MATHEMATICS HIGH SCHOOL

A businessman has 10 employees. His salary is equal to 6 times the average of employees salaries. If the 11 of them receive a total of $64,000 in one year, what was the business mans salary that year ??  a) $4000, b) $6000, c) $24,000, d) $ 40,000, e) $44,000

Answers

Answer 1
Answer: business man's salary = x
employee's salary = y

x + 10y = 64000
x = 6y

(6y) + 10y = 64000
16y = 64000
y = 4000

x = 6(4000)
x = 24000

Answer: (c) $24,000

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Solve 4^(2x) = 7^(x−1).

Answers

To solve for x in the given equation, use natural logarithms. Getting the natural logarithms of both sides, will be ln 4^(2x) = ln 7^(x-1). This is also equal to 2x ln 4 = (x-1) ln 7. Rearranging the equation, 2x/(x-1) = ln 7/ln 4. The right side is equal to 1.4037. Thus, the value of x is -2.3539. 

Alissa is analyzing an exponential growth function that has been reflected across the y-axis. She states that the domain of the reflected function will change because the input values will be the opposite sign from the reflected function. Simon disagrees with Alissa. He states that if an exponential function is reflected across the y-axis, the domain will still be all real numbers.

Answers

Answer:

Consider the exponential function

y=Ae^x

                     -----------(1)

and when it is reflected across y axis , it's equation becomes

y=Ae^(-x)

                --------------------------(2)

As, domain of a function is defined as the set of all values of x , for which y is defined.

So, for function 1,  domain is set of all real numbers.That is , x∈[-∞ ,∞]

And for function 2, which is reflection of function 1, it's domain will also be set of all real numbers.That is , x ∈ [-∞, ∞]

So, Simon is correct between Alissa and himself, as he is saying if an exponential function is reflected across the y-axis, the domain will still be all real numbers is true statement.
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input. 

Simplify with steps 9 to 3/2 power

Answers

9^(3/2)
9=3^(2)
=3^(2) ^3/2
=27

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 16 ft, express the area A of the window as a function of the width x of the window.

Answers

This answer uses NMF for which, if needed, the syntax can be found in my profile. Please ignore the LaTeX (the image), I cannot remove it/change it, and it is incorrect. The answer is: f(x)={π{{x}^{2}}/{4}+x(16-{πx}/{2}-x)}/{2}

Final answer:

The area A of a Norman window in terms of its width x can be expressed as the function A(x) = 8x - x²/2 - πx²/8, deriving this equation involves isolating variables from the given perimeter equation.

Explanation:

A Norman window has the shape of a rectangle topped with a semicircle. If we take x as the width of the window and y as the height of the rectangle, then the perimeter of the window is given by P = 2y + x + πx/2 = 16 (since the perimeter is the sum of the rectangle's two sides, the width, and half the circumference of a circle with diameter x).

From this equation, we can express y as a function of x: y = 8 - x/2 - πx/4.

Then, the area A of the window is the sum of the area of the rectangle and the area of the semicircle, which equals A = xy + πx²/8 = x(8 - x/2 - πx/4) + πx²/8 = 8x - x²/2 - πx²/4 + πx²/8.

Therefore, the area A of the window as a function of the width x of the window is A(x) = 8x - x²/2 - πx²/8.

Learn more about Function of Window Area here:

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PLSSSSSSSSSSSSSSSSSS IM TIMED What is the product of StartFraction 7 Over 9 EndFraction and One-fourth?StartFraction 7 Over 36 EndFraction
StartFraction 8 Over 36 EndFraction
StartFraction 7 Over 13 EndFraction
StartFraction 8 Over 13 EndFraction

Answers

Answer:

7 over 36

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Cuz 9x4=36 so thats your denomanator and 4x7=28 numerator for 28/36 but were not done yet, again 34 as a denomator and 9x1=9 so now u have 9/34!

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What does -1-6x-6>-11-7x equal

Answers

Hey there, first, we simplify -6x-7>-7x-11, second, add 7x to both sides, -6x-7+7x>-7x-11+7x=x-7>-11, third, add 7 to both sides, x-7+7>-11+7=x>-4. Therefore, the answer is x>-4
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