What is the initial value of the function?

Answer: Law of Sines: When we divide side a by the sine of angle A

it is equal to side b divided by the sine of angle B. It's also equal to side c divided by the sine of angle C.

After solving, we check that [tex]x^2[/tex] - 1 cannot be the quotient of p(x).

In the given question, we have to check whether the quotient is [tex]x^2[/tex] - 1.

The given polynomial is [tex]x^6 + 2x^3[/tex] + x - 1 is divided by a polynomial in x of degree 5.

Given a polynomial p(x) and a non-zero polynomial g(x), the division algorithm asserts that there are polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).

5th degree polynomial because the power of the dividend should equal the degree of the product of the quotient and the divisor.

Degree 1 will result from the division of a degree of polynomial 6 by a degree of polynomials 5 and 6.

From the given question,

P(x) = [tex]x^6 + 2x^3[/tex] + x - 1

g(x) = x in degree of 5

q(x) = x² - 1

So,

[tex]x^6 + 2x^3[/tex] + x - 1 = (x in degree of 5)([tex]x^2[/tex] - 1) + r(x)

[tex]x^6 + 2x^3[/tex] + x - 1 = x in degree of 7

Hence, [tex]x^2[/tex] - 1 cannot be the quotient of p(x).

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The complete question is:

Can [tex]x^2[/tex] - 1 be the quotient on division of [tex]x^6 + 2x^3[/tex] + x - 1 by a polynomial in x of degree 5?

There are several methods for finding the solution to a system of equations, which include:

1. Graphing: This method involves plotting the equations on a coordinate plane and finding the point(s) of intersection. This method is useful when the system has a small number of variables and the equations are in the form of y = mx + b.

2. Substitution: This method involves solving one of the equations for one variable and then substituting that expression into the other equation. This method is useful when one equation is easier to solve than the other or when one equation is a simpler form than the other.

3. Elimination: This method involves adding or subtracting the equations to eliminate one of the variables. This method is useful when the variables are in similar forms and the coefficients are easy to add or subtract.

4. Matrix method: This method involves solving the system of equations in matrix form using matrix algebra techniques such as Gaussian elimination, Gauss-Jordan elimination and Cramer's rule. This method is useful when the system of equations have a large number of variables and when you want to solve system of equations in a more efficient and less time-consuming way.

5. Numerical methods: This method involves using numerical techniques such as Newton-Raphson method, Iterative methods to approximate the solution of a system of equations.

It is important to note that in some cases, a system may have no solution or infinitely many solutions. A system has no solution when the equations are inconsistent, meaning they cannot be true at the same time. A system has infinitely many solutions when the equations are dependent, meaning one equation can be derived from the other equation

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For math equation, To eliminate a variable, it must have the same coefficient. So if the coefficients of the variables are not the same then first equate the coefficients by multiplying or dividing them.

Determine the set of solutions to the following system of equations using the elimination method, if x and y are variables in the set of real numbers.

Completion:

1. x + y = 1 and x + 5y = 5

To eliminate the y variable, remember that the coefficients of y must be the same, so the equation x + y = 1 times 5 and the equation x + 5y = 5 times 1, then:

x + y = 1     │× 5 => 5x + 5y = 5

x + 5y = 5   │× 1 => x + 5y = 5

5x + 5y = 5

x + 5y = 5

--------------- –

4x + 0 = 0

x = 0

Same as step I, there is no need to equate the coefficients to eliminate variable x because the coefficients are the same, then:

x + y = 1

x + 5y = 5

--------------- –

0 + –4y = –4

y = 1

So, the solution set is {(0, 1)}.

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The steps to evaluate an exponential expression include:

First, you need to identify the base which is the number being raised to a power, and the exponent is the power to which the base is being raised. Then replace this base with the value that is needed to be used.

Use this exponent such that you can find out the number of times the base will multiply itself and then do the multiplication and simplify the expression.

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The sum of a partial series is calculated by Sn=∑ni=1ai=n(a1+an)2.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.

A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums.

When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.

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Answer: $ 108.42

Step-by-step explanation: Take 20% of the total.

The measure of angle B is 50 degrees and angle C is 80 degrees.

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°.

In the given triangle, we can use the concept of triangle angle sum to find the unknown measures.

We know that the sum of the angles in a triangle is always 180 degrees.

Therefore, if we know two angles in a triangle, we can find the third angle by subtracting the sum of those angles from 180.

We are given that angle A is 50 degrees. We are also given that angles B and C are unknown. Therefore,

we can use the following equation to find the measure of angles B and C:

A + B + C = 180

50 + B + C = 180

B + C = 180 - 50

B + C = 130

So the sum of angles B and C is 130 degrees. Therefore, we can't find individual measures of angles B and C.

Alternatively, we can use the property of the angle pair which states that if two parallel lines are intersected by a transversal, the alternate interior angles are congruent.

If we know that angle A and angle B are congruent, we can find the measure of angle B as 50 degrees. As a result, angle C will be 180 - 50 - B = 130-50 = 80 degrees.

Hence, the measure of angle B is 50 degrees and angle C is 80 degrees.

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Answer: 1/8

Step-by-step explanation:

Standard deviation is a measure of variation.

The degree of variance or dispersion in a set of data values is measured statistically using the standard deviation. It reveals how far the data values differ from the data set's average. Data points tend to be close to the mean when the standard deviation is low, and are dispersed over a larger range when the standard deviation is high.

While measurements of the centre, such as mean, median, and mode, are used to describe a data set's central tendency. The median is the midway value when a data set is ordered, and the mode is the value that appears in a data set the most frequently. The mean is the sum of the data divided by the number of observations.

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Answer: 76.92%

Step-by-step explanation:

To find the percent decrease is simple. First let's find the difference: 65 - 15 which gives you 50. 50/65 * 100 = 76.92%.  Have a good day ;)

The value of x is 13 if QS is a midsegment of PRT

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that QS is a midsegment of PRT

IF PT=x+67 and QS=x+27,

We need to find the value of x

From midsegment theorem we have

QS=1/2(PT)

x+27=1/2(x+67)

x+27=x/2+67/2

x-x/2=67/2-27

x/2=13/2

x=13

Hence, the value of x is 13 if QS is a midsegment of PRT

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The solution of equation 3x + 4y = -12 for y is y = -3 - 3/4 x.

In the given question, we have to solve 3x + 4y = -12 for y.

The given equation is 3x + 4y = -12.

To solve this equation for y, we have to isolate the y.

Now solving the given equation.

3x + 4y = -12

Subtract 3x on both side, we get

4y = -12 - 3x

Divide by 4 on both side, we get

y = [tex]\frac{1}{4}[/tex](-12 - 3x)

Now simplifying the expression.

y = -12/4 - 3/4 x

y = -3 - 3/4 x

Hence, the solution of equation 3x + 4y = -12 for y is y = -3 - 3/4 x.

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The complete question is:

How do you solve 3x + 4y = -12 for y?

The scenario is best represented by a discrete or continuous domain is

a. discrete

b. continuous

c. discrete

d. continuous

e. discrete

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The total sales for bicycles for store 1 and 2 = 54 bicycles.

Thee total cost for bicycles for store 1 and 2= $7,530

The total profit for bicycles for store 1 and 2= $12,420

The total sales for bicycles for store 1 and 2 can be calculated as thus;

Store 1 = 15+20 = 35

Store 2 = 10+9 = 19

Total sales for store 1 and 2 = 35+19 = 54

The total cost for bicycles for store 1 and 2=

Store 1 = 150×35= $5,250

Store 2 = 19× 120 = $2,280

The total cost for bicycles in both stores= $5,250+$2,280= $7,530.

The total profit for bicycles for store 1 and 2=

Store 1 = 230×35 = $8,050

Store 2 = 230×19 = $4,370

The total profit from both stores = $8,050+$4,370= $12,420.

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Stella must run between 248 minutes and 252 minutes in order to meet the requirement.

What is the time-to-minute conversion?

As an hour consists of 60 minutes, we can convert hours into minutes by multiplying hour by 60. So, for example, if one wants to convert 3 hours into minutes, one can do it by multiplying 3 by sixty which will give 3 x 60 = 180 minutes.

To figure out the range of times within which Stella must finish the marathon in order to meet the requirement of finishing within 2 minutes of the 4:10 pace time,

we can use the following steps:

Convert the pace time of 4:10 to minutes.

Since there are 60 minutes in an hour, 4:10 is equal to 4 * 60 + 10 = 250 minutes.

Add 2 minutes to the pace time. Since Stella must finish within 2 minutes of the pace time, this gives us a finish time of 250 + 2 = 252 minutes.

Subtract 2 minutes from the pace time. Since Stella must finish within 2 minutes of the pace time, this gives us a finish time of 250 - 2 = 248 minutes.

The range of times within which Stella must finish the marathon in order to meet the requirement is 248 to 252 minutes.

Hence, Stella must run between 248 minutes and 252 minutes in order to meet the requirement.

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16x - 4y = 12

4x - y = 3

4x = 3+y

x= 3+y/4

for y = 1

x= 3+1/4 = 1

y = 2

x=3+2/4 = 5/4 = 1.25

y = 3

x = 3+3/4 = 6/4 = 1.5

The average rate of change between 2006 and 2010 is 172.

Average rate is a statistical measure used to compare a set of values or quantities. It is calculated by taking the sum of the values, then dividing by the number of values in the set. Average rate is most often used to measure the average performance of a group, individual, or business over a certain period of time.

The average rate of change between 2006 and 2010 is calculated by taking the difference in the values of the function for the two given years and then dividing it by the difference in the two years.
In this case, the difference in the values of the function for 2006 and 2010 is 1725 - 1037 = 688. The difference in the two years is 2010 - 2006 = 4.
Thus, the average rate of change is 688/4 = 172.
Therefore, the average rate of change between 2006 and 2010 is 172.

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The vehicle with best mileage per gallon is Minivan vehicle .The maximum milage value is 19 miles/gallon.

We have, a table as present in above figure. The table contains 4-column and 3 rows. Column 1 is labeled different Vehicles, Column 2 is labeled Miles Traveled and Column 3 is labeled Gasoline Used (gallon). We have determine the vehicle gets the best mileage per gallon. Milage of a vehicle means how many distance vehicle going to run per quantity of fuel. In this cas milage of vehicle is miles going to run per gallons of fuel.

The formula to calculate gas mileage is

Milage = Miles Traveled/ Gasoline used (gal).

Now, we consider each row one by one.

Milage for Sedan = 630/35 = 18 miles/gallon

Milage for Minivan = 798/42 = 19 miles/gallon

Milage for Truck = 864/54 = 16 miles/gallon

Hence, the required vehicle is Minivan with milage of 19 miles/gallon.

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Complete question:

Which vehicle gets the best mileage per gallon? The above table complete the question. A 4-column table with 3 rows. Column 1 is labeled Vehicle with entries Sedan, Minivan, Truck. Column 2 is labeled Miles Traveled with entries 630, 798, 864. Column 3 is labeled Gasoline Used (gallon) with entries 35, 42, 54. Column 4 is labeled Unit Rate with entries 18, 19, 16.

Answer:3 symmetrical lines

Step-by-step explanation: just look in the middle and draw a line

The graphical technique is a strategy for resolving a set of linear equations by creating a graph. The following are the steps needed to solve a system of two linear equations graphically.

Get the two-variable linear equation system that is supplied.

Plot the first equation's graph on the same coordinate system as the second equation.

Plotting the graphs may result in the following three situations:

The presented system has a singular solution provided by the coordinates at the point of intersection if the line intersects at that place.

The system is consistent and contains an endless number of solutions if the lines coincide.

If the lines are parallel, the provided equation system is inconsistent, meaning it cannot be solved.

Consider two linear equations,

y = x - 1

y = 2x + 2

The equations should now be graphed in the coordinate plane.

The graph shows that the common point (-3, -4) where the two linear equations cross is the answer to the given system of linear equations.

As a result, we can solve linear equations graphically by plotting the graph on the coordinate system.

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Answer:

It is A im preety sure

Step-by-step explanation:

very sorry if im wrong but im almost possitive its A

The quadratic polynomial whose sum and the product of zeroes is x^2 - √2x + 1.

A degree two polynomial is a quadratic polynomial. The formula for a univariate quadratic polynomial is f(x)=a 2x2+a 1x+a 0. A quadratic equation is one that contains a quadratic polynomial. For the answers of any arbitrary quadratic problem, there is a closed-form solution known as the quadratic formula.

A quadratic polynomial's general formula is represented as f(x)=ax2 + bx + ca. A parabola is the name of the quadratic polynomial's curve. A quadratic polynomial is one that has the formula ax2 + bx + c, where a, b, and c are all real values and an is 0.

Only a few quadratic polynomials are amenable to the factorization technique. The quadratic polynomial formula, however, can be used for any quadratic problem.

In addition, the discriminant's value can be used to examine the characteristics of a quadratic polynomial's roots.

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The 4 lines of symmetry is square.

In math the imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.

Here we need to find the 4 lines of symmetry.

As we all know that the line of symmetry is known as  a balanced and proportionate similarity that is found in two halves of an object.

So, based on these definition, we have identified that A square has four lines of symmetry.

Because it can be folded in half over either diagonal or the horizontal segment which cuts the square in half or the vertical segment which cuts the square in half.

Therefore the square has four lines of symmetry.

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Answer:

AB + CD → AD + CB

Explanation:

The double-replacement reaction generally takes the form of AB + CD → AD + CB where A and C are positively-charged cations, while B and D are negatively-charged anions.

Answer:

p is the dependant variable and w is the dependent variable

Step-by-step explanation:

The number of plots is dependent because the number of plots doesnt change. The amount of wheat depends on the amount of plots you have.

Carl is correct the value of x by using the side splitter theorem is 6

[tex]\frac{6}{3} = \frac{12}{x}[/tex]

Required

Is Carl correct?

The side splitter theorem is a theorem that states that when a line passes through the two sides of a triangle and is parallel to the third remaining side, the line divides the two sides proportionally.

Using the side splitter theorem, the proportion is:

[tex]\frac{AB}{BC} = \frac{AE}{ED}\\[/tex]

This gives:

[tex]\frac{6}{3} = \frac{12}{x}[/tex]

This proportion is equivalent to Carl's.

Hence, Carl is correct.

Solving further: Cross Multiply

6 * x = 12 * 3

6x = 36

Make x the subject

[tex]x=\frac{36}{6}[/tex]

x =6

Carl is correct the value of x by using the side splitter theorem is 6

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The solution to the equation 1 h 5 2 h 5 is 7.

In this case option A is correct

The solution can be obtained by following steps-

We group like terms to get, we expand the brackets to get, this simplifies to, we now divide through by three to get,

[tex]h+ 2h= 16-5+ 10\\3h= 21\\h=7[/tex]

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What is the solution to the equation 1 h 5 2 h 5?.