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3 years ago

What is the simplified expression for 3 a squared + 9 a b + 5 minus 4 a squared minus 4 a b + 3?

Mathematics

2 answers:

Oksanka [162]3 years ago

6 0

Answer:

Negative a squared + 5 a b + 8

Step-by-step explanation:

i took the test on edge

DENIUS [597]3 years ago

6 0

Answer: c

Step-by-step explanation:

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Find the sum of the series. ∞ 5(−1)nπ2n + 1 32n + 1(2n + 1)! n = 0

wlad13 [49]

Could you give the question more clear?

5 0

3 years ago

What is the product 1/5 x 2 ?

lukranit [14]

That would be 1

I hope I've helped!

3 0

3 years ago

Al has twice as many cards as Bob, and Jane has three times as many cards as Bob. Together, they have 372 cards. How many cards

Musya8 [376]

Answer: Bob has 62 cards.

All has 124 cards.

Jane has 186 cards

Step-by-step explanation:

Let x represent the number of cards that Bob has.

Al has twice as many cards as Bob. It means that the number of cards that All has is 2x.

Jane has three times as many cards as Bob. It means that the number of cards that Jane has is 3x.

Together, they have 372 cards. It means that

x + 2x + 3x = 372

6x = 372

x = 372/6

x = 62

The number of cards that Al has is

2 × 62 = 124

The number of cards that Jane has is

3 × 62 = 186

8 0

3 years ago

Consider the function f ( x ) = − 2 x 3 + 27 x 2 − 108 x + 9 . For this function there are three important open intervals: ( − [

Darya [45]

Answer:

Step-by-step explanation:

<u>Increasing and Decreasing Intervals of Functions</u>

Given f(x) as a real function and f'(x) its first derivative.

If f'(a)>0 the function is increasing in x=a

If f'(a)<0 the function is decreasing in x=a

If f'(a)=0 the function has a critical point in x=a

As we can see, the critical points may define open intervals where the function has different behaviors.

We have

$f ( x ) = - 2 x^3 + 27 x^2 - 108 x + 9$

Computing the first derivative:

$f' ( x ) = - 6 x^3 + 54 x - 108$

We find the critical points equating f'(x) to zero

$- 6 x^3 + 54 x - 108=0$

Simplifying by -6

$x^2 -9 x +18=0$

We get the critical points

$x=3,\ x=6$

They define the following intervals

$(-\infty,3),\ (3,6),\ (6,+\infty)$

Thus A=3 and B=6

3 0

3 years ago

For which function is f(x) equal to f^1(x) ( answer choices in picture )

Sonja [21]

Answer:

C. $f(x)=\frac{x+1}{x-1}$

Step-by-step explanation:

Let's find the inverse of each of the given options.

Option A:

$f(x)=\frac{x+6}{x-6}\\y=\frac{x+6}{x-6}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+6}{y-6}$

Rewrite in terms of 'y'. This gives,

$x(y-6)=y+6\\xy-6x=y+6\\xy-y=6x+6\\y=\frac{6x+6}{x-1}$

The given function $y=\frac{6x+6}{x-1}\ne y=\frac{x+6}{x-6}$

So, option A is incorrect.

Option B:

$f(x)=\frac{x+2}{x-2}\\y=\frac{x+2}{x-2}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+2}{y-2}$

Rewrite in terms of 'y'. This gives,

$x(y-2)=y+2\\xy-2x=y+2\\xy-y=2x+2\\y=\frac{2x+2}{x-1}$

The given function $y=\frac{2x+2}{x-1}\ne y=\frac{x+2}{x-2}$

So, option B is incorrect.

Option C:

$f(x)=\frac{x+1}{x-1}\\y=\frac{x+1}{x-1}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+1}{y-1}$

Rewrite in terms of 'y'. This gives,

$x(y-1)=y+1\\xy-x=y+1\\xy-y=x+1\\y=\frac{x+1}{x-1}$

The given function $y=\frac{x+1}{x-1}\ equals\ y=\frac{x+1}{x-1}$

So, option C is correct.

Option D:

$f(x)=\frac{x+5}{x-5}\\y=\frac{x+5}{x-5}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

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

Rewrite in terms of 'y'. This gives,

$x(y-5)=y+5\\xy-5x=y+5\\xy-y=5x+5\\y=\frac{5x+5}{x-1}$

The given function $y=\frac{5x+5}{x-1}\ne y=\frac{x+6}{x-6}$

So, option D is incorrect.

Therefore, only option C is correct.

7 0

3 years ago