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2 years ago

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The weekly pay for working a job is given by the function P(h) = 15h, where "h" is the number of hours worked. The company restr

icts workers to a maximum of 40 hours per week. The tax on the pay is given by the function T(P) = 0.18P, where "P" is the weekly pay. What is the BEST description of the domain for the tax function T(P)? A) {0, 1, 2, 3, ..., 40} B) {0, 15, 30, 45, ..., 600} C) {any nonnegative real number ≤ 40} D) {any nonnegative real number ≤ 600}

2 answers:

Soloha48 [4]2 years ago

8 0

Answer:

The answer is D

Step-by-step explanation:

Blababa [14]2 years ago

6 0

Answer:

Either B or D.

Step-by-step explanation:

I consider both options valid. It all depends on how the employer is keeping track of time, ie if the pay "ticks" every 60 minutes, or an employee is allowed to clock in half hours.

Will I be able to work 30 and a half hour for example? If I'm allowed to, D.

If I have to work multiple of 60 minutes, B.

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2 years ago

Mariulka [41]

Answer:

$A = 74.7^\circ$

$B = 42.5^\circ$

$C = 62.8^\circ$

Step-by-step explanation:

Given

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

For AB

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$d = \sqrt{(-1 - 2)^2 + (2 - 8)^2$

$d = \sqrt{(-3)^2 + (-6)^2$

$d = \sqrt{45$

So:

$AB = \sqrt{45$

For BC

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

$BC = \sqrt{(2 - 4)^2 + (8 - 1)^2$

$BC = \sqrt{(-2)^2 + (7)^2$

$BC = \sqrt{53$

For AC

$A = (-1,2) \to (x_1,y_1)$

$C = (4,1) \to (x_3,y_3)$

$AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2$

$AC = \sqrt{(-5)^2 + (1)^2$

$AC = \sqrt{26$

So, we have:

$AB = \sqrt{45$

$BC = \sqrt{53$

$AC = \sqrt{26$

By representation

$AB \to c$

$BC \to a$

$AC \to b$

So, we have:

$a = \sqrt{53$

$b = \sqrt{26$

$c = \sqrt{45$

By cosine laws, the angles are calculated using:

$a^2 = b^2 + c^2 -2bc \cos A$

$b^2 = a^2 + c^2 -2ac \cos B$

$c^2 = a^2 + b^2 -2ab\ cos C$

$a^2 = b^2 + c^2 -2bc \cos A$

$(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A$

$53 = 26 +45 - 2 * 34.21 * \cos A$

$53 = 26 +45 - 68.42 * \cos A$

Collect like terms

$53 - 26 -45 = - 68.42 * \cos A$

$-18 = - 68.42 * \cos A$

Solve for $\cos A$

$\cos A =\frac{-18}{-68.42}$

$\cos A =0.2631$

Take arc cos of both sides

$A =\cos^{-1}(0.2631)$

$A = 74.7^\circ$

$b^2 = a^2 + c^2 -2ac \cos B$

$(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B$

$26 = 53 +45 -97.67 * \cos B$

Collect like terms

$26 - 53 -45= -97.67 * \cos B$

$-72= -97.67 * \cos B$

Solve for $\cos B$

$\cos B = \frac{-72}{-97.67}$

$\cos B = 0.7372$

Take arc cos of both sides

$B = \cos^{-1}(0.7372)$

$B = 42.5^\circ$

For the third angle, we use:

$A + B + C = 180$ --- angles in a triangle

Make C the subject

$C = 180 - A -B$

$C = 180 - 74.7 -42.5$

$C = 62.8^\circ$

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2 years ago

Ashot borrowed $225, and paid $108 as an interest of eight years. What was the annual interest rate?

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Answer:

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Step-by-step explanation:

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2 years ago

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<u>Step-by-step explanation:</u>

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2 years ago

Write the equation of the line that is perpendicular to the line y = 2x + 2 and passes through the point (6, 3).

weeeeeb [17]

Answer:

\[y = (-1/2) * x + 6\]

Step-by-step explanation:

Equation of the given line: y=2x+2

Hence the slope of the line is given by 2

Any line which is perpendicular to the given line will have a slope m such that m*2 = -1

Or, \[m = \frac{-1}{2}\]

Only options 2 and 3 satisfy this condition.

The line is also supposed to pass through the point (6,3).

Substituting these values in the option 2:

\[3 = (-1/2) * 6 + 3\]

Or, \[ 3 =0 \] which is false . Hence option 2 is not valid.

Now substituting (6,3) in option 3:

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2 years ago