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.

According to the standard conversion rates 1.78 is equal to 5.696 feet.

We measure the distance between any two bodies in the terms of meter but when the distance is a small one, we can also use the unit called foot and these two units are interconvertible.

According to the standard us conversion rates one meter is equal to 3.2 ft.

We can use this same conversion rate to find the measurement of 1.78 m into ft.

So, we will write,

1 m = 3.2ft

1.78m = 1.78 x 3.2 ft

1.78m = 5.696 ft.

So, we have found that 1.78 m is equal to 5.696 feet.

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a. Line A represents Duncan's wages. b. We can determine this by equation of the line. Luke's equation of line has an additional constant and thus it starts from the point 30 above from the origin.

In mathematics, a variable is a symbol that designates a mathematical object (from the Latin variabilis, "changeable"). Any number, vector, matrix, function, function argument, set, or set element can be represented by a variable.

A variety of issues are resolved by algebraic calculations that treat variables like explicit integers in a single computation. The quadratic formula, for instance, can be used to solve any quadratic equation by exchanging the variables in the quadratic formula for the numerical values of the coefficients in the equation.

Let us suppose number of hours worked = x.

Given that,

Duncan gets paid R8,50 per hour. His equation of line is:

D = 850x

Luke gets R30 and R450 per hour. His equation of line is:

L = 450x + 30

a. From the graph we see that line A represents Duncan's wages.

b. We can determine this by looking at the equation of the line. Luke's equation of line has an additional constant and thus it starts from the point 30 above from the origin.

c. For x = 2 hours.

L = 450(2) + 30

L = 900 + 30 = R930

d. For D = 1000:

1000 = 850x

x = 1.17 hours.

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Answer:

12800 meters.

Hope that helps!!!

You travel 9600 meters after completing 8 laps on a 1 2/10 kilometers long go-kart track.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The length of the go-kart track is 1 2/10 kilometers, which can be converted to meters as follows:

1 kilometer = 1000 meters

2/10 kilometer = 2/10 x 1000 = 200 meters

So, the length of the go-kart track in meters is:

1 2/10 kilometers = 1 x 1000 + 2/10 x 1000 = 1200 meters

To find the total distance you travel after completing 8 laps, you need to multiply the length of the track by the number of laps:

Total distance = 8 x 1200 meters = 9600 meters

Therefore, you travel 9600 meters after completing 8 laps on a 1 2/10 kilometers long go-kart track.

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The number 1.07  × 10⁸ in standard form is 107,000,000.

To write 1.07 × 10⁸ in standard form, we need to move the decimal point to the left or right such that there is only one non-zero digit to the left of the decimal point.

In this case, we have 1.07 × 10⁸, which means we have a value of 1.07 times 10 raised to the power of 8. To convert this to standard form, we need to move the decimal point 8 places to the right since 10 is being raised to the power of 8.

1.07 × 10⁸ = 107,000,000

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in a regression model, outliers may be identified by examining the Residual.  Seeing how far the data points are away from the regression is how you can determine outliers.

What's a residual in finance?

A residual or balloon payment is a final lump sum you're needed to pay at the end of your loan term to enjoy an asset outright. generally, the lump sum is original to – or lower than – the downgraded value of the asset.

What are exemplifications of residual?

Residual describes what remains after utmost of commodity is gone. It's an nearly formal word for what is leftover. However, also you have some residual bitterness, If you've gotten over your bifurcation but you still have the appetite to protest your partner.

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The total number of pages in Rhett's book is 183 pages.

A solution to an equation is a number that can be substituted for the variable to provide a valid number statement.

To find the total number of pages in Rhett's book, we need to solve for p in the equation:

p + 31 = 214

First, we can isolate p on one side of the equation by subtracting 31 from both sides:

p + 31 - 31 = 214 - 31

Simplifying:

p = 183

Therefore, the total number of pages in Rhett's book is 183 pages.

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The requried slope of the given linear representation is -0.67.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

m = (y₂ - y₁) /  (x₂ - x₁)

Here,

From the figure,
Locate two points, on the line
(-3, -3) and (3, -5)

m = (y₂ - y₁) /  (x₂ - x₁)

Substitute the value in the above expression,
m = -5 + 3 / 3 + 3
m = -2/6
m = -1/3
m = -0.67

Thus, the requried slope of the given linear representation is -0.67.

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Answer:

24

Step-by-step explanation:

Rect = 3*4 = 12

Rect 2 = 1*6 = 6

Triangle = (6-3)*1/2*4 = 6

6 + 6 + 12 = 24

The variance for the sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores is 5.

The formula for the variance of a sample is:

[tex]s^2[/tex] = SS / (n - 1)

where SS is the sum of squared deviation scores, n is the sample size, and [tex]s^2[/tex] is the variance.

In this case, SS = 20 and n = 5, so we can substitute these values into the formula:

[tex]s^2[/tex] = 20 / (5 - 1)

[tex]s^2[/tex] = 5

Therefore, the variance for this sample is 5.

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The conversion of 28 Fahrenheit to Celsius is -2.22.

To convert 28 degrees Fahrenheit (28°F) to Celsius (°C), you can use the formula:

°C = (°F - 32) x 5/9

Substituting 28 for °F in the formula, we get:

°C = (28 - 32) x 5/9

Simplifying the expression inside the parentheses and performing the arithmetic operations, we get:

°C = (-4) x 5/9

°C = -2.22

Therefore, 28°F is equal to -2.22°C (rounded to two decimal places).

Celsius and Fahrenheit are two scales used to measure temperature.

Celsius, also known as the centigrade scale, is a temperature scale where the freezing point of water is 0 degrees Celsius and the boiling point of water is 100 degrees Celsius at standard atmospheric pressure.

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Correct Question :

What is the conversion of 28 Fahrenheit to Celsius?

The value x = 3 will result in the greatest relative frequency given discrete random variable X.

What is relative frequency?

A frequency is the number of times an event takes place. It's experimental, not theoretical, to study relative frequency. As it is an experimental one, it is likely that when we repeat the trials, we will get different relative frequencies.

The relative frequency of a discrete random variable increases with decreasing variable value.

This implies that,

A variable with x = 0 would occur more frequently than one with x = n, where n > 0.

So, the greatest relative frequency given discrete random variable X, when X ∼ B (4, 1/10) is  x = 3.

Hence, the value x = 3 will result in the greatest relative frequency given discrete random variable X.

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The prime factorization of 105 is 3 × 5 × 7. We can also write this as 3 × [tex]5^1[/tex] × [tex]7^1[/tex], where the exponents indicate the number of times each prime factor appears in the factorization.

To find the prime factorization of 105, we can use the following steps:

Find a factor of 105. One way to do this is to try dividing 105 by prime numbers (2, 3, 5, 7, 11, ...) until we find a factor. We can also notice that 105 is divisible by 3 since the sum of its digits (1 + 0 + 5) is a multiple of 3.

Divide 105 by the factor we found in step 1 to get a smaller number.

Repeat steps 1 and 2 with the smaller number until we get a prime number.

Using this method, we can find the prime factorization of 105 as follows:

105 ÷ 3 = 35

35 ÷ 5 = 7

Since 7 is a prime number.

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Angle between two vectors calculator is a vector calculator tool for finding the angle between two vectors in 2D or 3D space.

The vector calculator is a tool that can be used to find the angle between two vectors in a 2D or 3D space. Given two vectors, the calculator uses a formula to determine the angle between them, which is expressed in degrees or radians.

                               θ = [tex]cos^-^1(\frac{a.b}{|a||b|})[/tex]

where,

a and b are the two vectors

θ is the angle between them

|a| and |b| are the vectors' respective magnitudes.

This calculator can be used for various applications in physics, engineering, and mathematics, where finding the angle is important.

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The diameter of a circle is equal to twice the radius of the circle and is measured across the circle through its centre. The diameter of a circle can be calculated using either the radius or the circumference of the circle.

To calculate the diameter using the circumference, you can use the formula:

Diameter = Circumference / π

where π (pi) is a mathematical constant approximately equal to 3.14159.

For example, if the circumference of a circle is 31.4 cm, then the diameter can be calculated as follows:

Diameter = Circumference / π

Diameter = 31.4 cm / 3.14159

Diameter = 10 cm (rounded to the nearest tenth)

To calculate the diameter using the radius, simply multiply the radius by 2. The formula is:

Diameter = 2 x Radius

For example, if the radius of a circle is 5 cm, then the diameter can be calculated as follows:

Diameter = 2 x Radius

Diameter = 2 x 5 cm

Diameter = 10 cm

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The length of ZY to the nearest 10th is 69.5 units.

What is the triangle?

A triangle is a closed figure made of 3 line segments.

It has 3 sides, 3 vertices and 3 angles.

The sum of two sides is always Greater than the third side.

The sum of all angles is 180°.

We can start by finding the measure of angle YXZ:

m∠YXZ = 180° - m∠Y - m∠X = 180° - 90° - 58° = 32°

Now we can use the tangent ratio to find ZY:

tan(32°) = ZY / XW

ZY = XW * tan(32°) = 120 * tan(32°) ≈ 69.5

Hence, the length of ZY to the nearest 10th is 69.5 units.

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Answer:459.9

Step-by-step explanation:

Answer:9√2

Step-by-step explanation:

you divide 1134 and 7 in square root and it equals sqrt(162)

Then you simplify by taking out numbers out of the square root.

To convert meter into miles we simply have to divide meter by 1609.34 so we have 1500 m as 0.9321 miles.

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 base unit of length is the metre (or metre; US spelling), which is denoted by the letter m.

first described in 1793 as a ten millionth of the distance between the equator and the North Pole, but was later redefined in 1799 to refer to a prototype metre bar (this bar was changed again in 1889).

The imperial unit system uses the symbol mi to designate the mile as a unit of length.

Although it was initially an English unit, it was adopted by numerous nations, each of which had a somewhat different definition. However, the English mile is 63,360 inches, 5280 feet, or 1760 yards.

Miles = meter x 0.000621

= 1500 x 0.000621

= 0.9321 miles

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There is each person holding the sign for 3/4 hours.

What is the rate?

A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The 4 members of a robotics team held a car wash to raise money. To attract customers, each person held a sign by the road for an equal portion of the car wash, which lasted 3 hours in all.

If the car wash lasted 3 hours in all and there are 4 members in the robotics team, each person held the sign for 3 hours / 4 = 3/4 hours.

Hence, there are each person held the sign for 3/4 hours.

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The two points that also lie on the circumference of the circle are approximately (-9.2, -12.5) and (11.8, -7.1).

The circumference of a circle is the distance around its outer edge, also known as its perimeter. It is a key measurement in geometry, and is defined as the product of the circle's diameter and pi (π), a mathematical constant approximately equal to 3.14.

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference, r is the radius of the circle, and π is the mathematical constant pi.

C = πd

The circumference of a circle is proportional to its radius or diameter, which means that if you double the radius or diameter of a circle, its circumference will also double. This relationship is fundamental to many mathematical and scientific applications, such as calculating the area or volume of a circle or sphere.

The circumference of a circle can be measured using a variety of tools, including rulers, compasses, and string. In practice, it is often measured indirectly by measuring the diameter or radius of the circle and using the formula above to calculate its circumference.

In summary, the circumference of a circle is the distance around its outer edge or perimeter, and is calculated using the formula C = 2πr or C = πd. It is a key measurement in geometry and has many practical applications in mathematics, science, and engineering.

To find two more points on the circumference of the circle, we can use the fact that the distance between the center of the circle and any point on its circumference is equal to the radius of the circle.

The radius of the circle can be found using the distance formula, which gives:

radius = sqrt((9-0)^2 + (-12-0)^2) = sqrt(225) = 15

So the circle has a radius of 15.

Now, to find two more points on the circumference, we can use the fact that any point on the circle can be represented as (r cos θ, r sin θ), where r is the radius of the circle and θ is the angle that the line connecting the point and the origin makes with the positive x-axis.

Since we already know one point on the circle, (9,-12), we can find the angle θ that this point makes with the positive x-axis by using the inverse tangent function:

θ = arctan(-12/9) = -53.13 degrees (or -0.93 radians)

Now we can find two more points on the circle by adding or subtracting multiples of 360 degrees (or 2π radians) to the angle θ and using the formula (r cos θ, r sin θ). For example:

Point (15 cos (-53.13), 15 sin (-53.13)) ≈ (-9.2, -12.5)

Point (15 cos (306.87), 15 sin (306.87)) ≈ (11.8, -7.1)

Therefore, the two points that also lie on the circumference of the circle are approximately (-9.2, -12.5) and (11.8, -7.1).

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The third term in the recursive sequence is 9

A recursive sequence is a sequence of numbers where each term is defined by a formula that uses one or more of the previous terms in the sequence. In other words, each term depends on the term(s) that come before it.

Since a₁ = 3 and  [tex]a_{k+1}[/tex]= 2a[tex]_{k}[/tex] - 1

a₂  = 2a₁ - 1  

a₂  = 2(3) - 1 = 6 - 1 = 5

a₃ = 2a₂ - 1  

a₃ = 2(5) - 1 = 10 - 1 = 9  

Thus, the third term in the recursive sequence will be 9

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Since one side of a regular hexagon is extended to create an exterior angle, the measure of such exterior angle is: C. 60.

In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Note: The given geometric figure (regular polygon) represents a hexagon and it has 6 sides.

Sum of interior angles = 180 × (6 - 2)

Sum of interior angles = 180 × 4

Sum of interior angles = 720°.

Each interior angle = 720/6 = 120°.

When the hexagon is extended create an exterior angle, its measure is given by;

x + 120 = 180°.

x = 180° - 120°

x = 60°.

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The conversion of the weight 46 Kg to pounds (lbs) is 46 Kg is = 101.42 lbs .

The Pound and Kilogram are both units of measurement for weight or mass ; the unit used for pound is lbs , and for Kilogram the unit used is Kg .

The weight to be converted is = 46 Kg ,

We have to convert this weight to pounds ;

The conversion factor to convert the weight from Kilogram to pounds is : 1 Kg = 2.20462 lbs ;

On multiplying the given weight by the conversion factor ;

We get ;

⇒ 46 Kg = 46 × 2.20462 lbs ;

⇒ 46 Kg = 101.41252 ≈ 101.42 lbs .

Therefore , the weight 46 Kg is approximately equal to 101.42 lbs  .

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The required coefficient of y in  [tex](3xy + 2)^4[/tex] is 96x.

The binomial expansion is a formula for expanding a binomial expression of the form [tex](a + b)^n\\[/tex], where "a" and "b" are constants and "n" is a positive integer. The expansion gives the coefficients of each term in the expansion.

Here,
We can use the binomial theorem to expand the expression,

[tex](3xy + 2)^4 = C(4,0) (3xy)^4 (2)^0 + C(4,1) (3xy)^3 (2)^1 + C(4,2) (3xy)^2 (2)^2 + C(4,3) (3xy)^1 (2)^3 + C(4,4) (3xy)^0 (2)^4[/tex]

where C(n,k) represents the number of combinations of k objects that can be chosen from a set of n objects.

The coefficient of y in the fourth term is given by the coefficient of ([tex]3xy)^1 (2)^3[/tex]. That is, we need to find the coefficient of y in the term:

[tex]C(4,3) (3xy)^1 (2)^3 = 4 * 3xy * 2^3 = 96xy[/tex]

Therefore, the coefficient of y in  [tex](3xy + 2)^4[/tex] is 96x.

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Answer:

About 16 years

Step-by-step explanation:

The formula for compound interest is

[tex]P(t)=P_{0}(1+r/n)^n^t[/tex], where P0 is the principal, r is the interest rate, n is the number of compounding periods, and t is the time in years.

For this problem, our n = 12 because there are 12 months in a single year and we must convert our percentage to a decimal (3.60/100 = 0.0360): [tex]7000=4000(1+0.0360/12)^1^2^t\\7000=4000(1.003)^1^2^t\\1.75=1.003^1^2^t\\log(1.75)=log(1.003)^1^2^t\\log(1.75)=12t*log(1.003)\\\frac{log(1.75)}{log(1.003)} =12t\\1/12*\frac{log(1.75)}{log(1.003)}=t\\ 15.56818868=16=t[/tex]

x - 2x + 4 = -x + 4

Simplification of the expression x - 2x + 4.

D. -x + 4

4x - 3 - 6x + 2 = -2x - 1

Simplification of the expression 4x - 3 - 6x + 2.

B. -2x - 1

-2(x + 4) = -2x - 8

Simplification of the expression -2(x + 4).

-2x - 8

(12x - 6) = 6(2x - 1)

Simplification of the expression 12x - 6.

N/A (This expression is not listed as one of the options.)

3(x + 2) + 4 = 3x + 10

Simplification of the expression 3(x + 2) + 4.

C. 3x + 10

What is simplification?

In mathematics, simplification refers to the process of reducing an expression to its most basic or compact form by combining like terms, factoring, and applying various rules and properties of arithmetic and algebra.

Simplification is often used to make an expression easier to understand, to solve an equation or system of equations, or to identify patterns or relationships in mathematical models.

The goal of simplification is to reduce an expression to its simplest and most concise form without changing the underlying meaning or value of the expression.

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The length of side {x} in simplest radical form with a rational denominator is 2√6.

According to the Pythagoras theorem, we can write -

        (hypotenuse)² = (base)² + (perpendicular)²

        (h)² = (b)² + (p)²

Given is the right - angled triangle.

We can write using the Pythagoras theorem as -

x² = √12² + √12²

x² = 12 + 12

x² = 24

x = √2 x 2 x 2 x 3

x = 2√6

Therefore, the length of side {x} in simplest radical form with a rational denominator is 2√6.

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A ) The balance would be approximately $5562.35 when the interest is compounded quarterly.

B) The balance would be approximately $5565.09 when the interest is compounded monthly.

Annual interest rate refers to the interest rate over a period of one year with the assumption that the interest is compounded every year.

a) If the interest is compounded quarterly, we can use the formula:

A = P(1 + r/n)^(n*t)

where

In this case, P = $5500, r = 0.01356 (1.356% as a decimal), n = 4 (since interest is compounded quarterly), and t = 1 (since we are calculating the balance after one year).

Substituting these values into the formula, we get:

A = $5500(1 + 0.01356/4)^(4*1) ≈ $5562.35

So the balance would be approximately $5562.35 when the interest is compounded quarterly.

b) If the interest is compounded monthly, we can use the same formula, but with n = 12 (since interest is compounded monthly):

A = $5500(1 + 0.01356/12)^(12*1) ≈ $5565.09

So the balance would be approximately $5565.09 when the interest is compounded monthly.

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The two dimensions that should follow the sequence, 12 in. 24 in. 8 in. 20 in.​, are 4 in. and 16 in.

A sequence is an ordered list of numbers that follow a specific pattern.

Related events or things that follow each other in an orderly form are described as sequences.

24 inches are 12 inches more than 12 inches (24 -12).

20 inches are 12 inches more than 8 inches (20 - 8).

16 inches are 12 inches more than 4 inches (16 - 4).

The common difference between the dimensions is 12 inches and the sequence reduces in value by 4 inches from the previous length and width to the next.

Thus, we can identify some patterns in any sequence, whether they are arithmetic, geometric, quadratic, or special sequences.

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Which two dimensions should follow this sequence?

The value of conversion from Celsius to Fahrenheit for the value 31 Celsius is equal to 87.8 Fahrenheit.

Standard measuring  units for the temperature is known as Celsius and  Fahrenheit.

Formula used to convert the temperature from Celsius to Fahrenheit is written as

°F = 9 /5 ( ° C ) + 32.

Convert 31 Celsius  to Fahrenheit by substituting the given value in the above formula :

= 9 /5 ( 31° ) + 32

= (1/5) (279° ) + 32

= 55.8°  + 32

= 87.8°F

Therefore, the values after conversion for the 31Celsius to Fahrenheit is given by 87.8 Fahrenheit.

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