Given f(x) = x3 + kx + 16, and x + 2 is a factor of f(x), then what is the value
of k?

The derivative of the function y = x(6x + 1)⁵ is: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴

To find the derivative of the given function, we can apply the rules of differentiation. Using the product rule, we differentiate each term separately and then add them together.

For the first term x, the derivative is simply 1.

For the second term (6x + 1)⁵, we apply the chain rule. The derivative of (6x + 1)⁵ with respect to x is 5(6x + 1)⁴ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get (6x + 1)⁵ * 6 = 6(6x + 1)⁵.

For the third term x(6x + 1)⁴, we again apply the product rule. The derivative of x is 1, and the derivative of (6x + 1)⁴ is 4(6x + 1)³ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get x * 4(6x + 1)³ * 6 = 24x(6x + 1)³.

Finally, we add the derivatives of each term to get the derivative of the entire function: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴.

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Complete question:

Use the rules of differentiation to find the derivative of the function y= x(6x + 1)⁵

(6x + 1)⁵ + 30x(6x + 1)⁴

(6x + 1)⁴ (36x + 1)

x-1/6

No correct answer provided.

Answer: Yes.

This bowler is an outlier in the data set. In statistics, an outlier is a data point that differs significantly from other observations. In which this case, the bowler is significantly different than that of the other average scores.

Answer: -19.2

Step-by-step explanation:

Answer:

To prove the inequality P(X ≥ a) ≤ E[X] / a for a > 0, where X is a non-negative random variable, we can use Markov's inequality.

Markov's inequality states that for any non-negative random variable Y and any constant c > 0, we have P(Y ≥ c) ≤ E[Y] / c.

Let's apply Markov's inequality to the random variable X - a, where a > 0:

P(X - a ≥ 0) ≤ E[X - a] / 0

Simplifying the expression:

P(X ≥ a) ≤ E[X - a] / a

Since X is a non-negative random variable, E[X - a] = E[X] - a (the expectation of a constant is equal to the constant itself).

Substituting this into the inequality:

P(X ≥ a) ≤ (E[X] - a) / a

Rearranging the terms:

P(X ≥ a) ≤ E[X] / a - 1

Adding 1 to both sides of the inequality:

P(X ≥ a) + 1 ≤ E[X] / a

Since the probability cannot exceed 1:

P(X ≥ a) ≤ E[X] / a

Therefore, we have proved that P(X ≥ a) ≤ E[X] / a for a > 0, based on Markov's inequality.

The length of the arc opposite a central angle that measures 46 degrees is 2.72 cm.

What is circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

in a circle of radius 3.4 cm

central angle that measures 46 degrees

length of arc = (46/360) * 2π*3.4

=2.72cm

Hence the length of the arc opposite a central angle that measures 46 degrees is 2.72 cm

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Answer:

0, 5, 7

Step-by-step explanation:

You just follow the rule written at the top, if the left column is x, the right column is x/6. For example, if the right column is 0, the left would be 0/6, which is 0.

there are 1,320 different ways in which the winners can be drawn in the lottery game.

To determine the total number of different ways in which the three grand prize winners can be drawn, we can use the formula for combinations.

The number of ways to choose r items from a set of n items is given by the formula

nCr = n! / (r! × (n - r)!)

where n! represents the factorial of n, or n × (n-1) × (n-2) × ... × 2 × 1, and r! represents the factorial of r.

For the first prize, there are 12 possible winners, so there are 12 ways to choose the first prize winner.

For the second prize, there are 11 remaining finalists, since the first prize winner cannot win the second prize. So, there are 11 ways to choose the second prize winner.

For the third prize, there are 10 remaining finalists, since the first and second prize winners cannot win the third prize. So, there are 10 ways to choose the third prize winner.

The total number of different ways to choose the three grand prize winners is the product of the number of ways to choose each prize

12 × 11 × 10 = 1,320

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Answer:

     40

y = ----

      3

Step-by-step explanation:

\(\\ \rm\rightarrowtail \dfrac{3y-8}{12}=\dfrac{y}{5}\)

\(\\ \rm\rightarrowtail 5(3y-8)=12y\)

\(\\ \rm\rightarrowtail 15y-40=12y\)

\(\\ \rm\rightarrowtail 3y=40\)

\(\\ \rm\rightarrowtail y=40/3\)

Answer:

s = 76 cm

Step-by-step explanation:

Here, we want to find the value of s in the triangle STU

Since we have the other two sides and the angle facing the missing side, we can use cosine rule

Mathematically, that would be;

s^2 = t^2 + u^2 - 2tu Cos S

s^2 = 96^2 + 98^2 -2(98)(96) cos 46

s^2 = 5749.31

s = √(5749.31)

s = 75.82 which is approximately 76 cm

The length of the given curve between t=0 and t=1 is approximately 13.573 units.

Now, let's move on to the given parametric curve: r ( t ) = ⟨ 6t , t² , 1/9t³ ⟩ , 0 ≤ t ≤ 1. To find the length of this curve, we need to use a formula that involves integrating the length of small line segments along the curve.

The formula we'll use is the arc length formula:

\(L = \int _a^b \sqrt{(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt}\)

This formula calculates the length of a curve between two points a and b, by integrating the square root of the sum of the squares of the first derivatives of the x, y, and z coordinates with respect to the parameter t.

Using this formula, we can find the length of the given curve as follows:

\(L = \int _0^1 \sqrt{(6)^2 + (2t)^2 + (2/27t^4)^2 dt}\)

\(L = \int _0^1 \sqrt{(36 + 4t^2 + 4/729t^8) dt}\)

\(L = \int_0^1 \sqrt{(2916t^8 + 11664t^6 + 15552t^4 + 6912t^2 + 1296) / 729 dt}\)

This integral is not easy to evaluate directly, but we can simplify it by making a substitution. Let u = 6t² + 6/27t⁶. Then du/dt = 12t + 4/9t⁵, and we can write the integrand as:

\(= > \sqrt{(2916t^8 + 11664t^6 + 15552t^4 + 6912t^2 + 1296) / 729} \\ \\= \sqrt{(u^4 + 3u^2 + 1) / 18t^3}\)

Now we can express the integral in terms of u:

\(L = (1/9) \int _0^6 \sqrt{(u^4 + 3u^2 + 1) / u du}\)

This integral cannot be solved exactly, but we can approximate it numerically using a computer or a calculator. The result is approximately 13.573 units of length.

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Complete Question:

Find the length of the curve. r ( t ) = ⟨ 6t , t², 1/9t³ ⟩ , 0 ≤ t ≤ 1

Answer:

200+500

Step-by-step explanation:

its wrong i answered the wrong question

The possible dimensions (length and width) of the field are:(10 m × 13 m) or (13 m × 10 m) and (11 m × 12 m) or (12 m × 11 m).

Given that Aaron has 47m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. The fourth side of the enclosure would be the river.

The area of the land is 266 square meters.To find the possible dimensions (length and width) of the field, we can use the given information.The length of fencing required = 47 m.

Since the fence needs to be built on three sides of the rectangular plot, the total length of the sides would be 2l + w = 47.1. When l = 10 and w = 13, we have:

Length of the field, l = 10 m Width of the field, w = 13 mArea of the field = l × w = 10 × 13 = 130 sq. m2. When l = 11 and w = 12,

we have:Length of the field, l = 11 m

Width of the field, w = 12 m

Area of the field = l × w = 11 × 12 = 132 sq. m

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Solution for the question 2 :

It is given that ,

The population after n years is given by exponential function ,

Population after 9 years is calculated as,

Thus the population after 9 years is 956 .

Answer:

( 25 x 100 )

option 1 is the answer

Step-by-step explanation:

Remaining options are not correct since they don't have 100 as a factor.

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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Answer:

x = 3

Step-by-step explanation:

Given the information from the question, we can deduce that:

3 - x = x - 3

Now our goal here is to find x.

3 - x = x -3

3 - x - 3  = x - 3 - 3

- x = x - 6

- x - x = x - 6 - x

- 2x = - 6

x = \(\frac{-6}{-2}\) = 3

Answer: 3

Step-by-step explanation: The only value for x in which 3 - x is the same as x - 3 is where x does not affect the value of 3 whatsoever. We can also set this up algebraically to find this out algebraically.

x - 3 = 3 - x

Adding 3 to both sides, we have

x = 6 - x

Adding x to both sides we have

2x = 6

Dividing by 2 from both sides, we get

x = 3

Using the fact that the two angles are complementary, the we will find that the measures are:

∠1 = = 14°

∠2  = 76°

By looking at the diagram, we can see that the sum of the measures of angles 1 and 2 must be equal to 90° (this means that the two angles are complementary).

We also can see that:

∠1 = x - 5

∠2 = 4x

Then we can solve the linear relation:

(x - 5) + 4x = 90

x - 5 + 4x = 90

5x - 5 = 90

5x = 90 + 5 = 95

x = 95/5 = 19

Then the measures of the two angles are:

∠1 = (x - 5)° = (19 - 5)° = 14°

∠2 = 4x = 4*19° = 76°

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Answer:

I believe its A

Step-by-step explanation:

Substitue vales into the equation and check! Lmk if it was ccorrect!

Answer:

Base 9

Height 10

A 90

The answer is Series 1. It satisfies the given condition as it is a geometric series with a common ratio of 1/3. Each term in this series is obtained by multiplying the previous term by 1/3, which confirms that it is indeed a geometric series with the given condition.

We need to test each series to see if it is geometric with x = 1/3. Remember, a geometric series is one in which each term is obtained by multiplying the previous term by a constant value. In this case, that constant value is x = 1/3.  Let's test three series to see if they fit the given condition:  1) 3, 1, 1/3, 1/9, 1/27, ...
To see if this series is geometric with x = 1/3, we can check if each term is obtained by multiplying the previous term by 1/3.
1/3 ÷ 1 = 1/3
1/9 ÷ 1/3 = 1/3
1/27 ÷ 1/9 = 1/3
Since each term is obtained by multiplying the previous term by 1/3, this series is geometric with x = 1/3.

2) 1, 1/3, 3, 1/9, 9, ...
To test if this series is geometric with x = 1/3, we can check if each term is obtained by multiplying the previous term by 1/3.
1/3 ÷ 1 = 1/3
3 ÷ 1/3 = 9
1/9 ÷ 3 = 1/27
Since the terms are not consistently obtained by multiplying the previous term by 1/3, this series is not geometric with x = 1/3.
3) 1, 1/3, 1/9, 1/27, ...
To test if this series is geometric with x = 1/3, we can check if each term is obtained by multiplying the previous term by 1/3.
1/3 ÷ 1 = 1/3
1/9 ÷ 1/3 = 1/3
1/27 ÷ 1/9 = 1/3
Since each term is obtained by multiplying the previous term by 1/3, this series is geometric with x = 1/3.

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The difference in elevation between the height of mountain and height of valley measuring from sea level is equal to 6594 feet.

Since it is given that the height of mountain from the sea level is 6874 feet and the height of valley is 280 feet. Therefore to calculate the difference in elevation, the heights will be subtracted from one another to get a value which will show the elevation. Since both the heights are measured from the sea level which is taken as constant, so no extra calculations will be needed.

Elevation difference = Height of mountain - height of valley

Elevation difference = 6874 - 280 = 6594 feet

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it requires a detailed analysis of multiple transactions and the preparation of journal entries. This type of task is better suited for an accounting professional who can thoroughly review the provided information and accurately apply the relevant accounting principles.

However, I can provide a general overview of the journal entries that may be required based on the information given:

January 1, 2020:

Debit: Investment in Kinman Company (40% of cash paid)

Credit: Cash (Amount paid for the acquisition)

Recording Equity in Earnings for 2020:

Debit: Investment in Kinman Company (40% of net loss)

Debit: Investment in Kinman Company (40% of other comprehensive loss)

Credit: Equity in Earnings of Kinman Company

December 31, 2020:

Debit: Investment in Kinman Company (40% of dividend received)

Credit: Dividend Income

January 1, 2021:

Debit: Investment in Kinman Company (40% of additional investment)

Credit: Cash

Recording Equity in Earnings for 2021:

Debit: Investment in Kinman Company (40% of net income)

Credit: Equity in Earnings of Kinman Company

December 31, 2021:

Debit: Investment in Kinman Company (40% of dividend received)

Credit: Dividend Income

Please note that the above entries are a general guideline and may not capture all the necessary transactions. It is advisable to consult with an accounting professional or refer to the specific accounting standards applicable in your jurisdiction for a more accurate and comprehensive answer.

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The degree measure is which is equivalent to \(\frac{7 \pi}{11}\) is 114.54°.

The size of an angle is measured in terms of a unit of measurement. 1 degree is equivalent in magnitude to 1/360 of a whole rotation.

A rotational angle is said to have a measure of one degree, denoted by the symbol 1°, if it is (1/360)th of a revolution from the initial side to the terminal side. Radian scale. A unit circle's unit arc's centrally subtended angle is said to have a measure of 1 radian.

The radius of an arc divided by its length is known as the radian measure (r). Radian measure is a pure number that doesn't require a unit symbol because it is the ratio of one length to another.

Convert radians to degrees, multiply by 180/π, since a full circle is 360° or 2π radians.

= \($ \frac{7 \pi}{11} \times \frac{180}{\pi}\)

= \($ \frac{7 }{11} \times 180\)

=\($ \frac{1260}{11}\)

= 114.54°

Therefore, the correct answer is 114.54°.

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Full question:

Answer:

i only know the second answer

Step-by-step explanation:

according to the properties of parallel lines

alternate angles in parallel line are equal

therefore,

2x+12 = 3x - 22

2x = 3x -22 - 12

2x = 3x - 34

34 = 3x - 2x

34 = x

therefore x = 34

Answer:

x = 34

Step-by-step explanation:

The radical form for each expression is given as follows:

The general format of the exponential expression is given as follows:

\(a^{\frac{n}{m}}\)

To obtain the radical form, we have that:

Hence the radical form of the exponential expression is given as follows:

\(a^{\frac{n}{m}} = \sqrt[m]{a^n}\)

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Answer:

49 red marbles

Step-by-step explanation:

We should first make 5/12 have a base of 84, so that'll be

(5*7)/(12*7)=35/84. So we have 35 blue marbles and all the rest are red, so 84-35=49

DUBS

Please consider giving me a brainliest! Thank you.

Answer:

need help

Step-by-step explanation:

Carla is 1.3 miles away from the home.

Given that, Carla leaves home and walks 40° easy to the north for 1.5 miles, then turns and continues due west for 2 miles.

The formula for the cosine rule is c=√(a²+b²-2ab cosC)

Here, c=√(1.5²+2²-2×1.5×2 cos40°)

c=√(2.25+4-6×0.7660)

c=√1.654

c=1.28

c=1.3 miles

Therefore, Carla is 1.3 miles away from the home.

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All of the given options could be the lengths of the sides of a right triangle. None of them could NOT be the lengths of the sides of a right triangle.

To determine which of the options could NOT be the lengths of the three sides of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).

Option F: 13 ft, 14 ft, 15 ft

15^2 = 225

13^2 + 14^2 = 169 + 196 = 365

Since 15^2 is equal to the sum of the squares of 13 and 14, this set of side lengths could be the sides of a right triangle.

Option G: 5 yd, 12 yd, 13 yd

13^2 = 169

5^2 + 12^2 = 25 + 144 = 169

Since 13^2 is equal to the sum of the squares of 5 and 12, this set of side lengths could be the sides of a right triangle.

Option H: 7 yd, 24 yd, 25 yd

25^2 = 625

7^2 + 24^2 = 49 + 576 = 625

Since 25^2 is equal to the sum of the squares of 7 and 24, this set of side lengths could be the sides of a right triangle.

Option J: 7.5 ft, 18 ft, 19.5 ft

19.5^2 = 380.25

7.5^2 + 18^2 = 56.25 + 324 = 380.25

Since 19.5^2 is equal to the sum of the squares of 7.5 and 18, this set of side lengths could be the sides of a right triangle.

Therefore, all of the given options could be the lengths of the sides of a right triangle. None of them could NOT be the lengths of the sides of a right triangle.

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The expression which is equivalent to -10 is the option b, -3 - 7.

Explanation:

We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;

-3 - 7 = -10 (-3 - 7)

The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.

If we add -3 and -7 we will get -10. This makes the option b the correct answer.

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Answer:

35 your welcome have a day good

Step-by-step explanation: