x^3+12x^2+kx+7 is divided by(x+4),the remainder is -9 find k.

Answer:

The answer is B or -2

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

The y-intercept is the number that doesn't have a variable behind it in this form but if it does it's y.

The correct interpretation of the logarithm of a number L to any base M is that ln_M(N) = L, where N = M^L. This corresponds to option B.

In mathematics, the logarithm function is the inverse operation of exponentiation. It helps us find the power to which a base must be raised to obtain a certain number. In this case, ln_M(N) = L means that when we take the logarithm of N with base M, the result is L.

To clarify, N represents the number we want to find the logarithm of, M is the base of the logarithm, and L is the power to which the base M must be raised to obtain N. So, N = M^L represents the exponential form of the equation.

Option B, ln_M(N) = L N = L^M, correctly captures this relationship and provides the appropriate interpretation of the logarithm of a number L to base M.

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The half life for this radioactive substance is 40.76 years

As we know that radioactive decay is a first order reaction

For first order reaction, we can write

N = \(N^{0}\)\(e^{-kt}\)

Where N = Amount of substance at time ‘t’

N0 = Initial amount of substance

K = rate constant for first order reaction

t = time in years

Now, as per the question,

This substance is decaying at a rate of 1.7% that means 98.3% will remain after decaying.

For time t = 1 years , N/\(N^{0}\) = 0.983

Therefore, we have

N/\(N^{0}\) = \(e^{-kt}\)

0.983 = \(e^{-k }\)

-k = ln(0.983)

-k = -0.017

K = 0.017 \(year^{-1}\)

Now for half life, We can write N/\(N^{0}\) = 0.5

Therefore, N/\(N^{0}\) = \(e^{-kt}\)

              0.5 = \(e^{-0.017t}\)

ln(0.5) = -0.017t

-0.693 = -0.017t

t = 0.693/0.017 = 40.76 years

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The value of ML = 3, using the mid-point theorem of triangles.

According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."

In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.

Thus, by the midpoint theorem, we can say that:

Assuming AB = BC = AC = x units, we get:

Thus, the triangle LMN is an equilateral triangle.

Thus, MN = ML = NL.

Given MN = 3, we can write the value of ML = 3.

Thus, the value of ML = 3, using the mid-point theorem of triangles.

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The given question is in Spanish. The question in English is:

"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"

This shows that the food will only last 1 1/3 meals

Fractions are written as a ratio of two integers. Given the following

Total pounds of food bought = 24 pounds

Amount fed each per meal = 3/4 * 24 pounds = 18 pounds

Remains = 24 - 18

Remaining = 6 pounds

This shows that the food will only last 1 1/3 meals

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P(80 < X < 125) = 0.9525 - 0.0918

P(80 < X < 125) = 0.8607

This means that approximately 86.07% of people have IQ scores between 80 and 125.

To answer this question, we need to calculate the standardized score (also known as z-score) for both 80 and 125:

z-score for 80: (80-100)/15 = -1.33

z-score for 125: (125-100)/15 = 1.67

Once we have the z-scores, we can use a standard normal distribution table or calculator to find the proportion of scores between them. Alternatively, we can use the following formula:

P(80 < X < 125) = P(Z < 1.67) - P(Z < -1.33)

Using a standard normal distribution table or calculator, we can find that P(Z < 1.67) is approximately 0.9525 and P(Z < -1.33) is approximately 0.0918.

Therefore:

P(80 < X < 125) = 0.9525 - 0.0918

P(80 < X < 125) = 0.8607

This means that approximately 86.07% of people have IQ scores between 80 and 125.

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The interval where the derivative function f'(x) has a relative maximum is -2.478 and 1.732 (B) only.

To find the relative maximum of a function, we need to find the critical points of the derivative function. Critical points are where the derivative function is equal to zero or undefined. In this case, the derivative function is f'(x) = sin(x^2 − 3).

To find the critical points, we need to set the derivative function equal to zero and solve for x:
sin(x² − 3) = 0

x² − 3 = nπ, where n is an integer

x² = nπ + 3

x = ±√(nπ + 3)

We need to find the values of x that are in the interval −3 < x < 3. By plugging in different values of n, we can find the critical points in this interval:

n = 0: x = ±√3 ≈ ±1.732

n = 1: x = ±√(π + 3) ≈ ±2.478

n = 2: x = ±√(2π + 3) ≈ ±2.915 (not in the interval)

So the critical points in the interval are -2.478, -1.732, 1.732, and 2.478.

To determine which of these are relative maximums, we need to look at the sign of the derivative function on either side of the critical points. If the derivative function changes from positive to negative at a critical point, then that point is a relative maximum.

At x = -2.478, the derivative function changes from positive to negative, so this is a relative maximum.

At x = -1.732, the derivative function changes from negative to positive, so this is not a relative maximum.

At x = 1.732, the derivative function changes from positive to negative, so this is a relative maximum.

At x = 2.478, the derivative function changes from negative to positive, so this is not a relative maximum.

Therefore, the values of x in the interval −3 < x < 3 where f has a relative maximum are -2.478 and 1.732.

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The volume of the square pyramid is: B. One-third s^2h units^3.

An example of a square pyramid is given in the image attached below. It has a square base and 4 triangular faces.

A right pyramid that has a square base has a volume that can be calculated using the following volume formula, given as: 1/3(a² × h), where "a" is the length of the edge of the square base, and "h" is the height of the square pyramid.

Given the following parameters for a square pyramid:

The length of the edge of the square base (a) = s units

The height of the square pyramid = h units.

Plug in the values into 1/3(a² × h) to find the expression that represents the volume of the pyramid:

Volume of the square pyramid = 1/3(a² × h) = 1/3(s² × h)

Volume of the square pyramid = 1/3s²h units ³.

The expression that represents the volume of the square pyramid is: B. One-third s^2h units^3.

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1. Factor the denominators as follow:

2. Write the expresion with the less common denominator:

Multiply the first fraction by (x+6) (both parts, numerator and denominator):

Multiply the second fraction by 4 (both parts, numerator and denominator):

Rewrite the expression with the less common denominator:

3. Remove parentheses and simplify:

The value of the copier after 3 years and 6 months can be found by substituting t = 3.5 into the function and solving for V. The salvage value of the copier can be found by substituting t = 5 into the function and solving for V.

After 3 years and 6 months of use, the copier is worth $5,800. This can be found by substituting t = 3.5 into the function V(t)-3600t+20000: V(3.5) = 3600(3.5) - 20000 + 20000 = $5,800.

The salvage value of the copier after 5 years of use is $4,000. This can be found by substituting t = 5 into the function V(t)-3600t+20000: V(5) = 3600(5) - 20000 + 20000 = $4,000. This is the value of the copier when it is sold or replaced after 5 years of use.

The domain of the function is all real numbers because time and value can take on any real value. However, since the function is only defined for the first 5 years of use, t must be between 0 and 5.

The graph of the function is a downward-sloping line with an intercept of $20,000 on the y-axis and a slope of -3600. This means that the value of the copier decreases by $3,600 each year. At t = 0, the copier is worth $20,000, and after 5 years, it is worth $4,000. The graph is a straight line because the function is linear.

Complete Question:

The function V(t)-3600t+20000, where V is value and t is time in years, can be used to find the value of a large copy machine during the first 5 years of use. a. What is the value of the copier after 3 years and 6 months? After 3 years and 6 months, the copier is worth $ b. What is the salvage value of the copier if it is replaced after 5 years? After 5 years, the salvage value of the copier is ts c. State the domain of this function. d. Sketch the graph of this function. 20000 18000 16000 14000 12000 10000 8000 6000+ 4000 2000 4 .

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The area bounded by the graphs of y = x² + 17 and y = 0 over the interval -3 ≤ x ≤ 3 is 120 square units.

To find the area bounded by the two graphs, we need to calculate the definite integral of the difference between the upper function (y = x² + 17) and the lower function (y = 0) over the given interval.

Integrating the difference of the two functions, we have:

∫[from -3 to 3] (x² + 17 - 0) dx

Simplifying, the integral becomes:

∫[from -3 to 3] (x² + 17) dx

To evaluate this integral, we can use the power rule of integration. Integrating x² gives us (1/3)x³, and integrating the constant term 17 gives us 17x.

Applying the limits of integration, the integral becomes:

[(1/3)x³ + 17x] from -3 to 3

Evaluating the expression at the upper limit (x = 3) and subtracting the expression at the lower limit (x = -3), we get:

[(1/3)(3)³ + 17(3)] - [(1/3)(-3)³ + 17(-3)]

Simplifying further:

[(1/3)(27) + 51] - [(1/3)(-27) - 51]

= [9 + 51] - [-9 - 51]

= 60 + 60

= 120

Therefore, the area bounded by the two graphs is 120 square units.

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It is important to note that continuous random variables typically represent measured data, such as the weight or height of an individual, while discrete random variables typically represent counted data, such as the number of heads in a series of coin flips.

The mean of a probability distribution, also known as the expected value, is a measure of central tendency that represents the average value of a random variable in the long run. It is calculated by taking the weighted average of all possible values that the random variable can take, with the weights being the probabilities of each value occurring.

In the case of a discrete random variable, the mean is calculated by multiplying each possible value by its probability and then summing the results. For a continuous random variable, the mean is calculated by integrating the product of the value and its probability density function over the entire range of possible values.

The mean is significant because it provides a measure of the central tendency of a probability distribution, which can be used to make predictions about future outcomes. It is also used in various applications, such as calculating the expected value of a financial investment or the expected number of occurrences of an event in a given time period.

It is important to note that continuous random variables typically represent measured data, such as the weight or height of an individual, while discrete random variables typically represent counted data, such as the number of heads in a series of coin flips.

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Answer:

cos = adjacent/hypotenuse

3/square root13

now you do square root 13 x3 divided by square root 13^2

= 3square root13/13

hope that answers your question

Given:

A line passes through (1,-2) and is perpendicular to \(-4x+7y=21\).

To find:

The equation of that line.

Solution:

We have, equation of perpendicular line.

\(-4x+7y=21\)

Slope of this line is

\(m_1=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}\)

\(m_1=-\dfrac{-4}{7}\)

\(m_1=\dfrac{4}{7}\)

Product of slope of two perpendicular lines is -1.

\(m_1\times m_2=-1\)

\(\dfrac{4}{7}\times m_2=-1\)

\(m_2=-\dfrac{7}{4}\)

Now, slope of required line is \(-\dfrac{7}{4}\) and it passes through (1,-2). So, the equation of line is

\(y-y_1=m(x-x_1)\)

where, m is slope.

\(y-(-2)=-\dfrac{7}{4}(x-1)\)

\(4(y+2)=-7(x-1)\)

\(4y+8=-7x+7\)

\(4y+7x=7-8\)

\(7x+4y=-1\)

Therefore, the equation of required line is \(7x+4y=-1\).

The solution (2, 2) means that 2 adults and 2 children boarded the raft and the weight of the raft didn't exceed its maximum weight.

The solution (5, 0) means that 5 adults boarded the raft and the weight of the raft exceeded its maximum weight.

Based on the information provided above, a system of linear inequalities that represent both the minimum (least) and maximum (most) weight Chase can carry in terms of rafters is given by;

Minimum: 75x + 50y ≥ 150

Maximum: 200x + 100y ≤ 800

where:

For the first trip wherein, Chase guides 2 adults and 2 children;

75x + 50y ≥ 150

75(2) + 50(2) ≥ 150

150 + 100 ≥ 150

250 ≥ 150 (True).

200x + 100y ≤ 800

200(2) + 100(2) ≤ 800

400 + 200 ≤ 800

600 ≤ 800 (True).

For the second trip wherein, Chase guides 5 adults;

75x + 50y ≥ 150

75(5) + 50(0) ≥ 150

375 + 0 ≥ 150

375 ≥ 150 (True).

200x + 100y ≤ 800

200(5) + 100(0) ≤ 800

1,000 + 0 ≤ 800

1,000 ≤ 800 (False).

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Complete Question:

Chase estimates the weight of each adult as approximate 200 pounds and the weight of each child under age sixteen as approximate 100 pounds. Chase charges adults $75 and children under age sixteen $50 to ride down the river with him. His goal is to earn at least $150 each rafting trip.

To write an inequality to represent the most weight Chase can carry in terms of rafters. Define your variables.

After all the linking that will happen, there will be only one train left, moving at the speed of the slowest initial train.

If the three equally spaced trains had started in a different order, the final configuration would still be the same - one train moving at the speed of the slowest initial train.

On average, there will always be only one train left, regardless of the initial ordering of the trains. This is because after all the linking, the train with the slowest speed will always be at the front of the train and no other train can pass it.

If there are four equally spaced trains initially, after all the linking, there will be one train left moving at the speed of the slowest initial train. This is because any two faster trains that link up will then be slower than the train behind them, so the only train left will be the slowest one.

Similarly, if there are five or more equally spaced trains initially, after all the linking, there will be only one train left moving at the speed of the slowest initial train.

Therefore, regardless of the number of equally spaced trains initially, there will always be only one train left after all the linking.

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Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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The length of the base of the rectangle is B = 11 yards  

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

Let the base of the rectangle be represented as B

Area of rectangle A = 209 yards²

The length of the rectangle L = 19 yards

And , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = 19 x B

209 = 19 B

Divide by 19 on both sides of the equation , we get

B = 209 / 19

B = 11 yards

Hence , the length of the base of rectangle is 11 yards

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Answer:

Step-by-step explanation:

Look at the graph to identify its domain and range.

Domain, the set of x-values, is between - 1 on the left and 5 on the right.

The - 1 is included as closed circle and the 5 is not included as open circle.

So the domain is:

The range, the set of y-values, is between - 3 on the bottom and 3 on the top.

The - 3 is included as point on the graph, the 3 is excluded as represented by an open circle.

So the range is:

The transformation that maps triangle ABC onto triangle DEF is an enlargement with center of dilation at point D and scale factor of 2/3.

Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

Since triangle ABC is similar to triangle DEF, this means that the corresponding angles in both triangles are congruent, and the corresponding sides are in proportion. In other words, if we denote the length of side BC as x, then:

BC/AB = EF/DE

AC/AB = DF/DE

AC/BC = DF/EF

To map triangle ABC onto triangle DEF, we need a transformation that preserves the angles and the ratios of the sides. This transformation is a dilation or enlargement, which means that the image is similar to the original triangle.

To find the scale factor of the dilation, we can use the ratio of the corresponding sides:

EF/DE = BC/AB

Substituting the given values, we get:

EF/3 = x/2

Solving for x, we get:

x = 2EF/3

This means that the length of side BC is 2/3 times the length of side EF. Therefore, the transformation that maps triangle ABC onto triangle DEF is an enlargement with center of dilation at point D and scale factor of 2/3.

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Answer:

The answer would be Y= 1/4X -3

Step-by-step explanation:

Hope it was helpful .

Good luck ^.^

Answer: (-2, 1)

Step-by-step explanation:

The mass of a 2018 Olympic gold medal in hectograms is 58.6 hg.

First, we need to know the mass of the Olympic gold medal in grams. According to the question, the mass of an Olympic gold medal is 586 grams.

To convert grams to hectograms, we need to divide the mass in grams by 100. This is because there are 100 grams in 1 hectogram.

To do the division, we can use a calculator. Dividing 586 by 100 gives us 5.86.

The answer we get is in hectograms, so we can write it as 5.86 hg. This means that the mass of a 2018 Olympic gold medal is 5.86 hectograms.

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Answer:

The constant of proportionality is 5 minutes per bracelet

Step-by-step explanation:

If x and y are proportion, then y = k x, where

Let us solve our question

∵ Olivia is making bead bracelets for her friends

∵ She can make 3 bracelets in 15 minutes

We need to find the constant of proportionality in terms of minutes per bracelet, which means y represents the minutes and x represents the bracelet

∴ y = the time in minutes

∴ x = the number of bracelets

∵ y proportion with x

∴ k = \(\frac{y}{x}\)

∵ y = 15 and x = 3

∴ k = \(\frac{15}{3}\)

∴ k = 5

∴ The constant of proportionality is 5 minutes per bracelet

Answer:

True

Step-by-step explanation:

Actually, I'm pretty sure it can also be a reflection! :) Have a good day!!!

Answer:

Step-by-step explanation:

Conclusion:

Therefore, n = 1/9

Hoped this helped.

\(GeniusUser\)

Data collected over several time periods are called time series data.

Time series data refers to data that is collected over several time periods. It captures a sequence of observations of a variable of interest over time, such as sales figures, stock prices, temperature, and so on. The observations are usually taken at regular intervals, such as daily, weekly, monthly or yearly, and the data reflects the changes in the variable over time.

Time series data is useful for identifying trends, patterns, and seasonality in the data, and for making predictions about future values. It's often used in economic forecasting, weather forecasting, and other fields where understanding how a variable changes over time is important.

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Answer:

I think it's x=-4

Step-by-step explanation:

3x= -12

x= -4

Answer:

2,999,875

Step-by-step explanation:

3,000,000m -35=2,999,875

Answer:

51

Step-by-step explanation:

x + y + z  = 0   →-  -(x + y)  = z  →   z^3 =  - (x^3 + 3x^2y + 3xy^2 + y^3)

xyz  = 17

xy [ -(x + y) ]  = 17

xy (x + y)  = -17  →  x^2y + xy^2  = -17  →  3x^2y + 3xy^2  = -51

So......

x^3  + y^3  +  [ z^3 ]

x^3  + y^3  +  [ -  ( x^3 + 3x^2y + 3xy^2 + y^3) ]  =

-3x^2y - 3xy^2  =

-[ 3x^2y + 3xy^2]  =

- [-51]  =

51

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