Explain the synthetic division process for polynomials. Divide (2x4–3x³ - 5x² + 3x
+8) by (x - 2). Be as specific as possible. You may upload a picture of your work to
help explain the steps in the division process. Make sure to include the answer to
the division problem in your explanation.

Therefore , the solution of the given problem of inequality comes out to be Paul can drive at most 208 more miles before he will have to refill the tank.

A connection or collection of variables without the equal sign is a mathematical inequality. Equilibrium is typically followed by equity. Inequality happens when two values are not equal. Differences exist between equality and inequality. It was decided to utilize the most factors symbol because the quantities are not identical or equivalent (). Any discrepancy, regardless of how small or large, can be used to compare values.

Here,

Let x be the number of miles Paul can drive before he will have to refill the tank.

Since Paul's car can go at most 375 miles on one tank of gas, and he has already driven 167 miles, we can write the inequality:

x ≤ 375 - 167

Simplifying, we get:

x ≤ 208

Therefore, Paul can drive at most 208 more miles before he will have to refill the tank.

Interpretation: If Paul drives more than 208 miles, he will not have enough gas to complete the journey and will need to refill the tank.

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An equivalent to the expression 3x(2x+5) using distributive property is 6x²+15.

The distributive law of multiplication over addition and subtraction is another name for the distributive property. By its very name, the procedure implies that something will be divided or distributed. Both addition and subtraction are subject to the distributive law.

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

Example: 3x(2x+5)

By using distributive property, we get

3x×2x+3x×5

= 6x²+15

Therefore, an equivalent to the expression 3x(2x+5) is 6x²+15.

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A $100 bill and a dime differ by a magnitude of 3.

Orders of magnitude can be used in order to define large quantities efficiently and more easily. A dime is a currency used in the US that is equivalent to 0.10 dollars.

So we can represent a dime as 10-¹ of a dollar

and we can write 100 dollars as 10² of a dollar.

Therefore the difference in the order of magnitude of 100 dollars and a dime would be the difference between the powers or exponents of those two quantities,

That is,

2-(-1) = 3

So, the dollar differs by a magnitude of 3 from a dime.

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113.09724, is the diameter of craig's balloon.

What is volume ?

The area or capacity of a cone is determined by its volume.

A cone's circular base tapers from a flat base to a point known as the apex or vertex in three dimensions.

A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to each point on the base, which is in a plane without the apex.

A cone can be thought of as a collection of irregularly shaped circular disks placed on top of one another with the ratio of their radii remaining constant.

A three-dimensional shape's volume is determined by how much space it takes up.

According to our question-

V = 4/3 * * r3 is the formula for a sphere's volume.

Your balloon's diameter is 6,

hence its radius is 3.

V = 4/3 * 3.14159 * 33 = 113.09724

Hence, 113.09724, is the diameter of craig's balloon.

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Answer:

The number in the middle.

Example 1:

2 3 4 5 6

4 is in the middle, 4 is the median.

Example 2:

4 8 2 6 9

Put numbers in order:

2 4 6 8 9

6 is in the middle, 6 is the median.

Example 3:

4 7 2 3 9 8

Put numbers in order:

2 3 4 7 8 9

4 and 7 are in the middle, add them together and divide by 2 to get the median.

(4 + 7) / 2 = 11 / 2 = 5.5

5.5 is the median.

Answer:°

Based on the given information, we can see that the pair of parallel lines are intersected by a transversal, which creates corresponding angles on the two lines. Using this fact, we can set up the equation:

2x + 105 = 70^2

First, we simplify 70^2:

70^2 = 4900

Then, we solve for x:

2x + 105 = 4900

2x = 4900 - 105

2x = 4795

x = 2397.5

Therefore, x is equal to 2397.5.

The relationship between the angles is that they are corresponding angles, which means they are congruent. We can use this fact to find the measure of the other angle that is marked in the diagram.

From the diagram, we can see that the angle marked as (2x + 10^5)° is supplementary to the angle marked as 70^2°. This means that the sum of their measures is 180 degrees. We can use this fact to find the measure of the angle marked as (2x + 10^5)°:

(2x + 10^5) + 70^2 = 180

2x + 10^5 + 4900 = 180

2x + 10^5 = 175

2x = 175 - 10^5

2x = -99825

x = -49912.5

correct me if im wrong

Step-by-step explanation:

The value of centimeter to inches can be calculated by simply by dividing the length  value by 2.54 so 13 cm to 5.118 inches.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

You've also come to the right place if you've been wondering how many inches are in 13 centimetres or how many inches are in 13 centimetres.

On our website, inches are denoted by "in" or "′′, while centimetres are always written as cm.

You must divide 13 centimetres by 2.54 to get the answer in inches.

Hence, in inches, the comparable height, width, or length is:

13 cm equals 5.11811 inches.

13 cm is equal to 5.11811 inches.

5.11811 inches in 13 cm.

13 cm in inches: 13/2.54 = 5.11811 inches is the conversion factor for 13 cm.

You can convert 13 inches to centimetres here.

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The maximum number of people who can go to the amusement park is 6.

To determine the number of people who can go to the amusement park, use the following equation:

Total cost = Parking cost + Admission cost

The total cost cannot exceed $86, the amount of money the friends have. The parking cost is $5 and the admission cost per person is $13.50. Therefore, we can write the following equation:

86 ≥ 5 + 13.5x

To solve for x,  subtract 5 from both sides of the inequality and then divide both sides by 13.5. This gives us the following equation:

x ≤ (86 - 5) / 13.5

x ≤ 6

Therefore, the maximum number of people who can go to the amusement park is 6.

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Answer: Let the legs of the right triangle be a and b. We know that the radius of the inscribed circle is 4 cm, which means that the inradius is also 4 cm. The inradius is given by:

r = (a + b - c)/2

where c is the hypotenuse, so we can substitute the given values to get:

4 = (a + b - 35)/2

Multiplying both sides by 2, we get:

8 = a + b - 35

Adding 35 to both sides, we get:

a + b = 43

We also know that the area of the triangle is given by:

A = (ab)/2

where a and b are the legs of the triangle. We can use the Pythagorean theorem to relate the legs to the hypotenuse:

a^2 + b^2 = c^2

Substituting the given value for the hypotenuse, we get:

a^2 + b^2 = 35^2

Simplifying, we get:

a^2 + b^2 = 1225

Now we can use the equation for the sum of the legs to solve for one of the legs in terms of the other:

a + b = 43

b = 43 - a

Substituting this expression for b into the equation for the area, we get:

A = (a(43 - a))/2

Simplifying, we get:

A = (43a - a^2)/2

To find the maximum value of the area, we can take the derivative of A with respect to a and set it equal to 0:

dA/da = 43/2 - a = 0

Solving for a, we get:

a = 43/2

Substituting this value into the equation for the area, we get:

A = (43/2)(43/2 - 43/2)/2 = 0

This means that the area of the triangle is 0 when one of the legs has a length of 0, which is not possible. Therefore, the maximum area occurs when the legs have equal lengths, which means that the right triangle is an isosceles right triangle. In this case, we have:

a = b = (35/sqrt(2)) cm

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

A = (ab)/2 = ((35/sqrt(2))^2)/2 = 612.5 cm^2

Therefore, the area of the right triangle is 612.5 square centimeters.

Step-by-step explanation:

Answer:

n = 4

Step-by-step explanation:

Remove the radical by raising each side to the index of the radical.

The value of 104 kg into lbs can be converted by multiplying kilogram by 2.204622  so the answer is 229.3 pounds.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

The SI unit of mass is the kilogramme (kg). It has the same mass as the international kilogramme prototype. The International Bureau of Weights and Measures maintains a platinum-iridium international prototype similar to this one. A kilogramme is about equivalent to 2.20462262184878 pounds.

The legal definition of a pound, or the international avoirdupois pound, is 0.45359237 kilogrammes.

Pounds = kilograms × 2.20462262184878

= 104 x 2.20462262184878

= 229.3 pounds or lbs.

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To find the equation of the tangent line to a curve at a given point, we will need the equation of the curve and the place where you want to locate the tangent line in order.

Calculate the derivative by differentiating the curve's equation. This will reveal the tangent line's slope at any point along the curve.

Put the derivative you discovered in step 1's derivative into the x-coordinate of the place where you wish to find the tangent line. This will reveal the tangent line's slope at that particular position.

To determine the equation of the tangent line, use the point-slope form of the equation of a line. A line's point-slope formula is written as y - y1 = m(x - x1), where (x1, y1) is the line's point and m is its slope. Both the slope of the line and the location on the line where you wish to find the tangent line are known to you from step 2.

Put the tangent line's equation in a simpler, more conventional form,        as y = mx + b.

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The units of moment of inertia depend on the shape and dimensions of the object, and can be expressed in kg m², g cm², lb ft², or oz in².

The units of the moment of inertia depend on the shape and dimensions of the object. Some common units for a moment of inertia are:

kg m² (kilogram-meter squared)

g cm² (gram-centimeter squared)

lb ft² (pound-foot squared)

oz in² (ounce-inch squared)

These units represent the distribution of mass around an axis of rotation and are used in calculations involving rotational motion and torque.

The moment of inertia is a physical property of an object that determines its resistance to rotational motion. It depends on the mass distribution of the object and its orientation with respect to the axis of rotation. The moment of inertia is typically represented by the symbol I and is measured in units of kg m², g cm², lb ft², or oz in². The moment of inertia can be calculated using the object's mass, dimensions, and shape, and is used in calculations involving rotational motion, such as torque and angular acceleration. Different shapes and distributions of mass have different moments of inertia, which can affect the object's motion and stability.

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The stochastic process w's probability density function will look like this; W = 3: P(HHH) = (2/3)3 = 8/27

P(HHT) + P(HTH) + P(THH) = 3(2/3)2(1/3) = 12/27 = 4/9 W = 2

P(HTT) + P(THT) + P(TTH) = 3(2/3)(1/3) when W = 1.

3 = 6/27 =2/9

W = 0: P(TTT) = (1/3)

3 = 1/27

How does one calculate the probability of a random vector?

Step 1: Create a list of all simple events in the sample space. Step 2: Determine the likelihood of each simple event. Step 3: Determine the value with each simple event by listing all unique combinations for random variable X. Step 4: For each possible value of k, find all simple occurrences for which X = k.

When three coins are tossed at the same time, what is the likelihood of getting all heads?

When three coins are tossed, the positive outcome is HHH. As a result, the required probability equals 1/8.

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Your systolic and diastolic blood pressure are used by the Mean Arterial Pressure (MAP) calculator to calculate your mean arterial pressure.

In medicine, the term mean arterial pressure (MAP) refers to a person's average blood pressure throughout one cardiac cycle. On MAP, it is observed that both systemic vascular resistance and cardiac output have an impact.

Systolic and diastolic blood pressure can be used in a formula to calculate mean arterial pressure, or it can be measured directly. A blood pressure cuff provides the information required to estimate the mean pressure in the least invasive way possible.

A comparable method is to measure blood pressure with an oscillometric device, which computes the systolic and diastolic values using only a cuff and a microprocessor. Following the invasive insertion of an arterial catheter with a transducer, the waveform that is left behind establishes the mean pressure.

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The missing angles of the shape are

For a rhombus shape, the opposite angles are equal and the sum of the angles are equal to 360 degrees

The four shapes makes a fifth rhombus between them

2 < BIF + 2 < IBJ = 360

2 < BIF + 2 * 54 = 360

2 < BIF + 108 = 360

2 < BIF = 360 - 108

2 < BIF = 252

< BIF = 152

solving for < JBC

2 <JBC + < JBI = 180

< JBC = < IBA

2 < JBC + 54 = 180

2 < JBC = 180 - 54

2 < JBC = 126

< JBC = 63

Solving for < BJD

2 < JBC + 2 < BJD = 360

126 + 2 < BJD = 360

2 < BJD = 360 - 126

2 < BJD = 234

< BJD = 117

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The required it will take about 1.99 years for the car to be worth half its original amount. Rounded to two decimal places, the answer is  1.99 years.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
Let V be the value of the car after ⁿ years. Since the car loses 14% of its value each year, its value can be expressed as:

V = 24885(0.86)ⁿ

We want to find how many years it will take for the value of the car to be half its original amount, which means:

V = 24885/2 = 12442.5

So we need to solve for t in the equation:

12442.5 = 24885(0.86)ⁿ

Dividing both sides by 24885, we get:

0.5 = 0.86ⁿ

Taking the natural logarithm of both sides, we get:

ln(0.5) = ln(0.86ⁿ) = n ln(0.86)

Solving for n, we get:

n = ln(0.5) / ln(0.86) ≈ 1.99

Therefore, it will take about 1.99 years for the car to be worth half its original amount. Rounded to two decimal places, the answer is  1.99 years.

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The value of weight of 76 kg when converted to pounds is  167.55112 pounds.

kilogram is the standard unit of mass in the International System of Units (SI), while pounds are a common unit of mass used in the United States and other countries.

To Know how to convert between different units of measurement is essential for accurate calculations and comparisons. convert 76kg to pounds, you can use the formula: 1 kilogram is equal to 2.20462 pounds.

Therefore, to convert 76kg to pounds, you would multiply 76 by 2.20462.

76  x 2.20462 =  167.55112 pounds

So, weight of 76kg is equivalent to  167.55112 pounds

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The big idea in math are abstraction and infinity.

Mathematics is a vast and fascinating subject that involves exploring the concepts of numbers, shapes, patterns, and more. Within this subject, there are several big ideas that serve as the foundation for various mathematical theories and principles. One of the most prominent big ideas in math is that of abstraction.

Abstraction is a concept that allows mathematicians to generalize ideas and create models that can be applied to a wide range of situations. It involves taking a complex problem and breaking it down into smaller, more manageable components that can be easily analyzed and understood. This process often involves using symbols and equations to represent real-world situations and finding patterns and relationships between them.

Another big idea in math is that of infinity. This idea involves exploring the concept of endlessness and how it applies to different mathematical concepts. Infinity plays a critical role in calculus, where it is used to describe the behavior of functions as they approach limits and infinity.

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Answer:

a. AD = 28 mm

b. m/CBD = 90°

c. m/ADC = 90°

d. m/AEB = 45°

e. m/DAC = 135°

The mean and variance of the number x of unusable fasteners in a randomly selected box are about 150 and 150 respectively.

Poisson distribution is a distribution function useful for characterizing events with very low probabilities of occurrence within some definite time or space. It is used when the number of trials is very large and the probability of success is comparatively small.

In Poisson distribution, the mean is defined as:

λ = np

where n = number of items and p = probability of success

Given: n = 5000 and p = 3/100 = 0.03

Thus,  λ = np = 5000 * 0.03 = 150

Since the mean and variance are equal in Poisson distribution. Thus, the variance (σ²) =  150

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The 3 sided die is a unique type of dice with three sides instead of the usual six, and the probability of rolling any of the sides is equal to 1/3 or 33.3%.

A 3 sided die, also known as a triangular or tetrahedral die, is a unique type of dice that has three sides instead of the usual six. It is often used in games, puzzles, and simulations that require a random number generator.

Mathematically speaking, the probability of rolling any of the three sides on a 3 sided die is equal to 1/3 or 33.3%. This is because each of the sides has an equal chance of landing face up when the die is rolled.

To calculate the probability of rolling a specific number on a 3 sided die, we divide the number of ways that number can appear by the total number of possible outcomes.

For example, if we want to know the probability of rolling a 2, we would divide 1 (since there is only one side with a 2) by 3 (the total number of sides on the die). This gives us a probability of 1/3 or 33.3%.

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The division of [tex]14x^3-21x^2-7x $ by $-7x[/tex] is -2x-2.

What is polynomial division?

Polynomial division is a method used to divide two polynomials, which are algebraic expressions consisting of one or more terms, using long division.

To perform polynomial division of [tex]14x^3- 21x^2 - 7x[/tex] by −7x, we can follow these steps:

Write the dividend [tex](14x^3 - 21x^2 - 7x)[/tex] in descending order of powers of x, filling in any missing terms with a coefficient of 0:

[tex]14x^3 - 21x^2 - 7x + 0[/tex]

Write the divisor (-7x) to the left of a long division bracket and divide the first term of the dividend by the first term of the divisor. Place the result above the long division bracket.

-2x

Multiply the divisor by the quotient and write the result below the dividend. Subtract this product from the dividend and bring down the next term.

[tex]14x^3 - 21x^2 - 7x + 0\\\\-(-7x)(-2x)\\\\14x^2[/tex]

Repeat steps 2 and 3 with the new dividend (14x^2) and the same divisor (-7x).

[tex]-2x - 2\\\\14x^2 + 0x\\\\-(-7x)(-2x + 2)\\\\-14x[/tex]

Repeat steps 2 and 3 with the new dividend (-14x) and the same divisor (-7x).

2

[tex]14x^2 + 0x + 0[/tex]

[tex]-(-7x)(-2x + 2 - 2/7)[/tex]

0

The final result of the polynomial division is the quotient -2x - 2 with no remainder.

Therefore, the division of [tex]14x^3-21x^2-7x $ by $-7x[/tex] is:

[tex]14x^3-21x^2-7x \div -7x = -2x - 2.[/tex]

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The linear correlation coefficient for a sample is always b) between -1 and 1, inclusive

The linear correlation coefficient (also known as Pearson's correlation coefficient) is a measure of the strength and direction of the linear relationship between two variables.

It ranges from -1 to 1, with negative values indicating a negative correlation (inverse relationship), positive values indicating a positive correlation (direct relationship),

And a value of zero indicating no correlation between the variables.

The answer is (b) between -1 and 1, inclusive

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To be able to purchase the car, you would need to save around 198.67 every month for 24 months.

To determine how much money you would have to save every month for 12 months or 24 months, we need to divide the cost of the car by the number of months and round the result up to the nearest cent to ensure that you have enough money to buy the car at the end of the saving period.

For 12 months:

The amount of money you would have to save every month for 12 months is:

4,768 / 12 = 397.33 (rounded up to the nearest cent)

So, you would have to save about 397.33 every month for 12 months to be able to buy the car.

For 24 months:

The amount of money you would have to save every month for 24 months is:

4,768 / 24 = 198.67 (rounded up to the nearest cent)

So, you would have to save about 198.67 every month for 24 months to be able to buy the car.

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For sum of all angles of polygon=900°, no. of sides will be 7.

What exactly is a polygon?

Polygons are two-dimensional geometric objects that have the same number of sides on all sides. The sides of a polygon are made up of straight line segments linked end to end. As a result, the line segments of a polygon are referred to as sides or edges. The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result. A triangle of a polygon. A circle is a planar figure, however it is not regarded a polygon since it is curved and lacks sides and angles. As a result, we may argue that all polygons are 2d forms, but not all two-dimensional figures are polygons.

For a polygon with n no. of sides

sum of all interior angles=(n-2)*180°

Now,

As given the sum of all angles=900°

then number of sides of a polygon will be

(n-2)*180=900

n-2=5

n=7

Hence,

          For sum of all angles of polygon=900°, no. of sides will be 7.

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1/8 in a decimal, divide the denominator by the numerator to get 1/8 as a decimal 1/8 is 0.125.

We divide the numerator by the denominator to convert a fraction to a decimal number. This results in a decimal value because, when dividing, we add the decimal place and then add the necessary number of zeros to finish the division.

1/8

1/2 x 1/2 x 1/2

0.5 x 0.5 x 0.5

0.125

To convert a fraction to a decimal, all you have to do is divide the numerator by the denominator. We position the number over its place value when converting a decimal to a fraction.

Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal.

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Answer:

There are 2 iron (Fe) atoms, 3 oxygen (O) atoms, and 3 carbon (C) atoms on both the reactant and product side of the equation. Therefore, the equation is balanced.

Answer:

There is 2 Iron(Fe) atoms , 6 Oxygen atoms and 3 carbon atom on both side so this equation is balanced I believed.

The value of 5.9 feet after the conversion to centimeter is equivalent to   179.9 cm .

The "Feet" and "Centimeters" are both the units of measurement for length.

The unit "Feet" are primarily used in the United States and other countries that follow the Imperial system, while "centimeters" are part of the metric system used in most other parts of the world.

We know that 1 feet is approximately equal to 30.48 cm ;

So , the conversion factor is = 30.48cm ;

To convert the given number we multiply , by the conversion factor ,

We can write :

⇒ 5.9 feet = 5.9 × 30.48 cm ;

⇒ 5.9 feet = 179.832 cm ≈ 179.9 cm .

Therefore , the value of 5.9 feet is approximately equal to 179.9 cm  .

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Knowing that two bouquets of flowers and candies are bought, leaving 21.10, the money at the beginning of the purchase is $266.85.

To find out how much money she had in the beginning, we can use the following equation:
Starting money - (bouquets cost + candies cost) = money left

Let's plug in the given values:
Starting money - ((2 x 121.75) + (2.25 x candies)) = 21.10

Simplifying the equation, we get:
Starting money - (243.50 + 2.25 x candies) = 21.10

Now, we can rearrange the equation to solve for the starting money:
Starting money = 21.10 + 243.50 + 2.25 x candies

If we plug in the given values, we get:
Starting money = 21.10 + 243.50 + 2.25 x candies
Starting money = 266.85

Therefore, Arunima had a total of $266.85 in the beginning.

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