Contruct a polynomial function with the tated propertie. Reduce all fraction to lowet term. Third-degree, with zero of −3, −1, and 2, and pae through the point (0,-14)

An n x 11 matrix can have a maximum of n different eigenvalues, whereas a 2 x 2 matrix can only have a maximum of two. Below, there is a detailed explanation of this.

a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

The study of matrices is the main focus of the mathematical field known as matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics.

solution of a 2 x 2 matrix is in given form:

|A - λI| = 0

here,

A =  eigenvalue

I = identity matrix

now

|A - λI| = (a11 - λ)

(a22 - λ) - a12a21 = 0

the solutions of above equation are  2 x 2 matrix's eigenvalues.

just like this, a matrix of size n by n may have up to n different eigenvalues as its characteristic equation is a polynomial of nth degree with up to n roots (i.e. n eigenvalues). all due to the equation form: |A - I| = 0, where A is an eigen and I is an identity matrix.

by expanding the determinant:

|A - I| =  (-1)

having coefficients c1, c2,..., cn, having sum = zero.

which is nth degree polynomial equation consisting of n possible solutions, that are basically n x n matrix's eigenvalues .

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[tex](2x^2 + 5x + 7) + ( - 1,022 - 7x + 1)\\\\2x^2 + 5x + 7 - 1,022 - 7x + 1\\\\2x^2 + 5x + 7 - 1,022 - 7x + 1\\\\2x^2-2x-1,014[/tex]

In the given equation y = 3x + 12, x is the independent variable and y is the dependent variable.

A mathematical connection in which the values of one or more independent variables uniquely determine the values of a dependent variable.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equation is y = 3x + 12. Here in the equation, the value of the y variable is dependent on the value of x. Then the x variable is independent and the y variable is dependent and depends upon the x variable.

Therefore, in the given equation y = 3x + 12, x is the independent variable and y is the dependent variable.

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There were 14-floor seat tickets sold to their spring play.

A linear equation is defined as an equation in which the highest power of the variable is always one.

Let's assume x be floor seat tickets and y be balcony seats

As per the given formation, the equation would be as:

x + y = 800  ....(i)

110x + 8y = 7740 ...(ii)

Multiply by 8 into equation (i), and subtract into equation (ii),

110x + 8y - 8x - 8y = 7740 - 6400

102x = 1340

x = 1340/102

x = 13.7 ≈ 14

Therefore, there were 14-floor seat tickets sold.

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Answer:

A store has apples on sale for $21.00 for 6 pounds.if an apple approximately 5 ounces,how many apples can you buy for $168.00?  

you can buy approximately 256 apples

Step-by-step explanation:

Part 1 The cost per pound of the apples on sale is —3.50—-

Part 2 you can buy——48——pounds of apples for $168.00

Part 3 since 1 pound =16 ounces,so there are about __3__apples in each pound

Part 4 you can buy approximately—256— apples for $168.00

Answer:

1/14 xy (x² + 8y)

Step-by-step explanation:

common factor of the number = 1/14

common factor of letter part = xy

x³ : x = x²

y : y = 1

1/14 xy (x²

x : x = 1

y² : y = y

1/14 xy (x² + 8y)

The solution to the following system using substitution is (2,1).

What is system of equations ?
Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

[tex]$$\left[\begin{array}{c}y=-4 x+9 \\y=3 x-5\end{array}\right]$$[/tex]

Substitute y=3 x-5

[3 x-5=-4 x+9]

Isolate x for 3 x-5=-4 x+9: x=2

For y=3 x-5

Substitute x=2

[tex]y=3 \cdot 2-5[/tex]

Simplify

y=1

The solutions to the system of equations are:

y=1, x=2

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On solving the provided question, by substitution method we got that y=1.43 and x=o.65

To solve systems of linear equations, use the algebraic technique of substitution. The name of the technique implies that it involves substituting the values of variables from one equation into another.

x=cakes , y=donuts

3x+6y=$10.14 ------ eqt.1

4x+4y=$8.32 ------ eqt.2

solve eqt.1 for "y"

y=1.43

x=o.65

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The correct question is

Ellie and Mary went to the Stef bakery. Ellie bought 3 cakes and 6 filled donuts for ​$10.14. Mary bought 4 of each for ​$8.32. What is the price of each type The price of a  is The price

Answer:x=8

Step-by-step explanation:

3x/2-5=7

Move all terms not containing x to the right side of the equation by adding 5 to both sides

3x/2-5+5=7+5

3x/2=12

Multiply both sides of the equation by 2/3 to isolate x.

3x/2*2/3=12*2/3

x=24/3

x=8

Answer: x= 8

Step-by-step explanation:

3x/2-5=7

3x/2 = 12

3x = 24

x= 8

If you can, please give me a Brainliest, thank you!

Answer:

wednesday: 4

thursday: 32

Step-by-step explanation:

The speed of a cyclist rode 3.75 miles in 0.3 hours is 0.36 hours.

Given that, a cyclist rode 3.75 miles in 0.3 hours.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

A) We know that, speed =Distance/Time

Now, speed =3.75/0.3

= 12.5 miles per hour

B) Here, distance =4.5 miles and rate =12.5 miles per hour

Now, 12.5 =4.5/Time

⇒ Time =4.5/12.5

⇒ Time =0.36 hour

Therefore, the speed of a cyclist rode 3.75 miles in 0.3 hours is 0.36 hours.

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The smallest number of bags the groundskeeper must buy to cover the field is 165 bags.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr²

A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter. A store sells 50 pound bags of grass seed. One pound of grass seed covers about 400 square feet of field.

The smallest number of bags the groundskeeper must buy to cover the field.

Diameter of the field = 290 feet

Radius = 145 feet

Area of the circular field = πr²

= 3.14 ×145²

= 66018.5ft²

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As per the concept of compound interest, it take 62.915 years for the account to earn $7500

Compound interest:

The general formula to calculate the compound interest is written as,

A = P(1 + r/n)^nt

where

A = Accrued amount (principal + interest)

P = Principal amount

r = Annual nominal interest rate as a decimal

n = number of compounding periods per unit of time

t = time in decimal years;

Given,

Compounding frequency = Quarterly

Interest rate = 1.75%

Opening balance = $2500

Final amount = $7500

Now, we have to calculate the time time for the person to achieve the final amount,

First, convert R as a percent to r as a decimal

r = R/100

r = 1.75/100

r = 0.0175 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(7,500.00/2,500.00) / ( 4 × [ln(1 + 0.0175/4)] )

t = ln(7,500.00/2,500.00) / ( 4 × [ln(1 + 0.004375)] )

t = 62.915 years

Therefore, the  time required to get a total amount of $7,500.00 with compounded interest on a principal of $2,500.00 at an interest rate of 1.75% per year and compounded 4 times per year is 62.915 years.

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Answer:46 answers :)

Step-by-step explanation:

a) [tex]f(-4)[/tex] is equal to the output when [tex]x=-4[/tex]. Therefore, [tex]f(-4)=-7[/tex].

b) [tex]f(-3)=-11[/tex]

c) [tex]f(3)=-3[/tex]

d) [tex]f(4)=-1[/tex]

The equation of line is y = -2x - 8 and the slope is -2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = -2x - 8   be equation (1)

The equation is of the form y = mx + b where m is the slope and b is the y-intercept

Substituting the values in the equation , we get

The slope of the line m = -2

The y intercept of the line b = -8

Now , the graph of the linear equation is given below

Hence , the equation of line is y = -2x - 8

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Answer:

P ≈ 43.6 cm

Step-by-step explanation:

the perimeter (P) is the sum of the 2 radii and the arc

arc length = circumference of circle × fraction of circle

                 = 2πr × [tex]\frac{135}{360}[/tex]

                 = 2π × 10 × 0.375

                 = 20π × 0.375

                 ≈ 23.6 cm ( to 1 decimal place )

Then

P = 23.6 + 10 + 10 = 43.6 cm

The free throw accuracy of these players can be ranked from lowest to highest as Haller, Smith, Ballard, and Dennis.

What is a fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.

To rank the free throw accuracy of these players from lowest to highest, we need to compare the fraction of free throws made to the total number of free throws taken by each player.

The fraction of free throws made to the total number of free throws taken is called the free throw percentage.

The free throw percentage for each player can be calculated by dividing the number of free throws made by the number of free throws taken and expressing the result as a decimal.

For example, the free throw percentage for Smith can be calculated as follows:

Free throw percentage = 13/19 = 0.68

We can use this same method to calculate the free throw percentage for the other players:

Haller: Free throw percentage = 12/20 = 0.6

Dennis: Free throw percentage = 14/17 = 0.82

Ballard: Free throw percentage = 17/22 = 0.77

Based on these calculations, the free throw accuracy of these players can be ranked from lowest to highest as follows:

Haller: Free throw percentage = 0.6

Smith: Free throw percentage = 0.68

Ballard: Free throw percentage = 0.77

Dennis: Free throw percentage = 0.82

Hence, the free throw accuracy of these players can be ranked from lowest to highest as Haller, Smith, Ballard, and Dennis.

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Answer:

Step-by-step explanation:

The actual length of the explanation is 6 meters.

Probability is the possibility of happening an event.

Given that, the gold prospector panned for gold 1000 times and actually found 53 times of those times.

The probability that he will find the gold next time is:

53/1000

= 0.053

Hence, the probability that he will find the gold the next time he pans for gold is 0.053.

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S = 25x + 250 is the equation models the food truck's average sales in dollars, S, in terms of the price for taco, x.

Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws. also see equation system.

Given

A food truck vendor averages 150 tacos sold when the price per taco is $1.

A study shows that the average number of tacos sold will increase by 25

tacos for every $1 that the price per taco is lowered.

The calculation needed to determine which equation best represents the food truck's average sales in dollars, s, in terms of the price per taco, x, is as follows:

S = 25x + 250

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The system of equations to model this situation is given by;

x + y = 461

3x + 4y = 1624

The school sold 220 students tickets and 241 adult tickets.

let

Number of students tickets = x

Number of adults tickets = y

x + y = 461

3x + 4y = 1624

From (1)

x = 461 - y

Substitute into (2)

3x + 4y = 1624

3(461 - y) + 4y = 1624

1383 - 3y + 4y = 1624

- 3y + 4y = 1624 - 1383

y = 241

Substitute into (1)

x + y = 461

x + 241 = 461

x = 461 - 241

x = 220

In conclusion 220 students tickets and 241 adults tickets were sold.

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The correct option using linear equations is [tex]y\leq 2.85x[/tex].

What are linear equations?

A linear equation is one with variables of power 1, such as ax+b = 0, where x is the variable and a and b are fundamental values. Equations are claims that two mathematical expressions comprising one or more variables are equal. The term "linear equation" refers to an equation where the greatest power of the variable is one.

Since the budget is y, the total amount spent on fuel must be less than or equal to the budget. Since it is $2.85 per gallon, the correct equation would be [tex]y\leq 2.85x[/tex].

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490

472 <490<500

it fits the criteria

You can mail small things weighing 70 pounds or less to any location in the US for a set price using USPS Small Flat Rate boxes. The cost of a USPS Small Flat Rate package is only $8.45.

The United States Postal Service (USPS), often known as the Post Office, U.S. Mail, or Postal Service, is a separate executive branch agency that is in charge of delivering postal service across the United States, including its associated states and insular territories.

It is one of the few governmental organizations that the US Constitution expressly grants authority to. 516,636 career employees and 136,531 non-career employees work for the USPS as of 2021.

The first postmaster general of the United States Postal Service, Benjamin Franklin, was appointed in 1775 during the Second Continental Congress. He also held a comparable role for the colonies of the Kingdom of Great Britain.

With the passing of the Postal Service Act in 1792, the Post Office Department was established.

Hence, A USPS Small Flat Rate box only costs $8.45.

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Answer:

[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball &4\% & 17\%& 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&78\%&22\%& 100\%\\\cline{1-4}\end{array}[/tex]

Step-by-step explanation:

Create a blank frequency table:

[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & & &\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & &\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]

If 79% of the participants played pickleball, then 21% of the participants do not play pickleball.

Input these percentages into the table:

[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & & & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & & 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]

Of those who play pickleball, 6% are female.

Therefore, of those who play pickleball, 94% must be male.

The total percentage of those who play pickleball is 79%, so find 6% and 94% of 79%:

[tex]\begin{aligned}\textsf{Plays pickleball (female)}&=6\% \; \sf of \; 79\%\\&=0.06 \times 0.79\\&=0.0474\\&=5\%\; \sf (nearest\;percent)\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Plays pickleball (male)}&=94\% \; \sf of \; 79\%\\&=0.94 \times 0.79\\&=0.7426\\&=74\%\; \sf (nearest\;percent)\end{aligned}[/tex]

Input the found percentages into the table:

[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & & 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]

Of those who do not play pickleball, 21% are male.

Therefore, of those who do not play pickleball, 79% must be female.

The total percentage of those who do not play pickleball is 21%, so find 21% and 79% of 21%:

[tex]\begin{aligned}\textsf{Does not play pickleball (male)}&=21\% \; \sf of \; 21\%\\&=0.21 \times 0.21 \\&=0.0441\\&=4\%\; \sf (nearest\;percent)\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Does not play pickleball (female)}&=79\% \; \sf of \; 21\%\\&=0.79 \times 0.21\\&=0.1659\\&=17\%\; \sf (nearest\;percent)\end{aligned}[/tex]

Input the found percentages into the table and calculate the column totals:

[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball &4\% & 17\%& 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&78\%&22\%& 100\%\\\cline{1-4}\end{array}[/tex]

Answer:

c

Step-by-step explanation:

i took the test :)

Then the enrollment change rate from 2010 to 2020 is -52.2%.

Here ,

Formulate 860 - 1510 / 1510 based on the given condition.

We have calculate the difference or sum = -650/1245

By converting a fraction to a decimal we get, = -0.52208

we have to multiply a number by its numerator and denominator by 100,

We get,

= -0.52208*100/100

-52.208/100 is the product or quotient.

Hence ,

In 2010, a school had 1510 students enrolled. In 2020, there will be 860 students enrolled. Then the enrollment change rate from 2010 to 2020 is -52.2%.

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Answer: None of these

Step-by-step explanation:

The slope of the graph of [tex]f[/tex] is [tex]\frac{-224-64}{-2-1}=96[/tex].

Using point-slope form,

[tex]f(x)-64=96(x-1)\\\\f(x)-64=96x-96\\\\f(x)=96x-32[/tex]

Therefore, none of the options are correct. This can be confirmed by an online calculator.

Answer:

340

Step-by-step explanation:

550 - 210 = 340

The next time Maria will do both workouts on the same day is 15 days

Find the lowest common multiple (LCM) for both weight days and long-run days

3 = 3 , 6, 9, 12, 15, 18, 21

5 = 5, 10, 15, 20, 25, 30

The lowest common multiple (LCM) for both weight days and long-run days is 15

Therefore, Maria will do both workout again in 15 days time.

Complete question:

The chart shows Maria's workout schedule. Today she worked out with weights and then had a long run. When is the next time Maria will do both workouts on the same day? Weights every 3 days and long run every 5 days

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