Solve for x. Round to the nearest tenth of a degree, if necessary.

Answer:

Without a diagram or additional context, it's difficult to determine the values of x and y precisely. However, we can use the given information to set up some equations and solve for x and y in terms of each other.

First, since m is parallel to n, we know that angles 4 and 9 are alternate interior angles and angles 10 and 9 are corresponding angles. Therefore:

angle 4 = angle 9 (alternate interior angles)

angle 9 + angle 10 = 180 degrees (interior angles on the same side of the transversal)

angle 4 + angle 10 = 180 degrees (corresponding angles)

Substituting the given expressions for each angle, we have:

6x - 5 = 3y - 10

5x + 8 + 3y - 10 = 180

6x - 5 + 5x + 8 = 180

Simplifying the second equation by combining like terms, we get:

8x + 3y - 2 = 0

We can now solve for one variable in terms of the other. From the first equation, we have:

6x = 3y + 5

x = (3/2)y + (5/6)

Substituting this expression for x into the third equation, we get:

6((3/2)y + (5/6)) - 5 + 5((3/2)y + (5/6)) + 8 = 180

Simplifying and solving for y, we get:

y = 29/9

Substituting this value for y back into the expression we found for x, we get:

x = (3/2)(29/9) + (5/6) = 59/6

Therefore, the values of x and y that satisfy the given conditions are x = 59/6 and y = 29/9.

We can use a proportion to solve the problem:

Let x be the number of minutes it would take Mika to eat 35 hot dogs

Then we can set up the proportion:

21 hot dogs / 6 minutes = 35 hot dogs / x minutes

To solve for x, we can cross-multiply:

21 hot dogs * x minutes = 6 minutes * 35 hot dogs

21x = 210

x = 10

Therefore, it would take Mika 10 minutes to eat 35 hot dogs if she can keep up the same pace.

The coins take up approximately 35.259 cubic inches of space inside the treasure chest.

Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.

Solution:

The volume of each coin is a cylinder with radius 1.4 inches and height 0.0625 inches. The volume V of one coin is given by:

V = πr²h

= 3.14 x 1.4² x 0.0625

= 0.1533 cubic inches (rounded to four decimal places)

Since there are 230 coins in the treasure chest, the total volume of the coins is:

Total volume = 230 x V = 230 x 0.1533 = 35.259 cubic inches (rounded to three decimal places)

Therefore, the coins take up approximately 35.259 cubic inches of space inside the treasure chest.

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Therefore, it will take John 4 hours to catch up with Karabo.

In mathematics, an equation is a statement that shows the equality of two expressions. An equation usually contains one or more variables (represented by letters) and a mathematical expression on each side of an equals sign (=). The value of the variable(s) that make the equation true are called the solutions or roots of the equation. Equations are used in many areas of mathematics and science to describe relationships between variables or to solve problems. They are an important tool for modeling real-world phenomena and making predictions about how systems will behave under different conditions.

Here,

Let's call the time it takes for John to catch up with Karabo "t" (measured in hours).

In the hour that Karabo has been driving, she has covered a distance of:

distance = speed x time = 80 km/h x 1 h = 80 km

When John starts driving, he is behind Karabo by this distance. However, he is driving faster, so he will catch up to her eventually.

We can set up an equation to represent this situation:

distance covered by John = distance covered by Karabo

We know that John's distance is equal to his speed multiplied by the time he drives:

distance covered by John = 100 km/h x t

We also know that Karabo's distance is equal to the distance she covered in the hour before John started driving, plus the distance she covers during the time it takes John to catch up with her:

distance covered by Karabo = 80 km + 80 km/h x t

Now we can set these two expressions equal to each other and solve for t:

100 km/h x t = 80 km + 80 km/h x t

100 km/h x t - 80 km/h x t = 80 km

20 km/h x t = 80 km

t = 80 km / 20 km/h

t = 4 hours

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The number 100-x has a decreasing worth as x rises.

A mathematical statement is referred to as an expression or an algebraic expression if it contains numbers, factors, and a numerical operation between them..For example, the arithmetic sign + separates the terms 4m and 5 from of the variable m in the expression 4m + 5..

The number 100-x has a decreasing worth as x rises. This is due to the fact that the phrase 100-x denotes a linear equation with a -1 slope. This indicates that the expression's value drops by one for each unit rise in x. As a result, the expression's value decreases as x increases. For instance, if x is 50, the expression's value is 50; however, if x is 70, the expression's value is 30. The meaning of the equation decreases in proportion to how much x increases.

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Answer:

24 antelopes, 36 monkeys

Step-by-step explanation:

6 : 7 means that for every 6 antelopes, there are 7 monkeys, so

a/6 = m/7   (1)

where a is the number of antelopes, m is the number of monkeys (before the 8 were born).

After 8 monkeys are born, the new ratio becomes:

a/2 = (m+8)/3    (2)

You can solve a and m for these two equations:

Rewrite (1) as 7a = 6m (cross product)

Rewrite (2) as 3a = 2m+16  (cross product)

=> 2m = 3a-16 (isolate 2m)

=> 6m = 9a-48 (multiply by 3)

Plug in (2) into (1):

7a = 9a-48 =>

-2a = -48

a = 24 antelopes

m = (a/6)*7 = 28 monkeys BEFORE the 8 newborns, so now there are

24 antelopes and 28+8=36 monkeys

The value of the given trigonometric expression is -1.45.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

The given trigonometric expression is tan(-2π/3)/sin(7π/4) -sec(-π)

We know that, π=180°

tan(-2×180°/3)/sin(7×180°/4) -sec(-180°)

= tan(-2×60°)/sin(7×45°)-sec(-180°)

= tan(-120°)/sin315°-(-1)

= √3/(-√2/2)+1

= -2√3/√2 +1

= -√6+1

= -2.45+1

= -1.45

Therefore, the value of the given trigonometric expression is -1.45.

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The value of h is 18.

Polygons are closed figures which has at least three set of line segments joined together.

The polygon with least number of sides is triangle.

Given a polygon and all its interior angles are given.

Sum of the interior angles of a polygon is given by,

Sum = (n - 2) 180°, where n is the number of sides of the polygon.

Here, n = 7

6h + 132 + 146 + (6h + 10) + (6h + 10) + 146 + 132 = (7 - 2) 180

18h + 576 = 5 × 180

18h = 900 - 576

18h = 324

h = 18

Hence the value of h is 18.

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The possible range of y-values that form a solution to the inequality along with x=-4 is y<-12

The possible range of y-values that, along with x=-4, form a solution to the inequality 10x-3y>-4 can be found by isolating y on one side of the inequality. Here are the steps to do so:

1. Start with the given inequality: 10x-3y>-4
2. Plug in x=-4: 10(-4)-3y>-4
3. Simplify the left side of the inequality: -40-3y>-4
4. Add 40 to both sides of the inequality: -3y>36
5. Divide both sides of the inequality by -3 and reverse the inequality sign: y<-12

Therefore, the possible range of y-values that form a solution to the inequality along with x=-4 is y<-12. This means that any value of y that is less than -12 will satisfy the inequality when x=-4.

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Goldstar Bank will have $42,000 in excess reserves as a result of this deposit. These excess reserves can be used to make additional loans or investments.

When a customer makes a deposit in a bank, the bank is required to hold a certain percentage of that deposit as reserves. The reserve requirement is set by the central bank and is typically a percentage of the bank's total deposits.

In this case, the customer has deposited $50,000 into Goldstar Bank and the reserve requirement is 16 percent. This means that Goldstar Bank must hold 16 percent of the deposit as reserves and can loan out the remaining amount.

The amount of reserves that Goldstar Bank must hold is:

16% of $50,000 = 0.16 x $50,000 = $8,000

This means that Goldstar Bank can loan out:

$50,000 - $8,000 = $42,000

However, since the question asks for the number of excess reserves Goldstar Bank will have, we need to subtract the required reserves from the total reserves.

The total reserves after the deposit will be:

Required reserves = $8,000

Excess reserves = Total reserves - Required reserves = $50,000 - $8,000 = $42,000

Complete question:

Suppose that initially Goldstar Bank is completely "loaned up." A customer then deposits $50,000 into the bank. The reserve requirement is 16 percent.

1. What amount of excess reserves will Goldstar Bank now have as a result of this deposit?

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Isaiah's allοwance fοr the week wοuld be $43.75.

In mathematics, a fractiοn represents a part οf a whοle οr a ratiο between twο quantities. It is written as a number οr expressiοn (the numeratοr) abοve a line and anοther number οr expressiοn (the denοminatοr) belοw the line, and is typically expressed as a/b.

The numeratοr represents the number οf equal parts being cοnsidered, while the denοminatοr represents the tοtal number οf equal parts that make up the whοle. Fοr example, the fractiοn 3/4 represents three οut οf fοur equal parts, οr three-quarters οf the whοle.

Fractiοns can be used tο express values between whοle numbers, and they can be used in οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. Fractiοns can alsο be cοnverted tο decimals οr percentages fοr ease οf cοmparisοn οr calculatiοn.

Cοmmοn types οf fractiοns include prοper fractiοns (where the numeratοr is less than the denοminatοr, such as 1/2), imprοper fractiοns (where the numeratοr is greater than οr equal tο the denοminatοr, such as 5/3), and mixed numbers (where the fractiοn is represented as a whοle number and a prοper fractiοn, such as 3 1/2).

Isaiah's allοwance fοr the week can be calculated by adding up the amοunt he earned fοr each chοre he cοmpleted. Since he earned 1/8 οf his weekly allοwance fοr each chοre, the amοunt he earned fοr a single chοre can be calculated as:

1/8 * $70.00 = $8.75

Therefοre, if Isaiah cοmpleted n chοres in a week, his tοtal earnings fοr the week wοuld be:

Tοtal earnings = n * $8.75

Fοr example, if he cοmpleted 5 chοres in a week, his tοtal earnings wοuld be:

Tοtal earnings = 5 * $8.75 = $43.75

Sο Isaiah's allοwance fοr the week wοuld be $43.75 if he cοmpleted 5 chοres. The amοunt οf his allοwance wοuld depend οn the number οf chοres he cοmpleted during the week.

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The frequency of each interval is:

81-100: 2

61-80: 2

1-20: 1

21-40: 1

41-60: 2

What is frequency interval?

Frequency refers to the number of times a particular value or event occurs within a given dataset or sample. In statistics, frequency is used to describe the distribution of values in a dataset, and it is often represented as a frequency table or histogram.

Frequency is often used in conjunction with other statistical measures such as mean, median, and mode to describe the central tendency and variability of a dataset. By analyzing the frequency of values within a dataset, we can identify patterns and trends, and make inferences about the population from which the sample was drawn.

According to the question:
Using the given intervals, we can count the frequency of each interval as follows

81-100: 2 (81, 97)

61-80: 2 (65, 44)

1-20: 1 (2)

21-40: 1 (24)

41-60: 2 (25, 38)

Total: 8

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The total money Eva would have to pay for parking if she left her car in the lot for 5 hours is $32.

Eva would have to pay (12 + 4t) if she left her car in the lot for t hours.

Automatic fee = $12

Additional fee per hour = $4

Total fee paid = y

Number of hours = t

y = 12 + 4t

When t = 5 hours

y = 12 + 4t

= 12 + 4(5)

= 12 + 20

y = 32

Therefore, the total money Eva would have to pay for 5 and t hours is $32 and (12 + 4t) respectively.

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The Lowest Common Factor (LCF) and Highest Common Factor (HCF) are concepts used in mathematics to find the factors that are common to two or more numbers.

The LCF is the smallest factor that two or more numbers have in common, while the HCF is the largest factor that two or more numbers have in common.

For example, consider the numbers 12 and 18--

The factors of 12 are 1, 2, 3, 4, 6, and 12.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The common factors of 12 and 18 are 1, 2, 3, and 6.

Therefore, the LCF of 12 and 18 is 6, and the HCF of 12 and 18 is 3.

Note that the LCF and HCF are also called the Lowest Common Denominator (LCD) and Highest Common Factor (HCF) respectively.

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Step-by-step explanation:

To find the area of the rose garden, we need to find the sum of the areas of the rectangle and the semicircle.

Area of rectangle = length x width = 22 ft x 14 ft = 308 sq ft

Area of semicircle = (1/2) x pi x radius^2, where radius = diameter/2

The diameter of the semicircle is the width of the rectangle, which is 14 ft. So the radius is 7 ft.

Area of semicircle = (1/2) x 3.14 x 7^2 = 3.14 x 24.5 = 77.03 sq ft

Total area of rose garden = area of rectangle + area of semicircle

= 308 sq ft + 77.03 sq ft

= 385.03 sq ft

Therefore, the area of the rose garden is 385.03 square feet.

The simplified form of the rational expression is given as follows:

[(x - 5)/(x² - 3x - 10)] x [(x + 2)/(x² + x - 12)] = 1/[(x + 4)(x - 3)]

The rational expression for this problem is defined as follows:

[(x - 5)/(x² - 3x - 10)] x [(x + 2)/(x² + x - 12)].

To simplify the rational expression, first we must factor the quadratic equations at the denominator of each of the fractions, hence:

The simplification of the first quadratic function, x² - 3x - 10 = (x - 5)(x + 2), means that the numerators of each of the fractions can be simplified.

As the numerators of each of the fractions are simplified along with x² - 3x - 10, the remaining part is x² + x - 12, hence the simplified expression is given as follows:

[(x - 5)/(x² - 3x - 10)] x [(x + 2)/(x² + x - 12)] = 1/[(x + 4)(x - 3)]

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The coordinates of v with respect to the basis β are (cos(1), sin(1)).

The coordinates of a vector with respect to a given basis can be found by expressing the vector as a linear combination of the basis vectors and finding the coefficients of the linear combination. These coefficients are the coordinates of the vector with respect to the given basis.

(i) In the first case, we have V=R2, β={(1,1),(1,−1)}, and v=(1,2). We can express v as a linear combination of the basis vectors as follows:
v = a(1,1) + b(1,-1) = (a+b, a-b)
Equating the coordinates, we get:
a+b = 1
a-b = 2
Solving for a and b, we get a=3/2 and b=-1/2. Therefore, the coordinates of v with respect to the basis β are (3/2, -1/2).

(ii) In the second case, we have V=P2(R), β={1,1+x,1+x+x2}, and v=(x+1)2. We can express v as a linear combination of the basis vectors as follows:
v = a(1) + b(1+x) + c(1+x+x2) = a + (b+c)x + cx2
Equating the coefficients, we get:
a = 1
b+c = 2
c = 1
Solving for a, b, and c, we get a=1, b=1, and c=1. Therefore, the coordinates of v with respect to the basis β are (1, 1, 1).

(iii) In the third case, we have V=span{sin(x),cos(x)}, β={sin(x),cos(x)}, and v=sin(x+1). Using the trigonometric identity sin(x+1) = sin(x)cos(1) + cos(x)sin(1), we can express v as a linear combination of the basis vectors as follows:
v = a(sin(x)) + b(cos(x)) = (a)sin(x) + (b)cos(x)
Equating the coefficients, we get:
a = cos(1)
b = sin(1)
Therefore, the coordinates of v with respect to the basis β are (cos(1), sin(1)).

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In the molecule of phosphorus pentachloride:

In geometry, a plane is a flat, two-dimensional surface that extends infinitely in all directions. It can be thought of as a completely flat and level surface, like a tabletop or a sheet of paper.

Collinear points, on the other hand, are points that lie on the same straight line. If three or more points are collinear, they can be connected by a straight line, and the line they lie on is sometimes called a "collinear line".

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A(n) = 3 + 7(n-1)

Arithmetic sequences have common differences and change by the same amount between each term.

Arithmetic Sequences

Arithmetic sequences change by the same amount each term. In the sequence above, each term increases by 7. This means that 7 is added to the previous term to make the new term. Using this information we can write a function to represent this sequence.

Explicit Rule

The function that describes an arithmetic sequence is known as an explicit rule. Explicit rules are written as A(n) = A(1) + d(n-1). In this equation, A(1) represents the first term in a sequence and d represents the common difference. As you can see, the first term is 3, so A(1) = 3. The common difference is the change between terms. The previous paragraph shows that the common difference for this sequence is 7.

This means the explicit rule for this sequence is A(n) = 3 + 7(n-1).

Answer:

The answer to your problem is, B: It becomes less dense and rises to the surface

Step-by-step explanation:

Remember a conveyor belt is a system of oceans which can transports water and propel deep currents of water bodies across the world based on the differences in water densities.

The ocean water moves from the Antarctica to the equator the cold ocean water mixes within the warm ocean water at the equator or the middle, which makes the water less dense and rises up to the surface

Thus the answer to our problem is, B It becomes less dense and rises to the surface.

Answer:

A. The quantities that change in this problem situation are the number of books Ben orders and the total cost. The quantities that remain constant are the cost per book ($12) and the shipping and handling charge per order ($5).

The independent variable is the number of books Ben orders, as this is the variable that Ben has control over and chooses to change. The dependent variable is the total cost, as it depends on the number of books Ben orders.

B.
(imagine this as a chart)

Number of books                                                                            Total cost

1                                                                                                               $17

2                                                                                                              $29

3                                                                                                               $41

5                                                                                                              $65

10                                                                                                             $125

----------------------------------------------------------------------------------------------------------

To create this table, we used the formula:

Total cost = (Cost per book x Number of books) + Shipping and handling charge

For example, when Ben orders 3 books, the total cost is:

Total cost = ($12 x 3) + $5 = $41

Similarly, when Ben spends $65, the number of books he can order is:

Number of books = (Total cost - Shipping and handling charge) / Cost per book

Number of books = ($65 - $5) / $12 = 5

And so on for the other values in the table.

Answer:

See below

Step-by-step explanation:

Let x be he cost per book and y be the total cost including shipping and handling.

The relevant equation is

y = 12x + 5

A. Variables are number of books ordered(x) and total cost(y)
The constant is the shipping and handling cost

Since the total cost depends on the number of books ordered, the independent variable x = number of books

The total cost y is the dependent variable

--------------------------------------------------------------------------------------

B. Cost of 1 or 2 books can be found by plugging in x = 1 and x =2 into the equations and solving for y
Total Cost of 1 book = 12(1) + 5 = $17
Total cost of 2 books = 12(2) + 5 = 24 + 5 = $29

To compute the number of books that can be ordered for different total cost amounts is obtained by substituting for y and solving for x

For $41:
41 = 12x + 5
41 - 5 = 12x

36 = 12z

x = 36/12 = 3 books

For $65:
65 = 12x + 5
65 - 5 = 12x
60 = 12x
x = 60/12 = 5 books

For $125:

125 = 12x + 5
125 - 5 = 12x
120 = 12x
x = 120/12 = 10 books

Here is the table

Number                            Total Cost(y)
of books (x)                    

          1                                  $17

          2                                 $29

          3                                  $41

          5                                  $65

          10                                 $125

The equation is now in the form y=mx+b, where m is 2 and b is -4. The second equation is now in the form y=mx+b, where m is -0.5 and b is -2.

An equation is an expression that shows the relationship between two or more variables. It is made up of mathematical symbols and operators and is used to solve problems. Equations can be used to express a variety of relationships, such as addition, subtraction, multiplication, division, and more complex equations. They also help to identify patterns or trends in data or to forecast future values.

To change these equations into y=mx+b form, we must first rearrange the equations.

For the first equation, 2x-4=8, we can move the 4 to the other side of the equation, giving us 2x = 12. We can then divide both sides by 2, giving us x = 6. So the equation is now in the form y=mx+b, where m is 2 and b is -4.

For the second equation, -2x+4y=-8, we can move the -2x to the other side of the equation, giving us 4y=-8-2x. We can divide both sides by 4, giving us y=-2-0.5x. So the equation is now in the form y=mx+b, where m is -0.5 and b is -2.

Now that both equations are in y=mx+b form, we need to compare their m and b values to determine if there is one solution, no solution or infinite solutions. We can see that m for both equations is different, so this means that the two equations are not the same, and there is no solution. This means that the two equations have no solution.

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Answer: A

Step-by-step explanation:
To form a triangle, the two smaller lengths must be bigger than the largest side(Hopotonuse or sum, cant spell)

8 + 7 = 15
15>14

The possible lengths to complete a triangle with side lengths of 14 in. and 8 in. are  6 < x < 22.

The triangle inequality theorem states that for any given triangle, the total of the two sides is always greater than the sum of the three sides. The Triangle is a polygon with three line segments as its boundaries. That is the tiniest polygon imaginable.

We have side lengths of 14 in. and 8 in.

Using Triangle inequality we know that the sum of two is greater than the third side.

Also, the range for third side is

14 + 8 = 22 inch

14 - 8 =  6 inch

So, the third side lies between as 6 < x < 22.

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The solution is, after paying the agent commission, Brian will get 155.605265 pounds.

And, the percentage increase in the price 7.9%

the car travel in 2 hours 45 minutes is 291.5 km.

Currency conversion can be stated as the process of converting one currency into another currency. This is usually done in order to make transactions or investments in another country or to keep track of the value of assets held in different currencies.

here, we have,

we know.

The value of one currency is generally expressed in terms of another currency using exchange rates, which means  the value of one currency in terms of another currency at a specific point in time.

We know that, exchange rate can fluctuate over time, and currency conversion can be done manually or through various financial services or tools.

we have,

To calculate that how many pounds Brian will get for R2 100,

At first we need to calculate the amount of commission he will have to pay to the agent.

Commission = 1.5% of R2 100

Commission = 0.015 x R2 100

Commission = R31.50

Now we can calculate how much money Brian will have left after paying the commission:

Amount left after commission = R2 100 - R31.50

Amount left after commission = R2 068.50

Next, we can use the exchange rate given to convert Rands to Pounds:

1 Rand = 0.075199 Pounds

Therefore, to find out how many Pounds Brian will get for R2 068.50, we can multiply R2 068.50 by the exchange rate:

2 068.50 x 0.075199 = 155.605265 pounds

Next Part:

The price of petrol is increased from R12, 58 per litre to R13, 28 per litre.

i.e. increase of price = 100

so, the percentage increase in the price = 100 * 100/1258

                                                                   =7.9%

Next Part:

A motor car drives at an average speed of 106 km/h.

the car travel in 2 hours 45 minutes = 106* 165 / 60

                                                           =291.5 km

So The solution is, after paying the agent commission, Brian will get 155.605265 pounds.

And, the percentage increase in the price 7.9%

the car travel in 2 hours 45 minutes is 291.5 km.

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Answer:

I need a graph to answer this question

Step-by-step explanation:

The polynomial equation is solved and the value of A is given by the long division A = 3x³ + 6x² + 4x - 3 - 5/( x -2 )

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the polynomial equation be represented as A

Now , let the first equation be p

p = 3x⁴ - 8x² - 11x + 1

Let the second equation be q

q = ( x - 2 )

And , the value of A = p/q

On simplifying , we get

A = ( 3x⁴ - 8x² - 11x + 1 ) / ( x - 2 )

From the long division of polynomials , we get

Step 1 :

A = 3x³ + [ ( 6x³ - 8x² - 11x + 1 ) / ( x - 2 ) ]

The student went wrong while multiplying the quotient 3x³ with the divisor -2 , it should have been 6x³ instead of 6x²

Step 2 :

A = 3x³ + 6x² + [ ( 4x² - 11x + 1 ) / ( x - 2 ) ]

Step 3 :

A = 3x³ + 6x² + 4x + [ ( -3x + 1 ) / ( x - 2 ) ]

Step 4 :

A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

Therefor , the long division is solved , A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

Hence , the polynomial is A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

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The expression [tex]i^{8}+i^{9}+i^{10}+i^{11}[/tex] is equivalent to 0 + i - 1 - i, which simplifies to -1.

Using the property of imaginary unit i, we know that [tex]i^2=-1[/tex]. Therefore, i^8 can be written as [tex](i^2)^4[/tex] which is equal to[tex]1^4 = 1[/tex]. Similarly, i^9 can be written as i^8i which is equivalent to i, i^10 can be written as [tex]i^8i^2[/tex] which simplifies to -1, and i^11 can be written as i^8*i^3 which simplifies to -i. Thus, [tex]i^{8}+i^{9}+i^{10}+i^{11}[/tex] can be simplified to 1 + i - 1 - i, which equals 0 - 0i. Finally, 0 - 0i can be expressed as -1 + 0i, which means that the expression is equivalent to -1.

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The meaning of each of the labelled digits as required to be determined in the task content are;

As evident from the task content; it so required that the numbers as labelled to be identified in terms of what they represent.

Recall; mixed numbers result from the evaluation of improper fractions.

Hence, given the mixed number; 2 ⅓.

The number 2 which is whole is; the quotient.

The number 3 which is the denominator is the divisor.

The number 1 which is the numerator is the remainder.

Complete question; The number is 2⅓.

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Using single variable equation, we can conclude that Camilla received 11 likes and Kennedy received 16 likes.

Let x be the number of likes Camilla received and x+5 be the number of likes Kennedy received. We can set up an equation to solve for x:

x + (x+5) = 27

Simplifying the equation:

2x + 5 = 27

Subtracting 5 from both sides:

2x = 22

Dividing both sides by 2:

x = 11

So Camilla received 11 likes and Kennedy received 11+5=16 likes.

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The arclength of the circular sector with radius r = 5.1 and central angle θ = 145º is 13.06. The area of the circular sector is 32.54.

The arclength and area of a circular sector can be calculated using the following formulas:

Arclength = (θ/360) * 2πr

Area = (θ/360) * πr²

Where θ is the central angle in degrees, r is the radius, and π is the constant pi.

Plugging in the given values for r and θ, we get:

Arclength = (145/360) * 2π(5.1) ≈ 12.90

Area = (145/360) * π(5.1)² ≈ 32.91

So, the arclength of the circular sector is approximately 12.90 units and the area is approximately 32.91 square units.

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