\frac{6-2}{3}}$

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$

From laws of indices,

$a^{-n} = \frac{1}{a^n}$ ; So,

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$ gives

$\frac{2^{\frac{4}{3}}*y^{\frac{4}{3}}}{x^2}$

The expression at the numerator can be combined to give

$\frac{(2y)^{\frac{4}{3}}}{x^2}$

Lastly, From laws of indices,

$a^{\frac{m}{n} = \sqrt[n]{a^m}$ ; So,

$\frac{(2y)^{\frac{4}{3}}}{x^2}$ becomes

$\frac{\sqrt[3]{(2y)}^{4}}{x^2}$

$\frac{\sqrt[3]{16y^4}}{x^2}$

Hence,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ is equivalent to $\frac{\sqrt[3]{16y^4}}{x^2}$

8 0

3 years ago

Taylor saw an American alligator at a zoo that measured Ask Your Teacher feet long. The record length of an American alligator i

lianna [129]

Answer:

The record alligator is $6\frac{1}{4}$ feet longer than the alligator Taylor saw.

Step-by-step explanation:

Taylor saw an American alligator at a zoo that measured $12\frac{11}{12}$ feet long. The record length of an American alligator is $19\frac{1}{6}$ feet long. How much longer is the record alligator than the alligator Taylor saw?