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3 years ago

Carter’s semimonthly salary is $1,371.50. What is his annual salary

Mathematics

1 answer:

ch4aika [34]3 years ago

6 0

Answer:

His annual salary is $32,916.00

Step-by-step explanation:

Semimonthly means twice a month.

$1,371.50 × 2 = $2,743.00

So for 1 month, he earns $2,743.00

There are 12 months in one year (annual).

$2,743.00 × 12 = $32,916.00

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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.

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3 years ago

Ms. Zimmer pushes a trash can and it moves across the cafeteria floor

worty [1.4K]

Answer:

Step-by-step explanation:

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3 years ago

If John owes 300 dollars and pays 50 a week what are the dependent and independent variables

podryga [215]

300 dollars would be the independent variable and 50 dollars a week is dependent

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3 years ago

Whats the area of the trapezoid

Lelu [443]

Step-by-step explanation:

the area of a trapezoid is

(b1 + b2)/2 × h = (10 + 5)/2 × 4 = 15 × 2 = 30 in²

6 0

2 years ago

Read 2 more answers

F is a polynomial of degree 6. f has a root of multiplicity

frutty [35]

Answer:

f(x) = 0.43 * $(x - 3)^{2}$ * $(x-1)^{3}$ *(x + 10)

Step-by-step explanation:

We have a 6th degree polynomial f(x)

r = 3 is a root of f with multiplicity 2

r = 1 is a root of f with multiplicity 3

f(-5) = -29721.6

f(-10) = 0

Then: f(x) = a*((x -3)^2 ) * ((x - 1)^3)*(x + 10)

f(-5) = a * (-8)^2 * (-6)^3 * (5) = -29,721.6

a* (64) * (-216)* 5 = -29,721.6

-a*69,120 = -29,721.6

a = -29,721.6/-69,120

a = 0.43

f(x) = 0.43 * $(x - 3)^{2}$ * $(x-1)^{3}$ *(x + 10)

4 0

3 years ago