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3 years ago

Can the remainder in a division problem ever equal the divisor? Why or why not?

Mathematics

1 answer:

Korolek [52]3 years ago

8 0

The remainder can<span> never be </span>equal<span> to, or greater than the </span>divisor.

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3 years ago

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A "centroid" is defined as the center of mass of an object, or shape. How might the midpoint formula be used to find the midpoin

lesantik [10]

Answer:

we can use centeroid formula of a triangle

that is (x1+x2+x3)/3

hope that helps : )

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3 years ago

A neighborhood development that is 4 acres is to be divided into 2/3 acre lots. How many lots can be created?

Brilliant_brown [7]

Answer:

Step-by-step explanation:

4 = 12/3

12/3 divided by 2/3 = 6

2/3

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The answer is 6

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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

The graph below shows graph of f (x), its derivative f '(x), and its second derivative f "(x). Which of the following is the cor

Jet001 [13]

Answer:

A is f ", B is f, C is f '.

Step-by-step explanation:

Your answer is correct. B is the original function f. It has a local maximum at x=0, and local minimums at approximately x=-3/2 and x=3/2.

C is the first derivative. It crosses the x-axis at each place where B is a min or max. C itself has a local maximum at approximately x=-3/4 and a local minimum at approximately x=3/4.

Finally, A is the second derivative. It crosses the x-axis at each place where C is a min or max.

8 0

3 years ago