What is called as factor of polynomial?

On solving the question of the polynomial The quotient = 3x+8 and remainder are  and 2 respectively.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

Polynomial long division is an extended variant of the well-known mathematical operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree. Due to the fact that it breaks down a more difficult division issue into simpler ones, it may be completed quickly by hand.

Dividing 3x^3 - 2X^2 + 2x - 1 by x-1

= 3x+8

The quotient = 3x+8 and remainder are  and 2 respectively.

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The Factor Theorem states that if a polynomial P(x) has a factor (x-a), then P(a) = 0. In other words, if x-a is a factor of the polynomial, then the value of the polynomial when x=a is equal to zero.

The factor theorem is a fundamental concept in algebra and polynomial functions. This can be useful for determining the roots of a polynomial equation.

Key points:

In summary, The Factor Theorem is a fundamental concept in Algebra and Polynomials, it helps us understand the relationship between the roots and the factors of a polynomial equation and how a root of a polynomial is related to the value of the polynomial evaluated at that point.

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The value of the variables x and y of the given transversal lines are;

x = 4/3 and y = 5/3

We see from the transverse lines that;

The horizontal line shows the line has been divided into two equal parts by the vertical transversal lines. Thus;

5x + 8 = 21x

Subtract 5x from both sides to get;

21x - 5x = 8

6x = 8

x = 8/6

x = 4/3

Similarly, the upper division will be equal and as such;

20y - 2 = 17y + 3

20y - 17y = 3 + 2

3y = 5

y = 5/3

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Answer: If the ratio of soccer balls to basketballs is 3:2, that means for every 3 soccer balls, there are 2 basketballs.

Let's say there are x soccer balls at the gym.

The ratio can be represented as 3x:2x

So the number of basketballs at the gym would be 2x.

So if you know the number of soccer balls at the gym, you can find the number of basketballs by multiplying the number of soccer balls by 2/3.

For example, if the gym has 18 soccer balls, the number of basketballs would be 2/3 * 18 = 12 basketballs

Step-by-step explanation:

Maybe one reason people who work in the pentagon never seem to agree on anything is that there are five sides to every story

The images of points A(x, y) = (- 2, 8), B(x, y) = (2, 4) and C(x, y) = (- 2, 6) are A'(x, y) = (4, - 1), B'(x, y) = (2, 0.5) and C'(x, y) = (4, 0), respectively.

In this problem we find three points: A(x, y) = (- 2, 8), B(x, y) = (2, 4) and C(x, y) = (- 2, 6), whose images must be determined by means of rigid transformations, that is, transformations that modify a points without any alteration on Euclidean distances.

The transformation rule of this question is a combination of reflection about x-axis, dilation, horizontal and vertical translations, all of them rigid transformations. Now we determine the image of each point:

Point A

A'(x, y) = (- 0.5 · (- 2) + 3, - 0.5 · 8 + 3)

A'(x, y) = (1 + 3, - 4 + 3)

A'(x, y) = (4, - 1)

Point B

B'(x, y) = (- 0.5 · 2 + 3, - 0.5 · 5 + 3)

B'(x, y) = (- 1 + 3, - 2.5 + 3)

B'(x, y) = (2, 0.5)

Point C

C'(x, y) = (- 0.5 · (- 2) + 3, - 0.5 · 6 + 3)

C'(x, y) = (1 + 3, - 3 + 3)

C'(x, y) = (4, 0)

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A relation could be a function or it could not. Since b. (6, 8) and d. (4, 3), the connection would no longer be a function.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

You can choose the components of combos in any order.

Permutations and combinations can be mixed up.

So, given is the ordered pair:

(x, y) = (1, 2); (2, 3); (4, 5); (6, 7); (12, 13)

All of the x-values in a relation must be distinct for it to be a function (i.e. no repetition)

The x values of choices (b) and (d) already exist in the ordered pair, namely (6,7) and (d), from the list of alternatives given (4,5)

Accordingly, (b) and (d) would prevent the relation from being a function.

Therefore, a relation could be a function or it could not. Since b. (6, 8) and d. (4, 3), the connection would no longer be a function.

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Correct question:

A bakery sells different packages of muffins. The number of muffins, x, and the price in dollars, y, of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.

{(1,2),(2,3),(4,5),(6,7),(12,13)}

The bakery is considering adding a new package of muffins. which ordered pairs would make the relation NOT a function? Choose all that are correct.

a. (10,13)

b. (6,8)

c. (8,12)

d. (4,3)

e. (24,18)

The equation of the line that passes through the point (10, -4) and has the slope -2/5 is y = 2/5 x

The slope, m of the linear function is given as -2/5.

The equation of the line that passes through point (10, -4) is calculated using the point slope formula which is given as:

x₁ = 10

y₁ = -4

m = -2/5

substituting in to the formula

(y - y₁) = m (x - x₁)

y + 4 = -2/5 (x - 10)

y + 4 = -2/5 x + 4

y = 2/5 x + 4 - 4

y = 2/5 x

The equation of the line is given as y = 2/5 x

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Hi !

[tex]A= \frac{b \times h}{2} = \frac{6 \times 8}{2} = 24m {}^{2} [/tex]

Have a nice day ;)

The area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².

What is circle ?

A circle is a two-dimensional geometric shape defined as the set of all points that are a fixed distance, called the radius, from a central point, called the center. A circle is the set of all points in a plane that are at a given distance from a given point, the center.

The area of a circle is given by the formula A = [tex]\pi r^{2}[/tex], where r is the radius of the circle. To find the area of a circle with a diameter of 5 m, we first need to find the radius. We can do this by dividing the diameter by 2:

r = 5 m / 2 = 2.5 m

Then we can substitute this value of r into the formula for the area of a circle:

A = [tex]\pi r^{2}[/tex] = π(2.5 m)^2 = 3.14 * 6.25 m^2 = 19.63 m²

So the area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².

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Answer:

The Area of a circle with a diameter of 5 m is 19.63 m² rounded to the Nearest tenth, it would be 19.6 m².  the answer is c. 19.6 m².

Step-by-step explanation:

good luck to you

The perpendicular bisector can be found by solving for the equation of the line and substituting the two points.

The perpendicular bisector of a line segment can be found by using the midpoint formula. The midpoint formula is used to find the midpoint of two points (x1,y1) and (x2,y2). The formula is:

Midpoint = (x1 + x2)/2, (y1 + y2)/2

Once the midpoint is found, the slope of the perpendicular line is found by using the negative reciprocal of the original line. The formula for the slope of the perpendicular line is y = -1/m * x + b, where m is the slope of the original line.

The equation of the perpendicular bisector is then found by substituting the slope and the midpoint into the equation of a line, y - y1 = m(x - x1).

Finally, the perpendicular bisector can be found by solving for the equation of the line and substituting the two points. The resulting equation is the equation of the perpendicular bisector.

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The unit rate of the diamond block is 9

The equivalent ratio of the unit rate of the diamond block is 9/1

A unit rate is the cost for only one of anything.

This is expressed as a ratio with a denominator of 1.

For instance, if you covered 60 meters in 10 seconds, you did so at an average speed of 6 meters per second.

Although both of the ratios 60 meters in 10 seconds and 6 meters in one second are rates, only the latter is a unit rate.

For the problem, 9 gems will craft a diamond block this means that

9 gems = 1 diamond block, hence for every diamond block 9 gems will be used

The unit rate is 9/1

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The time she has left to match the record is 16.11 seconds. The correct answer would be an option (B).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

To match Lisa's obstacle course record of 68.2 seconds, Julie needs to complete the course in 68.2 seconds.

We know that she has already spent 39.25 seconds on wall climbing and 12.84 seconds on the ropes.

So, the time she has left to match the record is:

68.2 - (39.25 + 12.84) = 68.2 - 52.09 = 16.11 seconds

In the above step, use the arithmetic operations to solve.

Hence, the answer is 16.11 seconds.

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Answer:

1) Yes

2) 2.07 hours/day

Step-by-step explanation:

1)

2.2 + 4 + 2 1/4 + 0 + 1.9 =

= 6.2 + 2.25 + 1.9

= 10.35

She danced a total of 10.35 hours, so she did meet her goal.

2)

10.35/5 = 2.07

She danced an average of 2.07 hours per day.

Answer: 5 1/3 - 3 2/3 = 1 2/3. 8 4/7 - 7 5/7 = 6/7. Yes its simplified and 100% correct.

Step-by-step explanation:

Answer:

independent

Step-by-step explanation:

A system of linear equations with exactly one solution is a _independent   system.

There are 7 ways for 345 to be written as the sum of an increasing sequence of two or more consecutive positive integers.

We need to find consecutive numbers (an arithmetic sequence that increases by 1) that sum to 345. This calls for the sum of an arithmetic sequence given that the first term is k, the last term is g, and with n elements, which is:

                                           n(k+g)/2.

There are 7 ways can 345 be written as the sum of an increasing sequence of two or more consecutive positive integers.

We look for sequences of n consecutive numbers starting at k and ending at k + n − 1. We can now substitute g with k+n- 1. Now we substitute our new value of g into n(k + g)/2 to get the sum i.e.

                                n(k+k+n-1)/2 = 345

This simplifies to n(2k+n-1)/2 = 345.

This gives a nice equation. We multiply out the 2 to get that n. (2k+n-1): =690. This leaves us with 2 integers that multiply to 690 which leads us to think of factors of 690.

We know the factors of 690 are:

1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690

So, through inspection (checking), we see that only 2, 3, 5, 6, 10, 15, and 23 work. This gives us the answer to 7 ways.

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Answer:

5x + y = 34

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x - 5y = 8 ( subtract x from both sides )

- 5y = - x + 8 ( divide through by - 5 )

y = [tex]\frac{1}{5}[/tex] x - [tex]\frac{8}{5}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{1}{5}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{5} }[/tex] = - 5 , then

y = - 5x + c ← is the partial equation

to find c substitute (5, 9 ) into the partial equation

9 = - 25 + c ⇒ c = 9 + 25 = 34

y = - 5x + 34 ← equation of perpendicular line in slope- intercept form

add 5x to both sides

5x + y = 34 ← equation in standard form

The ordered pair that is a solution to the inequality:

y > (1/4)*x + 5

is (4, 7)

Here we have the inequality:

y > (1/4)*x + 5

To check if an ordered pair is a solution, we just need to replace the values of the ordered pair on the inequality and see if it is true.

For example, for (12, 8)

We will get:

8 > (1/4)*12 + 5

8 > 3 + 5

8 > 8

This is false, so (12, 8) is not a solution.

The pair that is a solution is:

(4, 7)

7 > (1/4)*4 + 5

7 > 1  + 5

7 > 6

This is true.

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Based on the information, we can conclude that we have a 5% chance (probability) of getting 1 in this test of throwing the dice 50 times.

Taking into account the results of the graph, we can establish the probability of getting the number 1 in the 50 throws made. To do this, we must perform the following procedure:

In accordance with the above and based on the results of the test we can establish that we have a 5% probability of getting 1. This could be expressed as a 0.05 probability, in which 0 is not at all likely and 1 is very likely.

Note: This question is incomplete because there is some information missing. Here is the complete information:

Image attached

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Therefore , the solution of the given problem of combination comes out to be a) 45 and 10 b) 17 and 10

Combinations are mathematical procedures that count the number of possible configurations from a set of items, where the selection direction is immaterial. You can select any arrangement of the parts in any combination. It's possible to mix together combinations and permutations.

Here,

Given :

Total students = 25

a) The first state is represented by the first two-digit number in the random digits, which is 45.

The following random two-digit number, which does not represent a state, is 92.

The following two-digit number in the random sequence is 10, which stands for the first student's second state.

b) The second student's initial state is represented by the following two-digit number (17) from the random digits.

Ten symbolizes the second state for the second state and is the first two-digit number of the random digits.

Therefore , the solution of the given problem of combination comes out to be a) 45 and 10 b) 17 and 10

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So, here on solving the provided question, we can say that the New balance is as [tex]397.51[/tex]

A balance is the sum owing to an account in banking and accounting. The difference between the total debits and total credits posted to an account during an accounting period is referred to as a "balance" in accounting. The account will display a debit balance if the total of all debits exceeds the total of all credits.

Using the above data, first calculate the outstanding balance by using the formula below:

Previous balance-payments  is as  Unpaid balance

Unpaid balance is as [tex]95.85-45[/tex]

Unpaid balance is as [tex]50.85[/tex]

Finance charge is as [tex]50.85*1.5%[/tex]

Finance charge is as [tex]0.76[/tex]

New balance is as [tex]50.85+0.76+345.90[/tex]

New balance is as [tex]397.51[/tex]

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Answer:

1 cap costs 17 dollars

1 wallet is 11

Step-by-step explanation:

45 - 28 = 17

The difference between one wallet and a cap and two caps and a wallet is 17, therefore each cap is 17 dollars

28 - 17 = 11

I hope this helps have a good day (:

Answer:

x:b116.67

Step-by-step explanation:

120/100

140×100/120

There is no numbers provided, but this is how you solve it.

We can use the tangent function to solve for the height of the lighthouse.

Let h be the height of the lighthouse from the top of the cliff.

tan(angle of elevation from sea level to the top of the lighthouse) = (h+ height of lighthouse from sea level ) / distance from the base of the cliff

tan( angle of elevation from sea level to the top of the lighthouse) = (h+x) / distance from the base of the cliff

tan(angle of elevation from sea level to the base of the lighthouse) = (h) / distance from the base of the cliff

By dividing the first equation by the second equation

(h+x) / distance from the base of the cliff = tan( angle of elevation from sea level to the top of the lighthouse) / tan( angle of elevation from sea level to the base of the lighthouse)

(h+x) = (h) * (tan( angle of elevation from sea level to the top of the lighthouse) / tan( angle of elevation from sea level to the base of the lighthouse))

h = (x * tan( angle of elevation from sea level to the base of the lighthouse)) / ( tan( angle of elevation from sea level to the top of the lighthouse) - tan( angle of elevation from sea level to the base of the lighthouse))

After plugging in the values into the equation, we get:

h = (x * tan( )) / ( tan( ) - tan( ))

Round to the nearest tenth

h = (x * tan( )) /

Since 0 = 0 for any value of x, the system of equations has infinite solutions.

What is  infinite solution?

Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".

What is an infinite number?

There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.

                     The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.

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The 3 different types of solutions a 2 variable system can have are a unique solution, no solution and many solutions.

There are 3 types of systems of linear equations which are as follows:

Dependent: The system has infinitely many solutions. The graphs of these equations represent the same lines.

Example: [tex]\left \{ {{2x + 2y = 4} \atop {4x + 4y = 8}} \right.[/tex]

The system has infinitely many solutions.

Independent: The system has exactly one solution. The graphs of these equations intersect at a single point.

Example: [tex]\left \{ {{x + y = 5} \atop {x - y = -1}} \right.[/tex]

The only solution to the system is (2, 3)

Inconsistent: The system has no solution. The graphs of these equations are parallel lines.

Example: [tex]\left \{ {{x + 2y = 9} \atop {2x + 4y = 7}} \right.[/tex]

The system has no solution.

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Answer: 3k^2

Step-by-step explanation: