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3 years ago

What is the volume, in cubic inches, of a rectangular prism with a height of 19 inches,

Mathematics

1 answer:

Mnenie [13.5K]3 years ago

7 0

Answer:

2584

Step-by-step explanation:

height of 19 inches,

a width of 8 inches, and a length of 17 inches

17 times 19 times 8

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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

WILL GIVE BRAINLIEST FOR A CORRECT ANSWER:

guapka [62]

Answer:

Solution:

the boat's speed in still water: x

The speed with current: (x+3)

The speed against current: (x-3)

The equation is

3(x+3) = 4(x-3)

x = 21 mph

The distance = 3*(21+3)= 72 miles

I choose (A)

Step-by-step explanation:

7 0

3 years ago

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A line with a slope of -3 that passes through the point (-2, 6)

scZoUnD [109]

I believe the equation is y = -3x + 0

3 0

2 years ago

Translate the following sentence into an equation. Then solve the equation.

AfilCa [17]

the answer is

3x+7=25

-7 -7

3x=18

3x/3=18/3

x=6

8 0

2 years ago

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Calculate simple interest earned on a deposit of $500 at a rate of 5% for 5 years. $125 $500 $625 $12,500

Sergio [31]

Answer:

$125

Step-by-step explanation:

Given:

deposit, P= $500

rate,i = 5%

time,t= 5 years

I=P*i*t

where P is principal amount

i is interest rate

t is time

I is simple interest

Putting values we get:

I=500*0.05*5

= 125 !

8 0

3 years ago

Read 2 more answers