if f(x)= 1 over 9x -2, what is f^-1(x)?

The domain cannot be (–∞, ∞) as it includes values that are not valid inputs for the inverse cosine function.

The domain of the inverse cosine function, y = cos^(-1)(x) or y = arccos(x), is the set of values for which the function is defined.

In this case, the range of the cosine function, which is the set of values that x can take, is [-1, 1]. Therefore, the domain of the inverse cosine function is the range of the cosine function.

Hence, the correct answer is [–1, 1]. This is because the inverse cosine function is only defined for values of x that fall within the range of the cosine function, which is from -1 to 1.

To clarify further, the inverse cosine function is defined as the inverse of the restricted cosine function. The restricted cosine function is defined on the interval [0, π], which means that its range is [–1, 1]. The inverse cosine function "undoes" the cosine function and maps values from [-1, 1] back to the corresponding input values in [0, π]. Therefore, the domain of the inverse cosine function is [-1, 1].

The options [0, π] and (–∞, ∞) are not correct because they do not correspond to the domain of the inverse cosine function. The range of the inverse cosine function is [0, π], and the inverse cosine function is not defined for values outside the range of the cosine function. Therefore, the domain cannot be (–∞, ∞) as it includes values that are not valid inputs for the inverse cosine function.

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The function F(x)=0.2F(x)=0.2 is not an exponential decay function. It is a constant function where the output value is always equal to 0.2, regardless of the input value xx.

An exponential decay function is typically in the form f(x)=a⋅bxf(x)=a⋅bx, where aa and bb are constants and bb is a value between 0 and 1. As xx increases, the exponential decay function decreases exponentially.

For example, an exponential decay function could be f(x)=0.2⋅(0.5)xf(x)=0.2⋅(0.5)x, where the base 0.50.5 represents the decay factor. As xx increases, the value of the function decreases rapidly.

In summary, an exponential decay function follows the pattern of decreasing values as xx increases, while the function F(x)=0.2F(x)=0.2 represents a constant value regardless of the input xx.

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The original price of the wool suit was $795.

Let's denote the original price of the wool suit as "P."

We know that the suit was discounted by 20%, which means the discounted price is 80% (100% - 20%) of the original price.

Given that the discounted price is $636, we can set up the following equation:

0.8P = $636

To find the original price, we need to solve for P. We can do this by dividing both sides of the equation by 0.8:

P = $636 / 0.8

P = $795

Therefore, the original price of the wool suit was $795.

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The missing term in the polynomial X^3 - 95 is 0x^2.

Option A (Both 0x^2 and 0x) is the correct answer choice, as 0x represents the missing term with a degree of x (linear term) as well.

In the polynomial expression X^3 - 95, we can observe that there is a missing term with an x^2 degree.

To identify the missing term, we need to consider the standard form of a polynomial expression, which is written in descending order of exponents. In this case, the highest exponent present is x^3, followed by a constant term (-95).

To fill in the missing term, we look for the term with an x^2 degree. Since it is not present in the given expression, we can conclude that the missing term is 0x^2.

Therefore, the missing term in the polynomial X^3 - 95 is 0x^2.

Option A (Both 0x^2 and 0x) is the correct answer choice, as 0x represents the missing term with a degree of x (linear term) as well.

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Answer:

  (c)  The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

Step-by-step explanation:

You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).

The inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...

  f(a) = b

then the graph of f(x) contains the ordered pair (a, b).

The inverse function will have the ordered pair (b, a). That is,

  f⁻¹(b) = a

If an ordered pair (x-intercept) of the inverse function is ...

  (P, 0)

Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.

The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

__

Additional comment

The graphs of the two functions are mirror images of each other across the line y=x.

<95141404393>

To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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The Lagrange interpolating polynomial of degree 1 is P₁(x) = (f₁ - fo)x + (foxo - f₁xo) / (x₁ - xo).

To derive the Lagrange interpolating polynomial of degree 1, let's consider two distinct points: (x₁, f₁) and (xo, fo). The Lagrange interpolating polynomial of degree 1 can be expressed as:

P₁(x) = L₁(x)f₁ + L₂(x)fo,

where L₁(x) and L₂(x) are the Lagrange basis polynomials defined as:

L₁(x) = (x - xo) / (x₁ - xo),

L₂(x) = (x - x₁) / (xo - x₁).

Substituting these expressions into P₁(x), we have:

P₁(x) = [(x - xo) / (x₁ - xo)]f₁ + [(x - x₁) / (xo - x₁)]fo.

Simplifying further:

P₁(x) = [f₁(x - xo) + fo(x - x₁)] / (x₁ - xo).

Expanding the numerator:

P₁(x) = [f₁x - f₁xo + fox - fox₁] / (x₁ - xo).

Finally, we can rearrange the terms to obtain the Lagrange interpolating polynomial of degree 1:

P₁(x) = (f₁ - fo)x + (foxo - f₁xo) / (x₁ - xo).

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The missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18 is y = 2/3. Hence, the complete ordered pair is (5, 2/3).

To determine the missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18, we can substitute the given x-coordinate, which is 5, into the equation and solve for y.

Let's substitute x = 5 into the equation:

4(5) - 3y = 18

20 - 3y = 18

Now, we can solve for y by isolating it on one side of the equation:

-3y = 18 - 20

-3y = -2

Divide both sides of the equation by -3 to solve for y:

y = -2 / -3

y = 2/3

Therefore, the missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18 is y = 2/3. Hence, the complete ordered pair is (5, 2/3).

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Question

Following equation. 4x-3y=18 Determine the missing coordinate in the ordered pair (5,?) so that it will satisfy the given equation.

Answer:

{e, 24}

Step-by-step explanation:

U = {a, b, c, d, e, f, 19, 20, 21, 22, 23, 24}

X = {a, b, c, 20, 21, 22}

Y = {b, d, f, 19, 21, 23}

X' ∩ Y' = (X U Y)'

= ({a, b, c, 20, 21, 22} U {b, d, f, 19, 21, 23})'

= ({a, b, c, d, f, 19, 20, 21, 22, 23})'

={e, 24}

Answer: (C) 1/3

Step-by-step explanation:

Look at the base lengths. For A'B'C', the length is 2. For ABC, it is 6. The ratio of the length of A'B'C' to the length of ABC is 1/3. Thus the answer is C.

Answer:

True

Step-by-step explanation:

The easiest way to understand this problem is to first breakdown the notation. In words, the problem is stating 9 is NOT an element of the set containing the elements 4, 1, 8, and 7. Since 4[tex]\neq[/tex]9, 1[tex]\neq[/tex]9, 8[tex]\neq[/tex]9, and 7[tex]\neq[/tex]9 then 9 is not an element of this set and the statement is true.

The three friends practiced together for 1 hour and 25 minutes.

Valerie practiced the viola for 15 minutes, while Chuck practiced the cello for an hour. Floyd practiced the flute for 10 minutes longer than Chuck.

So, Floyd practiced the flute for 1 hour + 10 minutes.

To find the total practice time, we add the individual practice times together: 15 minutes + 1 hour + 10 minutes = 1 hour and 25 minutes.

In summary, Valerie, Chuck, and Floyd practiced their instruments for a total of 1 hour and 25 minutes.

Valerie contributed 15 minutes, Chuck practiced for 1 hour, and Floyd practiced for 1 hour and 10 minutes.

Adding these times together gives us a total practice time of 1 hour and 25 minutes.

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The triangles are congruent because of S.A.A

Congruent triangles are triangles having corresponding sides and angles to be equal. This means that for two triangles to be congruent, the corresponding angles must be equal and the corresponding sides must also be equal.

In the triangles the corresponding angles are equal.

In triangle ABC, the third angle is calculated as;

180-(90+30)

= 180-120

= 60°

I'm triangle DCE, the third angle is calculated as;

180-(90+30)

= 180-120

= 60°

Therefore the two triangles are congruent because the corresponding angles are equal.

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Answer: x=15

Step-by-step explanation:

If JH is a midsegment, then J is the midpoint of LK and H is the midpoint of KM. This also means that triangles JKH and triangles LKM are similar. Since H is the midpoint of KM, assume KM = 2y (KH=y). 30/x=2/1. Thus x=15.

Answer:

x = 15

Step-by-step explanation:

The midsegment of a triangle is a line segment that connects the midpoints of two sides of a triangle.

Therefore, if JH is the midsegment of ΔKLM then JH is parallel to LM, and triangles KJH and KLM are similar: ΔKJH ~ ΔKLM.

In similar triangles, corresponding sides are always in the same ratio.

Since JH is the midsegment of ΔKLM, then KJ is half the length of KL, and KH is half the length of KM. This means that JH is half the length of LM.

Given the measure of LM is 30:

[tex]x=\overline{JH}=\dfrac{30}{2}=15[/tex]

Therefore, the slope-intercept equation of the line passing through the points (2,3) and (6,11) is y = 2x - 1.

To find the slope-intercept equation of the line passing through the points (2,3) and (6,11), we can use the formula for slope:

slope (m) = (change in y) / (change in x)

First, calculate the change in y and change in x using the given points:

change in y = 11 - 3 = 8

change in x = 6 - 2 = 4

Now, substitute the values into the slope formula:

slope (m) = 8 / 4 = 2

Next, we can use the point-slope form of the linear equation:

y - y1 = m(x - x1)

Choose one of the given points, let's use (2,3), and substitute the values into the equation:

y - 3 = 2(x - 2)

Simplifying the equation:

y - 3 = 2x - 4

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 2x - 1

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Since each child buys a double scoop with 2 flavors and no two children choose the same combination, we can determine the number of children by finding the number of unique flavor combinations possible.

To calculate the number of unique flavor combinations, we can use the concept of combinations without repetition. The formula for this is given by nCr = n! / ((n-r)! * r!), where n is the total number of flavors and r is the number of flavors chosen for each double scoop.

In this case, there are 9 flavors available and each child chooses 2 flavors. Using the formula, we have:

9C2 = 9! / ((9-2)! * 2!) = 9! / (7! * 2!) = (9 * 8) / 2 = 36 / 2 = 18.

Therefore, there are 18 children in the group, as each child can choose from 18 unique flavor combinations without repetition.

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To calculate the monthly house payment for a $65,000 home loan with a 5.25% annual percentage rate (APR) over a 25-year term, we can use the formula for calculating the monthly payment on an amortizing loan. The formula is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Loan principal amount

r = Monthly interest rate (APR divided by 12 and expressed as a decimal)

n = Total number of monthly payments (number of years multiplied by 12)

Let's calculate the values and substitute them into the formula:

P = $65,000

r = 5.25% / 100 / 12 = 0.004375

n = 25 * 12 = 300

Now, let's plug these values into the formula:

M = 65000 * (0.004375 * (1 + 0.004375)^300) / ((1 + 0.004375)^300 - 1)

After evaluating this expression, the monthly house payment, rounded to the nearest cent, would be approximately $406.23.

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If Product X is discontinued, the company would have a monthly financial advantage of $61,600.

To determine the monthly financial advantage or disadvantage for the company if Product X is discontinued, we need to calculate the total revenue and total expenses associated with Product X.

Total Revenue:

Product X sells 15,100 units per month at a price of $21 per unit. Therefore, the total revenue can be calculated as:

Total Revenue = Number of Units Sold × Price per Unit

Total Revenue = 15,100 units × $21 = $317,100

Total Variable Expenses:

The variable expenses per unit for Product X are given as $15. Therefore, the total variable expenses can be calculated as:

Total Variable Expenses = Number of Units Sold × Variable Expenses per Unit

Total Variable Expenses = 15,100 units × $15 = $226,500

Total Fixed Expenses:

Out of the $101,000 in monthly fixed expenses, $72,000 would still be incurred even if Product X is discontinued. Therefore, the avoidable fixed expenses would be:

Total Fixed Expenses - Avoidable Fixed Expenses = $101,000 - $72,000 = $29,000

Monthly Financial Advantage (Disadvantage):

To calculate the monthly financial advantage or disadvantage, we subtract the total expenses (fixed and variable) from the total revenue:

Monthly Financial Advantage (Disadvantage) = Total Revenue - Total Variable Expenses - Total Fixed Expenses

Monthly Financial Advantage (Disadvantage) = $317,100 - $226,500 - $29,000

Monthly Financial Advantage (Disadvantage) = $61,600

Therefore, if Product X is discontinued, the company would have a monthly financial advantage of $61,600.

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Answer/Step-by-step explanation:

A cook has 6 onions that have a total mass of 900 grams and 8 apples that have a total mass of 1 kilogram. All onions are the same size, and all apples are the same size. Which has the greater mass, an onion or an apple? Explain.

1. Underline the question you need to answer.

See above

2. What units are used in the problem?

The units used are grams and kilograms.

3. What should you do before comparing the masses?

Before comparing masses you should make sure that the apples and onions unit's are both the same.

4. How many kilograms is 900 grams?

0.9 kilograms

---

This is solved by creating a proportion:

Proportion is a mathematical comparison between two ratios (or fractions) and are equal to each other.

We know that 1 kilogram = 1000 grams

You can remember this by the fact that the prefix kilo = 1000

Your proportion would be set up as:

1 kilogram/ 1000 grams = x kilograms/ 900 grams

we can multiply 900 grams on both sides to isolate x (get x by itself)

900 grams * 1 kilogram/ 1000 grams = 900 grams * x kilograms/ 900 grams

simplified it would look like:

900 kg/1000 = x kg

x = 0.9 kg

So 0.9 kilograms is equal to 900 grams.

---

5. How many grams is 1 kilograms?

There are 1000 grams in 1 kilograms.

6. What do you need to do find the mass of 1 onion and 1 apple? Explain.

To find the mass of one onion you must divide the total mass of onions (900 grams) by 6, and you get that one onion is equal to 150 grams. To find the mass of one apple you can first convert its total mass (1 k) to grams, which equals 1000 grams. Now you can take its total mass in grams and divide it by 8. You get that one apple is equal to 125 grams.

Which has the greater mass, an onion or an apple? Explain

An onion has a greater mass than the apple because one onion has mass of 150 grams, which is greater than one apple's mass of 125 grams.

Answer:

  26.1°

Step-by-step explanation:

You want the value of angle x° in a right triangle that has the side adjacent to x being 53 cm, and the side opposite being 26 cm.

The tangent ratio is ...

  Tan = Opposite/Adjacent

The side opposite the angle is 26 cm; the side adjacent is 53 cm. The ratio of these is ...

  tan(x) = 26/53

The arctangent function is used to find the angle when the tangent is known.

  x = arctan(26/53) ≈ 26.1°

The angle x° is approximately 26.1°.

__

Additional comment

The calculator must be in degrees mode.

<95141404393>

We can make the decision as per rational or irrational from the solution of the equations.

A. The solution is irrational

B. The solution is rational

C. The solution is rational

D. The solution is irrational

A rational solution refers to a solution that can be expressed as a ratio of two integers, where the denominator is not zero. It is a value that satisfies an equation or inequality and can be written in the form of a fraction.

For the equation[tex]5x^2 + 4x - 14 = 0[/tex], we obtain the solution as;

-2/5 ±1/5√74

For the equation we have that[tex]4x^2 + 8x - 5 =0[/tex]. The solution would be x = 1/2 or -5/2

For the third equation we have that [tex]x^2 + x - 42 = 0[/tex] The solution is x = 6 and -7

For the fourth equation; is 3x^2 + 4x - 2= 0. The solution of the equation is -2/3 ± 1/3√10

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About of Bhutan's population lives in Thimphu Dzongkhag. Chhukha Dzongkhag has about of 3 4 the population of Thimphu Dzongkhag. Approximately 3/7  fraction of Bhutan's population resides in Chhukha Dzongkhag.

Let's denote the population of Thimphu Dzongkhag as T and the population of Chhukha Dzongkhag as C. We are given that "about 3/4" of Thimphu Dzongkhag's population is the population of Chhukha Dzongkhag.

Mathematically, this can be represented as:

C = (3/4) * T

Now, we need to determine the fraction of Bhutan's population that lives in Chhukha Dzongkhag. To do this, we need to calculate the fraction C/(T+C).

Substituting the value of C from the equation above:

C/(T+C) = [(3/4) * T] / (T + [(3/4) * T])

Simplifying the expression:

C/(T+C) = (3/4) * T / (T + (3/4) * T)

        = (3/4) * T / (4/4 * T + 3/4 * T)

        = (3/4) * T / (7/4) * T

        = (3/4) / (7/4)

        = 3/7

Therefore, the fraction of Bhutan's population that lives in Chhukha Dzongkhag is 3/7.

This calculation is based on the given information that Chhukha Dzongkhag has about 3/4 the population of Thimphu Dzongkhag.

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The manufacturing cycle efficiency (MCE) of Navems for its elevators is 38.6%

The correct answer choice is option A.

Manufacturing cycle efficiency (MCE) = Value-added production time / Total cycle time.

Value-added production time;

Inspection time = 12 days

Process time = 5 days

Total = 17 days

Total cycle time:

Wait time = 12 days

Inspection time = 12 days

Process time = 5 days

Move time = 6 days

Queue time = 9 days

= 44 days

Hence,

Manufacturing cycle efficiency (MCE) = Value-added production time / Total cycle time × 100

= 17 days / 44 days × 100

= 38.63636363636363

Approximately,

38.6%

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Answer:

The Answer Will Be 16

Step-by-step explanation:

Beacuse , To Find Number of subsets we can use 2n Where 2 is number can't be changed but n is cardinal number so it's 16

type the whole number 16

The type of the function is a cube function

The equation of the parabola is y = -1/18(x - 4)² - 1

From the question, we have the following parameters that can be used in our computation:

y = (x + 1)³ - 2

The above function has a degree of 3

This means that the type of the function is a cube function

To translate the function from the parent function, we have

Translate left by 1 unit and translate down by 2 units

Also, the function has no minimum or maximum

Here, we have

Vertex = (4, -1)

Point (-2, -3)

A parabola is represented as

y = a(x - h)² + k

Using the vertex, we have

y = a(x - 4)² - 1

Using the point, we have

a(-2 - 4)² - 1 = -3

This gives

a(-2 - 4)² = -2

So, we have

36a = -2

Evaluate

a = -1/18

Recall that

y = a(x - 4)² - 1

So, we have

y = -1/18(x - 4)² - 1

Hence, the equation is y = -1/18(x - 4)² - 1

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The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that [tex]c^2 = a^2 + b^2[/tex] - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get [tex]c^2 = 43^2 + 67^2[/tex] - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get [tex]c^2[/tex] ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have [tex]c^2[/tex] ≈ 6338 - 5156.898.

7. Calculating [tex]c^2[/tex], we find [tex]c^2[/tex] ≈ 1181.102.

8. Finally, taking the square root of [tex]c^2[/tex], we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

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To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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