how do you solve this ?

The value of k⁻¹(8) in for k(x) = 4 ÷ 5x - 6 is 2/35.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, k(x) = 4 ÷ 5x - 6.

k(x) = (4/5x) - 6.

Let, y = k(x).

y =  (4/5x) - 6.

(4/5x) = y + 6.

1/x = 5(y + 6)/4.

x = 4/{5(y + 6)}.

y = 4/{5(x + 6)}.

k⁻¹(x) = 4/{5(x + 6)}.

k⁻¹(8) = 4/{5(8 + 6)}.

k⁻¹(8) = 4/{5(14)}.

k⁻¹(8) = 4/70.

k⁻¹(8) = 2/35.

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There are 6 values of the displacement of the string at x = 5.0 m at 1 s intervals from t = 0 s to t = 6 s.

All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤x≤ 1.

Given

A snapshot graph at t = 0 s of two waves on a string approaching each other at 1 m/s.

The values of the displacement of the string at x = 5.0 m at 1 s intervals from t = 0 s to t = 6 s are,

At t = 0

s,=>Y₀= 0 cm

At t =1

s,=>Y₁= 0 cm

At t = 2

s,=>Y₂= 0 cm

At t =3

s,=>Y₃= 0 cm

At t =4

=>Y₄= 0 cm

At t = 5 s,

=>Y₅=0 cm

At t = 6

s,=>Y₆= 0 cm

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When receiving ammunition, unit personnel perform three tasks: ensuring items requested match item numbers on DA Form 3151-R, loading and securing the ammunition, and placarding the vehicle.

The first task performed by unit personnel when receiving ammunition is to ensure that the items requested match the item numbers on DA Form 3151-R. This form serves as a record of the types and quantities of ammunition being received. By comparing the requested items with the item numbers on the form, personnel ensure accuracy and prevent any discrepancies or errors in the delivery.

The second task involves the loading and securing of the ammunition. Unit personnel are responsible for safely and efficiently loading the ammunition onto the designated vehicle or storage area. This includes following proper handling procedures, using appropriate equipment, and adhering to safety protocols. The ammunition must be securely stored and arranged to prevent shifting or damage during transportation.

The final task is to placard the vehicle. Placarding involves visibly displaying the necessary warning signs or labels on the vehicle that indicate the presence of ammunition. This step is crucial for safety and compliance purposes, as it alerts other personnel and drivers to exercise caution when approaching or handling the vehicle. Clear and prominent placarding helps prevent accidents and ensures that everyone involved is aware of the potential hazards associated with transporting ammunition.

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Answer:

The x which is not in the domain of the function is the root of the denominator

6) x+3=0, x=-3 is the x which is not in the domain of the function

7) |2x+5|=0, x=-5/2 is the x which is not in the domain of the function

8) x^2-16=0, x=±4 are the x which are not in the domain of the function

To solve this problem, we need to find the intersection of the circle with a 61-mile radius centered at the transmitter and the straight line connecting the two cities.

First, let's draw a diagram of the situation:

r

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T (transmitter)

|\

| \

|  \

|   \

|    \

|     \

|      \

|       \

C1      C2

Here, T represents the transmitter, C1 represents the city 68 miles north of the transmitter, and C2 represents the city 81 miles east of the transmitter. We want to find out how much of the straight line from C1 to C2 is within the range of the transmitter.

To solve this problem, we need to use the Pythagorean theorem to find the distance between the transmitter and the straight line connecting C1 and C2. Then we can compare this distance to the radius of the transmitter's range.

Let's call the distance between the transmitter and the straight line "d". We can find d using the formula for the distance between a point and a line:

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d = |(y2-y1)x0 - (x2-x1)y0 + x2y1 - y2x1| / sqrt((y2-y1)^2 + (x2-x1)^2)

where (x1,y1) and (x2,y2) are the coordinates of C1 and C2, and (x0,y0) is the coordinate of the transmitter.

Plugging in the values, we get:

scss

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d = |(81-0)*(-68) - (0-61)*(-68) + 0*0 - 61*81| / sqrt((81-0)^2 + (0-61)^2)

 = 3324 / sqrt(6562)

 ≈ 41.09 miles

Therefore, the portion of the straight line from C1 to C2 that is within the range of the transmitter is the portion of the line that is within 61 miles of the transmitter, which is a circle centered at the transmitter with a radius of 61 miles. To find the length of this portion, we need to find the intersection points of the circle and the line and then calculate the distance between them.

To find the intersection points, we can solve the system of equations:

scss

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(x-0)^2 + (y-0)^2 = 61^2

y = (-61/68)x + 68

Substituting the second equation into the first equation, we get:

scss

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(x-0)^2 + (-61/68)x^2 + 68(-61/68)x + 68^2 = 61^2

Simplifying, we get:

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(1 + (-61/68)^2)x^2 + (68*(-61/68))(x-0) + 68^2 - 61^2 = 0

Solving this quadratic equation, we get:

makefile

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x = 12.58 or -79.23

Substituting these values into the equation for the line, we get:

scss

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y = (-61/68)(12.58) + 68 ≈ 5.36

y = (-61/68)(-79.23) + 68 ≈ 148.17

Therefore, the intersection points are approximately (12.58, 5.36) and (-79.23, 148.17). The distance between these points is:

scss

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sqrt((12.58-(-79.23))^2 + (5.36-148.17)^2)

≈

Answer:

61

Step-by-step explanation:

The formula of the sequence given is;

    aₙ = -5 + 6(n-1)  

problem is to find the 12th term;

   a₁₂  = -5 + 6 (12  - 1)

     a₁₂ = -5 + 6(11)

       a₁₂ = -5 + 66

        a₁₂ = 61

a. Each flip has two possible outcomes (H or T), so the total number of outcomes is \(2^6 = 64\)

b. To reach f(6) = 0, he must have an equal number of heads and tails, which has a probability of (6 choose 3) / 64 = 5/32. To reach f(6) = 1, he must have one more head than tail or one more tail than head, which has a probability of 4 * (6 choose 3) / 64 = 5/16.

c. The bars would indicate the number of times each outcome occurred   in the 64 possible paths.

d. f(6) = 3 is the most likely outcome for Scott after the six coin flips.

a. To determine the number of different outcomes for the sequence of 6 coin tosses, we need to consider the number of possible combinations of heads (H) and tails (T) in 6 flips. Each flip has two possible outcomes (H or T), so the total number of outcomes is \(2^6 = 64\).

b. To calculate the probability of different outcomes for f(6), we need to analyze the possible paths Scott can take. Starting at position 0, he can move either to the left or right after each coin flip. To reach f(6) = 0, he must have an equal number of heads and tails (HHHHTT or TTTTHH), which has a probability of (6 choose 3) / 64 = 5/32.

To reach f(6) = 1, he must have one more head than tail or one more tail than head (HHHHTH, HHHHHT, TTTTHH, TTTTTH), which has a probability of 4 * (6 choose 3) / 64 = 5/16.

To reach f(6) = 6, he must have all heads (HHHHHH), which has a probability of (6 choose 6) / 64 = 1/64.

c. A bar graph showing the frequency of the different outcomes for this random walk would have the x-axis representing the possible outcomes (from 0 to 6) and the y-axis representing the frequency of each outcome. The bars would indicate the number of times each outcome occurred in the 64 possible paths.

d. Scott is most likely to land on f(6) = 3. This is because to reach f(6) = 3, he needs to have an equal number of heads and tails (HHHHTT or TTTTHH), which has the highest probability of 5/32. Other outcomes require an additional favorable condition (e.g., having one more head or all heads) and have lower probabilities. Thus, f(6) = 3 is the most likely outcome for Scott after the six coin flips.

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The income you need to afford a $425,000 house is largely dependent on your debt-to-income ratio, credit score, and down payment. However, a general rule of thumb is to have an annual income that is at least three times the purchase price of the home, which in this case would be $1,275,000.

To more accurately determine the income needed to afford a $425,000 house, consider factors such as the interest rate on the mortgage, property taxes, homeowners insurance, and any homeowner association fees.

These additional expenses can significantly impact your monthly mortgage payment and thus your income requirements.
It's important to keep in mind that lenders have varying criteria when determining mortgage eligibility and income requirements, so it's best to speak with a mortgage professional to get a more accurate estimate based on your individual circumstances.

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Answer:

I'm Sorry?

Step-by-step explanation:

The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

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The price of each book is $6 and the price of each backpack is $14.

Given that,

Cost of 2 books and a backpack = $26

Each book cost $8 less than the backpack.

Let the cost of each book be b and the cost of the backpack be p

2b + p =26  (i)

Each book cost $8 less than a backpack

b=p-8  (ii)

Substitute for b in equation (i)

2(p-8) +p = 26

2p - 16 +p =26

3p = 42

p =14 (Cost of backpack)

b = cost of book = 14-8 =6

Thus, the price of each book is $6 and the price of each backpack is $14.

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(a) The exponential function that models the data is f(t) = 530.54 * (1.05)^t.

(b) The predicted rent per square foot in 2016 would be approximately $70.12.

(c) The price per square foot exceeded $50 for the first time in the year 2011.

(a) To find an exponential function that models the data, we need to determine the growth rate and the initial value. In this case, the initial value is $530.54 in 2004, so we have f(0) = 530.54.

The growth rate can be calculated by dividing the value in 2015 ($67.38) by the initial value ($530.54), which gives us approximately 0.127. Therefore, the exponential function can be written as f(t) = 530.54 * (1.05)^t, where t represents the number of years after 2004.

(b) To predict the rent per square foot in 2016, we substitute t = 12 (since 2016 is 12 years after 2004) into the exponential function: f(12) = 530.54 * (1.05)^12 ≈ $70.12.

(c) To estimate the first full year in which the price per square foot exceeded $50, we can experiment with different values of t until we find the year where f(t) > 50.

Alternatively, we can use a graphing calculator to solve the equation 530.54 * (1.05)^t > 50. By experimenting or using a calculator, we find that the price per square foot exceeded $50 in the year 2011.

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Answer:

Real number

Step-by-step explanation:

Unless it has an i with it then it's an imaginary number but because it doesn't have an i with it it's real

Answer:

real number

Step-by-step explanation:

Hi! -4 is a real number because imaginary numbers are characterized as i= sqrt -1

If you see a number with an i in it, then it is imaginary. In this case, however, we have a real number.

I hope this helps!

We want to find the value of x, which is the hypotenuse of the triangle on the image.

We will see that the value of x is 5.77 units.

On the figure we can see a right triangle, we want to find the value of x, which is the hypotenuse of this triangle.

To do so, we can use the trigonometric relation:

cos(θ) = (adjacent cathetus)/(hypotenuse)

Where θ is an internal angle of the triangle, and the adjacent cathetus is the cathetus that forms the angle.

Here we can use θ = 30°, and the adjacent cathetus is the one that has a measure of 5 units,  then the value of x is given by the equation:

cos(30°) = 5/x

Solving that for x we will get:

x = 5/cos(30°) = 5.77

The hypotenuse measures 5.77 units.

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Answer:

First question: a

Second: d

Third: b

Fourth: a

Fifth: a

Sixth: b

Step-by-step explanation:

Ask me if you need an explanation for any of the questions because there isn't much to explain for rounding.

Fifth: The reason that the answer is not b is because the 6 in that equation should have a - (if it was a typo, the answer should be b)

The difference between a number and 9 is written as;

⇒ 9 - x = 34

And, The number is - 25.

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The algebraic expression is;

'' The difference between a number and 9 is 34. ''

Now,

Let a number = x

So, We can formulate;

⇒ 9 - x = 34

Solve for x as;

⇒ 9 - 34 = x

⇒ - 25 = x

⇒ x = - 25

Therefore, The difference between a number and 9 is written as;

⇒ 9 - x = 34

And, The number is - 25.

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Answer:

3/8

Step-by-step explanation:

To solve, set up a proportion

\(\frac{juice}{water}\) = \(\frac{juice}{watter}\)    Plug in the numbers you know and solve for x

\(\frac{\frac{1}{4} }{\frac{2}{3} }\) = \(\frac{x}{1}\)    Cross multiply and solve for x

\(\frac{2}{3}\) x = \(\frac{1}{4}\)  Multiply both sides by \(\frac{3}{2}\)

x = \(\frac{3}{8}\)

Answer:

More than 1 (2.5 is the answer)

Step-by-step explanation:

more than 1.

Step-by-step explanation:

5/8 ÷ 2/8 is 40/16. when simplified, you get 5/2. change it to decimals and you get your answer

Answer: (25, 1) ? i'm not sure what the question is.

Step-by-step explanation:

Answer:

option 3

Step-by-step explanation:

Avery walked for 0.25 miles in 5 minutes. Then she stopped for 5 minutes to meet her friend.After that both of them walked 0.75 miles in 15 minutes.

Again this option is also correct.

Avery walked for  5 minutes at a pace of 20 minutes per mile. Then she stopped for 5 minutes to meet her friend.After that both of them walked for 15 minutes at a pace of 20 minutes per mile.

Because, Time taken to travel 1 mile is 20 minutes.

So, time taken to travel 0.25 miles = 20 * 0.25 = 5 minutes

Time taken to travel 0.75 miles = 20 * 0.75 = 15 minutes

Answer:

a=c

Step-by-step explanation:

This is because of the transitive property; which states that if a=b and b=c, then a=c.

Answer: -117

Step-by-step explanation: I added a photo of the work to show you what I did to get the answer, hope it helps!

Answer:

10) min = 5

max = 225

IRQ = 60

That's all I got

sorry

Step-by-step explanation:

Answer:

See attached

Step-by-step explanation:

Solution is in the picture

Step-by-step explanation:

All steps are in pic above.

Note:if you have any questions about it let me know.

Answer:

256

Step-by-step explanation:

8×8=64

64×4=256

64

4

256

Answer:

256 in^3

Step-by-step explanation:

formula is

volume = length × width × height

4 * 8 * 8 =

256

An equation of the question is 250 × 0.94^n = 150 and in approx 8 years it will have about 150 students.

The population of its high school decreases by 6% each year.

The senior class has 250 students now.

Each year decrease in population = 6% = 0.06

So it can be = 1 - 0.06 = 0.94

Total student now = 250

Let n be the number of years before the class will have  students.

So the equation should be = 250 × 0.94^n

After years left students = 150.

Now the equation should be

250 × 0.94^n = 150

Now solving the equation.

Divide by 250 on both side, we get

0.94^n = 150/250

0.94^n = 3/5

Taking log on both side, we get

log(0.94^n) = log(3/5)

Using the formula log(m^n) = n logm and log(m/n) = log m - log n

n log(0.94) = log3 - log5

Now finding the value of log using calculator

n (-0.062) = 1.099 - 1.61

(-0.062)n = -0.511

Divide by (-0.062) on both side, we get

n = 8.242

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The complete question is:

As a town gets smaller, the population of its high school decreases by 6% each year. The senior class has 250 students now. In how many years will it have about 150 students? Write an equation. Then solve the equation without graphing. Write an equation to represent this situation. Let n be the number of years before the class will have  students.

Answer:

18

Step-by-step explanation:

Given expression:

\(2 \times (6 \div 2 + 8) - 4\)

Step-1: Simplify the expression in the parenthesis using PEMDAS

Expression obtained                        Operation of PEMDAS

 \(\implies 2 \times (6 \div 2 + 8) - 4\)                                  

 \(\implies 2 \times (3 + 8) - 4\)                                  D - Division

 \(\implies 2 \times (11) - 4\)                                      A - Addition

 \(\implies2 \times 11 - 4\)

Step-2: Simplify the expression obtained from step-1

Expression obtained                        Operation of PEMDAS

 \(\implies 2 \times 11 - 4\)

 \(\implies 22 - 4\)                                          M - Multiplication

 \(\implies 18\)                                                  S - Subtraction

Answer:

Subtraction Property of Equality.

Step-by-step explanation:

To solve x + 8 = 9, you need to subtract 8 from both sides of the equation. So, you would be using the Subtraction Property of Equality.

Hope this helps!

Answer:

subtraction property of equality

Step-by-step explanation:

x + 8 = 9

Subtract 8 from each side using the subtraction property of equality

x+8-8 = 9-8

x = 1

The final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).

To express the given description as a symbolic expression and then convert it into an exponential expression in fractional form, we'll follow these steps:

Step 1: Symbolic Expression

The description states "the eighth root of fifty-seven to the sixth degree." Let's denote this as √[57]^(1/8)^6.

Step 2: Removing Radical

To eliminate the radical (√), we can rewrite it as a fractional exponent. The numerator of the fractional exponent corresponds to the power (6) applied to the base, and the denominator corresponds to the index of the root (8).

So, the expression becomes (57^(1/8))^6.

Step 3: Simplifying Exponents

To simplify the exponent, we multiply the powers:

(57^((1/8)*6))

Simplifying further:

(57^(6/8))

Step 4: Fractional Form

The exponent 6/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

(57^(3/4))

Therefore, the final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).

This means that we raise 57 to the power of 3/4 to represent the original description. The fraction 3/4 indicates taking the eighth root of 57 and then raising it to the sixth power.

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Answer:

5x - 10

Step-by-step explanation:

7x - 2(x + 5)

= 7x - 2x -10

Please mark me brainliest if my answer is correct! Thanks!

= 5x - 10