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3 years ago

Take a factor out of the square root:

Mathematics

1 answer:

Nat2105 [25]3 years ago

6 0

Answer:

See below.

Step-by-step explanation:

Lets take √72:

Factoring 72 to find perfect squares:

72 = 2*2*2*3*3

The largest perfect square in the above = 2*2*3*3 = 36.

So we can write 72 as 36*2.

√72 = √(36 * 2)

√36 * √2

= 6√2.

One more example:

√18 = √(2*3*3)

= √9*√2

= 3√2.

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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

Jon paid $20 towards the cost of an $80 sweater. Write a numeric equation to show how much he still owes on the sweater.

Tju [1.3M]

Answer:

$80 - $20 = $60 left.

Step-by-step explanation:

8 0

3 years ago

Solve the following: a) 3x = 18 b) 2x = 9 c) $ = 7 d) Ž = 6.5

Leno4ka [110]

Answer:

a) 6

b) 4.5

Step-by-step explanation:

6= 18/3 = x

4.5= 9/2 = x

7 0

2 years ago

20 km is how many dam

ZanzabumX [31]

Hello!

OK, so we need to find out 20 km = ? dam

What we know:
1 km = 100 dam

Now, lets multiply to get our answer:

20 × 100 = 2,000

This tells us that 20 km = 2,000 dam

Check:

2,000 ÷ 20 = 10

This tells us that we are CORRECT!

Answer: 20 km = 2,000 dam

Hope this helps! Good luck! (:

3 0

2 years ago

How are the diagonals of a parallelogram related?

NikAS [45]

Answer:

they bisect each other

Step-by-step explanation:

The diagonals of a parallelogram bisect each other.

If they are the same length, the parallelogram is a rectangle. If they cross at right angles, it is a rhombus.

4 0

3 years ago