3 |2x +4| – 2 = 6x + 28
Solve

The quotient and remainder are x³ -5x² + 10x - 17 and 55.

What is Synthetic division?

When the divisor is a linear factor, synthetic division is a technique used to carry out the division operation on polynomials.

Here, (x+2) is a linear factor which indicates that synthetic division can be applied.

So, we will divide the x^4 - 3x^3 - 7x + 1 by x+2.

(refer the attached solution)

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Answer:

Greenland.

North America.

South America.

Europe.

The Middle East.

North Africa.

Sub- Saharan Africa.

Asia.

Step-by-step explanation:

The expression for the cubic function f is -5x^3 + 20x^2 - 25x.

To find an expression for a cubic function f(x) given specific values, we can start by using the general form of a cubic function: f(x) = ax^3 + bx^2 + cx + d.

We are given three points on the graph of the function: (5, 300), (-5, 0), and (0, 0), as well as (6, 0) which gives us a fourth point.

Substituting the x and y values into the equation, we get the following system of equations:

For point (5, 300):

300 = a(5^3) + b(5^2) + c(5) + d

For point (-5, 0):

0 = a(-5^3) + b(-5^2) + c(-5) + d

For point (0, 0):

0 = a(0^3) + b(0^2) + c(0) + d

For point (6, 0):

0 = a(6^3) + b(6^2) + c(6) + d

Simplifying these equations, we obtain a system of linear equations in terms of a, b, c, and d. Solving this system will give us the coefficients for the cubic function.

After solving the system, we obtain the expression for the cubic function:

f(x) = -5x^3 + 20x^2 - 25x

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The capitalized cost for the solid waste treatment plant, based on a 6% MARR, is approximately $579 million.

To calculate the capitalized cost for the solid waste treatment plant, we need to determine the present value of all the costs over the project's lifespan.

The costs involved in the project are as follows:

Initial installation cost: $35 million.

Minor repair and renovation (R&R) after 10 years: $14 million.

Major R&R after 20 years: $18 million.

Operating and maintenance (O&M) costs each year, increasing at a compound rate of 6% per year.

First, let's calculate the present value of the O&M costs over the 20-year period: Using the TVM Factor Table calculator, the present value factor for a 6% MARR and 20 years is 10.206.

The total O&M costs over 20 years can be calculated as follows: O&M costs for the first year: $3 million. O&M costs for the subsequent years: $3 million * (1 + 0.06) + $3 million * (1 + 0.06)^2 + ... + $3 million * (1 + 0.06)^19.

Using the formula for the sum of a geometric series, the O&M costs over the 20-year period can be calculated as: O&M costs = $3 million * (1 - (1 + 0.06)^20) / (1 - (1 + 0.06)) = $3 million * (1 - 1.418519) / (-0.06) = $3 million * (-0.418519) / (-0.06) = $2.91038 million.

Now, let's calculate the present value of the costs: Present value of the initial installation cost: $35 million.

Present value of the minor R&R cost after 10 years: $14 million * 10.206 (present value factor for 6% MARR and 10 years) = $142.884 million. Present value of the major R&R cost after 20 years: $18 million * 10.206^2 (present value factor for 6% MARR and 20 years) = $371.001 million.

Present value of the O&M costs: $2.91038 million * 10.206 = $29.721 million. Finally, the capitalized cost of the solid waste treatment plant is the sum of all the present values: Capitalized cost = $35 million + $142.884 million + $371.001 million + $29.721 million = $578.606 million.

Rounding the final answer to the nearest whole number, the capitalized cost for the solid waste treatment plant is $579 million.

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The complete question is:

A new solid waste treatment plant is to be constructed in Washington County. The initial installation will cost $35 million (M). After 10 years, minor repair and renovation (R&R) will occur at a cost of $14M will be required; after 20 years, a major R&R costing $18M will be required. The investment pattern will repeat every 20 years. Each year during the 20 -year period, operating and maintenance (O\&M) costs will occur. The first year, O\&M costs will total $3M. Thereafter, O\&M costs will increase at a compound rate of 6% per year. Based on a 6% MARR, what is the capitalized cost for the solid waste treatment plant? Click here to access the TVM Factor Table calculator. $ Carry all interim calculations to 5 decimal places and then round your final answer to a whole number. The tolerance is ±25,000.

The statement Total mechanical energy is conserved is "false".

We are given that;

Object is launched at escape velocity

Now,

The total mechanical energy \(E_{total}\)  of an object launched at its escape velocity at a very large distance from the planet is zero.

This is because the object has just enough kinetic energy to escape the gravitational pull of the planet, and no potential energy at infinite distance.

The statement “Angular momentum about the center of the planet is conserved” will be; true.

This is because there are no external torques acting on the object-planet system, so angular momentum is conserved.

The statement “Total mechanical energy is conserved” will be false.

This is because there is an external force (gravity) acting on the object-planet system, so mechanical energy is not conserved.

Therefore, by escape velocity, the answer will be false.

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The stated margin of error account for this possible bias is random error.

The term margin of error is defied as a statistic expressing the amount of random sampling error in the results of a survey

Here we know that the bias due to nonresponse is not accounted for by the margin of error.

And the people who have longer travel times to work might have less time to respond to a survey.

And the calculated estimate from the sample to be less than the true mean travel time to work.

Where as the bias due to nonresponse is not accounted for by the margin of error.

Here we have also know that the the margin of error doesn't account for any mistakes that we've made.

So now we have to look at longer travel times might have less time to respond for a survey right.

Then we get that  it only accounts for random error.

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If billion dollars in taxes were collected in 2005, then 30 billion was collected in 2017.

In 2005 the population was 2 million and it had increased to 3 million by 2017.

If 20 billion dollars in taxes were collected in 2005 then we have to determine how much tax was collected in 2017.

The amount of taxes of the city is proportion to the population of that city.

Tax(T) = kP(Population)

where k is a constant.

In 2005 Population = 2 millions and T = 20 billion. So

20 = 2k

Divide by 2 on both side, we get

k = 10

In 2017 Population = 3 millions and k = 10. So the tax collection in 2017 is:

t = 10 × 3

t = 30 billion

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The complete question is:

The amount of taxes a city collects is proportional to the population of the city. In 2005 the population was 2 million and it had increased to 3 million by 2017. If 20 billion dollars in taxes were collected in 2005 how much was collected in 2017? billion dollars help?

Answer:

6x^2 + 5x + 6

Step-by-step explanation:

Distributive property

Answer:

=6x^2+5x−6

Step-by-step explanation:

Using the foil method, 3x*2x+3x*3+-2*2x+-2*3

Answer:

D. 95800

Step-by-step explanation:

958x10^2

958 x 100

95800 Alternative Form: 9.58 x 10^4

Answer:D

Step-by-step explanation: All you need to do is move the non existent decimal in 958 2 spaces to the right. So it would go from 958. to 95,800.

Answer:

D

Step-by-step explanation:

Yu

Answer: 1st option, 3rd option, 1st option

Step-by-step explanation:

Step-by-step explanation:

3x+8y=27

3x=27-8y

x=27-8y/3

4(27-8y/3) + 3y=13

36-32/3y +3y =13

36-23/3y=13

36-13=23/3y

y=3

x=1

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of x is 1.

The value of y is 4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 = 5 is an equation.

We have,

-4.5x - 2y = -12.5 ____(1)

3.25x - y = -0.75 _____(2)

From (1) we get,

-4.5x + 12.5 = 2y

y = (-4.5x + 12.5) / 2 _____(3)

Now,

3.25x - y = -0.75

Putting (3) in (2) we get,

3.25x - (-4.5x + 12.5) / 2 = -0.75

6.5x + 4.5x - 12.5 = 2 x -0.75

11x - 12.5 = -1.5

11x = -1.5 + 12.5

11x = 11

x = 1

Now,

From (3) we get,

y = (-4.5x + 12.5) / 2

y = (-4.5 x 1 + 12.5) / 2

y = (-4.5 + 12.5) / 2

y = 8/2

y = 4

Thus,

The value of x is 1.

The value of y is 4.

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its a personal essay...

Answer:

y=5

Step-by-step explanation:

Use the given slope and point to substitute into the point-slope formula then you can solve for slope/intercept form

Tip: If the slope is 0 the equation is going to be y= the y of your original point (-2,5)

To find the consumer's and producer's surplus, we need more information about the demand and supply functions or the market equilibrium.

You provided the demand function D(x) = 25, but we require additional details to proceed with the calculations. The consumer's surplus is the difference between the maximum price consumers are willing to pay and the price they actually pay. It represents the benefit or surplus gained by consumers in a market transaction.

The producer's surplus is the difference between the minimum price producers are willing to accept and the price they actually receive. It represents the benefit or surplus gained by producers in a market transaction.

To calculate these surpluses, we typically need information about the supply function, equilibrium price, and equilibrium quantity. These values help determine the areas of the consumer's and producer's surpluses on the supply-demand graph.

Please provide the necessary information about the supply function, equilibrium price, or any other relevant details so that I can assist you in calculating the consumer's and producer's surplus accurately.

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The graph of triangle JAR and its reflection across the line x = 1 consists of the points (3,4), (7,5), (5,2), and their reflections (−1,4), (−5,5), (−3,2).

To graph triangle JAR, we plot the three given points J(3,4), A(7,5), and R(5,2) on a coordinate plane. Connect these three points to form the triangle JAR.

To find the reflection of triangle JAR across the line x = 1, we need to reflect each point across this line. The line x = 1 is a vertical line passing through x = 1 on the coordinate plane.

To reflect a point across a vertical line, we keep the y-coordinate the same and change the sign of the x-coordinate. So, the reflection of J(3,4) will be J'(−1,4), the reflection of A(7,5) will be A'(−5,5), and the reflection of R(5,2) will be R'(−3,2).

We then connect the three reflected points J', A', and R' to form the reflected triangle J'A'R'.

In summary, the graph of triangle JAR and its reflection across the line x = 1 will consist of the triangle JAR and its reflected image J'A'R'.

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*see attachement.

Answer:

Country A because it has a smaller interquartile range

Step-by-step explanation:

A smaller interquartile range connotes that the data in the distribution do not vary much, while a larger interquartile range would suggest the data vary much.

Therefore, the island that would have an average speed close to its median would be the island whose interquartile range is smaller.

Thus, Country A has a smaller interquartile range, so therefore, it would have a daily wind speed close to its median.

Answer:

C

Step-by-step explanation:\

Ur welcome

Travis's checking account new balance, after wrote five checks to the employees of his business is - $235

To solve this problem, we have to state the equation using the information of the problem

Information about the problem:

Calculating the checks total amount Travis wrote to the employees of his business:

Total amount for his employers = Check amount of each employer * No. of checks

Total amount for his employers = $225 * 5

Total amount for his employers = $1125

Calculating the final balance, we have:

Final balance = Original balance - Total amount for his employers

Final balance = $890 - $1125

Final balance = - $235

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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The graph will cross the x-axis if the multiplicity of the real root is odd.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)

(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)

(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)

(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.

The graphs: (a) black, (b) red, (c) green

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Answer:

The answer to your problem is, 156

First lets find out how many feet or in one yard ?

Well 1 yard = 3 feet.

Now that we know that we can use our knowledge to answer the next question:

If Bill ran 52 yards, how many feet did he ran?

We can do math to solve our answer. :

1 x 52 = 52.

Now we need to multiply 52 x 3.

That is a little bit to much, so lets make the problem easier!

By breaking up the problem \/ to make it more easier.

50 x 3. ( 5 x 3 = 15, just add a zero! ) = 150

3 x 2 = 6.

Next add:

150 + 6 = 156.

Thus the answer to your problem is, 156

Answer:

x=33

Step-by-step explanation:

-23-11x=-12x+10

+11x +11x

-23 = -x + 10

-10 -10

-33 = -×

/-1 /-1

33=x

Answer:

-23-11x=-12x+10

Step-by-step explanation:

collect like terms , then you have this

-11x+12x=10+23

having done that you would have your answers

x= 33

Answer: Nonresponse, voluntary, and convenience.

Step-by-step explanation:

For the first question, it should be noted that everyone cannot respond as only the people who have strong opinions will respond. Therefore, it's a nonresponse error.

For the second question, the people will have to volunteer. Therefore, it's a voluntary bias while the third one is a convenience sample as it's an easily available sample.

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9 kilograms of cashews were mixed with 3 kilograms of nuts to make 12 kg of the mixture.

What are the arithmetic operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

Let's assume that x kilograms of cashews were mixed with (12 - x) kilograms of nuts costing $10 per kilogram to make 12 kg of the mixture.

The total cost of the cashews used in the mixture is 8x dollars, and the total cost of the nuts used is 10(12 - x) dollars. The total cost of the mixture is (12)(8.50) = 102 dollars.

Since the mixture contains 12 kg of nuts and cashews, we can set up the following equation to solve for x:

8x + 10(12 - x) = 102

Expanding the equation gives:

8x + 120 - 10x = 102

Simplifying and solving for x gives:

-2x + 120 = 102

-2x = -18

x = 9

Hence, 9 kilograms of cashews were mixed with 3 kilograms of nuts to make 12 kg of the mixture.

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The slope of the line is -32, and the y-intercept is 480 if the equation of the line is y = -32x + 480.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

The equation of the line uses two points:

(0, 480) and (15, 0)

y = (-480/15)[x - 15]

y = -32(x - 15)

y = -32x + 480

y = mx + c

m = -32

c = 480

Thus, the slope of the line is -32, and the y-intercept is 480 if the equation of the line is y = -32x + 480.

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The vertical component of the final velocity (vfy) of the motorcycle is approximately 11.82 m/s. The magnitude of the final velocity (vf total) of the motorcycle is approximately 31 m/s.

A. To find the vertical component of the final velocity (vfy) of the motorcycle, we need to use the principles of projectile motion. Since the motorcycle is launched from the ramp, we can treat it as a projectile in free fall after leaving the ramp. The vertical component of the final velocity can be calculated using the equation:

vfy = v0y + gt,

where v0y is the vertical component of the initial velocity, g is the acceleration due to gravity (9.8 m/s^2), and t is the time of flight.

To calculate v0y, we can use the fact that the initial velocity (v0) of the motorcycle is 31 m/s, and the angle of the ramp (θ) is 16.5 degrees. The vertical component of the initial velocity is given by:

v0y = v0 * sin(θ).

Substituting the values, we have:

v0y = 31 m/s * sin(16.5 degrees) ≈ 8.36 m/s.

The time of flight can be calculated using the equation:

t = 2 * v0y / g.

Substituting the values, we have:

t = 2 * 8.36 m/s / 9.8 m/s^2 ≈ 1.70 s.

Finally, we can calculate vfy:

vfy = v0y + gt = 8.36 m/s + (9.8 m/s^2) * 1.70 s ≈ 11.82 m/s.

Therefore, the vertical component of the final velocity (vfy) of the motorcycle is approximately 11.82 m/s.

B. The magnitude of the final velocity (vf total) can be calculated using the Pythagorean theorem. Since the horizontal component of the velocity remains constant throughout the motion, vf total is equal to the initial velocity (v0) of the motorcycle, which is 31 m/s.

Therefore, the magnitude of the final velocity (vf total) of the motorcycle is approximately 31 m/s.

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Answer:

x \(\geq\) 5 ( the last one)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The inequality of C says the amount of hours of tv that kenny can watch (x) can be exactly or anything below 5 hours