write the matrix of the quadratic form q(x)=−3x21 3x22 9x23 3x1x2−9x1x3 3x2x3.

Answers

Answer 1

The matrix whose quadratic form is q(x)=−3x21 3x22 9x23 3x1x2−9x1x3 3x2x3 is Q = [ -3, 3,  -9/2 ]

                     [ 3, 3,  3/2    ]

                    [ -9/2,  3/2,  9 ]

The matrix of a quadratic form is a symmetric matrix that encodes the coefficients of the quadratic terms of the form. To obtain the matrix of the given quadratic form q(x), we need to identify the quadratic terms and their coefficients and then arrange them in a matrix.

The quadratic terms in q(x) are:

-3x1^2, 3x2^2, 9x3^2, 3x1x2, -9x1x3, 3x2x3

To obtain the matrix, we write the coefficients of each term in the corresponding entry of the matrix, taking care to ensure that the matrix is symmetric. Therefore, the matrix of q(x) is:

Q = [ -3, 3,  -9/2 ]

      [ 3, 3,  3/2 ]

     [ -9/2,  3/2,  9 ]

where the (i,j) entry of the matrix is the coefficient of the quadratic term involving xi and xj. We can verify that this matrix is symmetric, which is a necessary condition for it to be the matrix of a quadratic form.

In summary, the matrix of the given quadratic form q(x) is Q = [-3 3 -9/2; 3 3 3/2; -9/2 3/2 9].

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Related Questions

is 15.5 a rational number​

Answers

Answer:

yes!

Step-by-step explanation:

a rational number is a number that you can get by a fraction, like in this case 31/2

Answer:

Yes.

Step-by-step explanation:

15.5 is a rational number, because it can be expressed as a fraction.

15 1/2

= 31/2

Find the area of the semicircle.​

Find the area of the semicircle.

Answers

Answer:

39.25 centimeters squared is the area of the semicircle

g(6) + f(4)
I need help with this ASAP can you pls help me

Answers

Answer:

2(3g+2f)

Step-by-step explanation:

g(6) + f(4)

rewrite 4 as 2 . 2

rewrite 6 as 3 . 2

3 . 2g + 2 . 2f

factor out the common term 2

= 2(3g+2f)

how can we use models to estimate percent questions? Give examples to support your answer.

Answers

Answer:

Percent questions can be estimated using models by dividing the given number by the total number of parts in the model. For example, if there are ten students in a classroom and 30 candy bars, then each student would get three candy bars. Another example would be if there are ten students in a classroom and 30 candy bars, and one student takes five candy bars, then the remaining nine students would get two candy bars each.

Answer:

Percent questions can be estimated using models by dividing the given number by the total number of parts in the model. For example, if there are ten students in a classroom and 30 candy bars, then each student would get three candy bars. Another example would be if there are ten students in a classroom and 30 candy bars, and one student takes five candy bars, then the remaining nine students would get two candy bars eac

Step-by-step explanation:

consider an example with 100 students where 20 are taking discrete math, 30 are taking java, 25 are taking web design, 6 are taking discrete math and java, 8 are taking discrete math and web design, 10 are taking java and web design and 5 are taking all three classes. how many students are not taking any of these three classes?

Answers

There are 44 students taking discrete math and web design any of the three classes.

To determine the number of students taking any of the three classes (discrete math, Java, and web design), to subtract the total number of students taking at least one of the classes from the total number of students.

Let's calculate it step by step:

Total number of students = 100

Number of students taking discrete math (D) = 20

Number of students taking Java (J) = 30

Number of students taking web design (W) = 25

Number of students taking both discrete math and Java (D ∩ J) = 6

Number of students taking both discrete math and web design (D ∩ W) = 8

Number of students taking both Java and web design (J ∩ W) = 10

Number of students taking all three classes (D ∩ J ∩ W) = 5

Now, let's calculate the number of students taking :

Total number of students taking at least one class = (D) + (J) + (W) - (D ∩ J) - (D ∩ W) - (J ∩ W) + (D ∩ J ∩ W)

= 20 + 30 + 25 - 6 - 8 - 10 + 5

= 56

Finally, to find the number of students not taking any of the three classes:

Number of students not taking any class = Total number of students - Total number of students taking

= 100 - 56

= 44

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\( 350 \mathrm{y} \) C P sas \( \cos u \)

Answers

The given expression, \(\(350y \cdot C \cdot \cos(u)\)\), involves variables \(\(y\), \(C\)\), and \(\(u\)\) and their respective operations and functions.

The expression \(\(350y \cdot C \cdot \cos(u)\)\) represents a mathematical equation involving multiplication and the cosine function. Let's break down each component:

1. \(\(350y\)\) represents the product of the constant value 350 and the variable \(y\).

2. \(\(C\)\) is a separate variable that is being multiplied by \(\(350y\)\).

3. \(\(\cos(u)\)\) represents the cosine of the variable \(\(u\)\).

The overall expression represents the product of these three terms: \(\(350y \cdot C \cdot \cos(u)\)\).

To evaluate this expression or derive any specific meaning from it, the values of the variables \(\(y\), \(C\)\), and \(\(u\)\) need to be known or assigned. Without specific values or context, it is not possible to provide a numerical or simplified result for the given expression.

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Triangle XYZ has coordinates X(2, 4), Y(−3, 4), and Z(−3, 1). If the triangle is translated using the rule (x, y) → (x − 2, y + 1), what are the coordinates of Y'?

Y'(–5, 5)
Y'(0, 5)
Y'(–5, 2)
Y'(–1, 3)

Answers

Answer:

Y'(-5, 5)

Step-by-step explanation:

To find the coordinates of Y' after the translation, we apply the given rule to the coordinates of point Y(-3, 4).

Using the translation rule (x, y) → (x - 2, y + 1), we can substitute the coordinates of Y(-3, 4) into the rule:

x' = x - 2 = -3 - 2 = -5

y' = y + 1 = 4 + 1 = 5

Therefore, the coordinates of Y' are (-5, 5).

When subtracting two polynomials how does subtraction impact each monomial in the second polynomial?

Answers

Answer:

The signs of each monomial in the second polynomial are changed.

When subtracting two polynomials, the subtraction affects each monomial in the second polynomial by inverting the sign of each coefficient. That is, every coefficient in the second polynomial is multiplied by -1.

Polynomials are mathematical expressions that contain one or more terms. These terms are made up of coefficients and variables raised to powers, like x^2, y, or z^3.

When subtracting two polynomials, we need to keep in mind that each term within the polynomial is affected.

Example: Consider the following polynomial:

2x^2 + 3xy + 4y^2

When we subtract the polynomial 3x^2 - 2xy - 5y^2 from the above polynomial, we need to invert the sign of each coefficient in the second polynomial. That is, we have:

2x^2 + 3xy + 4y^2 - (3x^2 - 2xy - 5y^2)

Now, inverting the sign of each coefficient in the second polynomial, we get:

-3x^2 + 2xy + 5y^2

So the final result is:

2x^2 + 3xy + 4y^2 - (3x^2 - 2xy - 5y^2)

= 2x^2 + 3xy + 4y^2 - 3x^2 + 2xy + 5y^2

= -x^2 + 5xy + 9y^2

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The scatterplot below shows the relationship between millions of square miles of arctic sea ice and the year. the line of best fit can be represented by the equation y= -0.44x + 886.7. Show how you would use the equation to determine the amount of sea ice left in 2015. show your work!​

The scatterplot below shows the relationship between millions of square miles of arctic sea ice and the

Answers

Answer:

y = 0.10

Step-by-step explanation:

Using the equation, y = -0.44x + 886.7:

You can plug in the year (2015) as the value of x into the given equation. In doing so, you'll be able to determine what the value of y is (the amount of sea ice left).

y = -0.44x + 886.7

y = -0.44(2015) + 886.7

y = -886.6 + 886.7

y = 0.10

Therefore, the amount of sea ice left in 2015 is 0.10.  

Note: I'm not sure which unit of measure to follow because on the graph, it states that the "Area of Sea Ice" is (in millions of sq km); while in your given instructions, it states that "The scatterplot below shows the relationship between millions of square miles of arctic sea ice and the year."  I don't know if the unit of measure matters, but no matter what, the y-value should be 0.10.

In slope intercept y=mx+b if the slope is 3/4 and the -y intercept is -2

Answers

Answer:

y = \(\frac{3}{4}\) x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Here m = \(\frac{3}{4}\) and b = - 2 , then

y = \(\frac{3}{4}\) x - 2 ← equation of line

Write a story that can be represented using the equation y=x+1/5x

Answers

A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

How to illustrate the equation?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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fifa is expected to make how much revenue from the world cup?

Answers

Answer:

Step-by-step explanation:

$4.7 billion ..

math!!

PLEASE HELP!!

what is the angle indicated in the triangle below??

a) 46 degrees

b) 65°

c) 44°

d) 35°

e) 55°

f) 90°

math!! PLEASE HELP!! what is the angle indicated in the triangle below?? a) 46 degreesb) 65c) 44d) 35e)

Answers

Answer:

e) 55°

Step-by-step explanation:

use the tangente ratio

\(tan\alpha =\frac{10}{7} =1.42857\)

\(angle(?)=tan^{-1} (1.42857)=55^{0}\)

Hope this helps

Answer:

55 degrees (e)

Step-by-step explanation:

This is a trigonometry problem. We are given a right triangle with an unknown angle in which the opposite and adjacent sides of the angle are known (10 and 7). We also know that the tangent of any angle is the length of the opposite divided by the length of the adjacent. If we let the unknown angle be Ф, we can say that tan(Ф) = 10/7. To isolate Ф, all we have to do is take the inverse. In other words, Ф = arctan(10/7). Using a graphing calculator, we find that arctan(10/7) is approximately 55 degrees.

find the size of deb

find the size of deb

Answers

Answer:

\(4x + 3 = 6x - 53 \\ 6x - 4x = 3 + 53 \\ 2x = 56 \\ x = \frac{56}{2} = 28\)

irst consider a public good of value to Ann and Bob with the property that the value of the good can be expressed in monetary terms. In this case, the Samuelson condition states that the efficient level of the good is determined by MV +MVP where p is the per A B unit price of the good, and, for example, MV is Ann's marginal value of the good. Now consider a public good of value to Ann and Bob, the value of which CANNOT be expressed in monetary terms. In this case A O a. The Samuleson condition continues to work as in the case where values CAN be expressed in monetary terms. O b. We need more information before we can know how to modify the Samuelson condition. O c. The Samuelson condition is of no use because we cannot compare Ann's utility to Bob's. O d. The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.

Answers

The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.

When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.

Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.

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A circle's radius is 25 inches.
What is the circle's circumference (use 3.14 for pi and round to
nearest tenth

Answers

Answer:

C≈157.08in

Step-by-step explanation:

C=2πr=2·π·25≈157.07963in

2•pi•25
Answer: 157.1

2.1Simplifying Expressions: Problem 1 (1 point) Simplify the following expression. 6- 4(x - 5)-

Answers

The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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$9,400 x 8% commission rate

Answers

the commission rate is 752.

What is the value of p ?
A. 47
B. 43
C. 133
D. 90

What is the value of p ? A. 47B. 43C. 133D. 90

Answers

Answer:

I think 43 is the answer

Step-by-step explanation:

Pls mark brainliest if 43 is the correct answer

The value of p which is one of the angles of the given figure of the triangle is 43°, which is option B.

Given a figure.

The figure can be taken as a triangle.

One of the angles of the triangle is p.

It is required to find the value of p.

Given two exterior angles of the other two angles other than p of the given triangle.

The measures are 90° and 133°.

The interior angle corresponding to the exterior angle of 90° is 180° - 90° = 90°.

The interior angle corresponding to the exterior angle of 133° is 180° - 133° = 47°.

So, by the angle sum property of the triangle,

90° + 47° + p = 180°

137° + p = 180°

p = 180° - 137°

  = 43°

Hence, the angle p is 43°, which is option B.

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the following table shows the probability distribution for the prize amounts that will be awarded at a school raffle. prize $1 $5 $10 $20 $50 probability 0.60 0.30 0.05 0.04 0.01 let the random variable p represent a randomly selected prize amount. what is the expected value of p ? responses

Answers

Let the random variable p represent a randomly selected prize amount the expected value of p is $3.90  by using probability.

Prize                $1          $5            $10            $20              $50

Probability     0.60      0.30         0.05           0.04              0.01

It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.

The expected value is defined as the the sum of each outcome is multiplied by its probability.

p=x1p1+x2p2+x3p3+x4p4

p=1.0.60+5.0.30+10.0.05+20.0.04

p=3.90

Therefore, the correct option is A, i.e. $ 3.90 is the expected value of P.

Three Types of Probability

Classical: (equally probable outcomes) Let S=sample space (set of all possible distinct outcomes).

Relative Frequency Definition.

Subjective Probability.

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This table shows the number of goals scored in 25 Premier League football matches

Work out the
mean range and median

I need help with number 3 plz! And if u can can u also help me with 4 and 5!

This table shows the number of goals scored in 25 Premier League football matchesWork out themean range

Answers

The answer is attached above. I hope this helps!

This table shows the number of goals scored in 25 Premier League football matchesWork out themean range

Function w is a nonlinear function. Which representation could represent function w?

Function w is a nonlinear function. Which representation could represent function w?

Answers

A representation that could represent function w (nonlinear function) is: D. table D.

What is a linear function?

In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, a linear function has the same slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

Therefore, table D represents a non-linear function because the slope is not constant and the common difference is not constant between successive data points.

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QuestionThe mean monthly salary of the 12 employees of a firm is Rs. 1450. If one more person joins the firm who gets Rs. 1645 per month, what will be the mean monthly salary of 13 employees?ARs. 1465BRs. 1954CRs. 2175DRs. 2569Medium

Answers

1465 will be the mean monthly salary .The answer is (A) Rs. 1465.

Let the sum of the 12 employees' salaries be S.

Then, the mean monthly salary of the 12 employees is given by:

S/12 = 1450

S = 12 * 1450

S = 17400

If one more person joins with a salary of Rs. 1645, the new sum of the 13 employees' salaries is:

S' = S + 1645

S' = 17400 + 1645

S' = 19045

The new mean monthly salary of the 13 employees is:

S'/13 = 19045/13

S'/13 = 1465

Therefore, the answer is (A) Rs. 1465.

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How many coins would you need to make all possible rows of 6 coins (not necessarily with equal numbersof pennies and nickels)

Answers

Using combination, a) the number of coins = 120 b) the number of coins would needed to make all possible rows of 6 coin is 384.

a) Based on the provided information, each row is a 6-bit string (6 coins) and its weight is 3 (3 pennies). Therefore, using combination the possible number of rows will be 6C3. The formula for combination is given by:

nCr = n!/r!(n – r)!

Hence,

6C3 = 6!/3!(6 – 3)! = 6!/3!3! = 6*5*4*3!/ 3*2*1*3! = 20

And in case each row requires 6 coins simultaneously, the number of coins = 6*20 = 120 coins

b) Based on the provided information, the possible number of rows will be 2^6 = 64. It can also be obtained using combination the possible number of rows will be sum of 6C0, 6C1, 6C2, 6C3, 6C4, 6C5, and 6C6.

Hence,

6C0 + 6C1 + 6C2 + 6C3 + 6C4 + 6C5 + 6C6

6!/0!(6 – 0)! + 6!/1!(6 – 1)! + 6!/2!(6 – 2)! + 6!/3!(6 – 3)! + 6!/4!(6 – 4)! + 6!/5!(6 – 5)! + 6!/6!(6 – 6)!

6!/0!6! + 6!/1!5)! + 6!/2!4! + 6!/3!3! + 6!/4!2! + 6!/5!1! + 6!/6!0!

1 + 6 + 15 + 20 + 15 + 6 + 1

64

Therefore, the number of coins needed = 6*64 = 384 coins. The number of coins in each row = 384/2 = 192 coins

Hence,

Note: The question is incomplete. The complete question probably is: You break your piggy-bank to discover lots of pennies and nickels. You start arranging these in rows of 6 coins. (a) You find yourself making rows containing an equal number of pennies and nickels. For fun, you decide to lay out every possible such row. How many coins will you need? b) How many coins would you need to make all possible rows of 6 coins (not necessarily with equal number of pennies and nickels)?

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how to solve -×-(×-6)=8

Answers

Solve -x-(x-6)=8

Distribute the minus sign

-x-x+6=8

Solve and clear x

-2x+6=8

-2x=8-6

-2x=2

x=2/-2

x=-1

Find an example of a fallacious argument online, but it doesn't really specify what sort of websites you should choose. What's important for this assignment is that you find an example of a fallacy and explain why the argument commits that fallacy. You can feel free to use examples from academic sites, but you need to provide a citation for whatever cite you use to get examples of arguments with fallacies.

Answers

An example of a fallacious argument can be found on the website "LogicalFallacies.info" under the section on the fallacy of ad hominem. The argument commits the fallacy by attacking the person making the argument instead of addressing the merits of the argument itself.

One example of a fallacious argument can be found on LogicalFallacies.info under the section on the fallacy of ad hominem. The website provides an example of an ad hominem fallacy as follows: "John claims that we should lower taxes, but we can't trust him because he cheated on his taxes in the past." This argument commits the fallacy of ad hominem by attacking John's character and previous actions instead of addressing the substance of his argument regarding tax reduction. By focusing on John's personal conduct, the arguer attempts to discredit his viewpoint without providing any valid reasons or evidence against the proposal to lower taxes. This fallacy diverts attention from the actual issue at hand and undermines the rational evaluation of the argument based on its merits. It is important to recognize and understand fallacious arguments like this to promote critical thinking and constructive discourse. (Source: LogicalFallacies.info, "Ad Hominem")

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_____ consists of a series of 0s and 1s representing data or instructions.

Answers

The series of 0s and 1s representing data or instructions is called binary code. It is the foundation of digital communication and computing systems. Each binary digit, or bit, can be thought of as a switch that is either off (0) or on (1), allowing for the representation of complex information.



Binary code is a system used to represent data or instructions using only two symbols: 0 and 1. It is the foundation of digital communication and computing systems. Each digit in binary code is called a bit, which is short for "binary digit." Bits can be thought of as switches that can be in one of two states: off (0) or on (1).

By arranging these bits in different patterns, we can represent and manipulate complex information. For example, in binary code, the letter "A" is represented as 01000001. This binary representation allows computers to process and store information using electronic circuits that can easily interpret and manipulate 0s and 1s.

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In triangle ABC, If cos (A) = 12/13 and sin (A) = 5/13, what is tan(A)?

Answers

Answer:

tan(A) = 5/12

Step-by-step explanation:

Tan = opp/adj

opp= 5

adj = 12

Answer:12/13

Step-by-step explanation:

7. Drag the fractions in order from least to greatest value.7/4, 4/8, 7/8, 3/4

Answers

7/4 can be expressed as

\(\frac{7}{4}=\frac{7}{4}\cdot\frac{2}{2}=\frac{7\cdot2}{4\cdot2}=\frac{14}{8}\)

3/4 can be expressed as

\(\frac{3}{4}=\frac{3}{4}\cdot\frac{2}{2}=\frac{3\cdot2}{4\cdot2}=\frac{6}{8}\)

Then, the fractions to compare are:

14/8, 4/8, 7/8, 6/8

We can order them only considering the numerators. from least to greatest value the ordered list is:

4/8, 6/8, 7/8, 14/8

or

4/8, 3/4, 7/8, 7/4

Jane has nickles and quarters in her pocket. There are 20 coins, totaling $3​

Answers

Answer:

It is 10 quarters and 10 nickels

10 x 25 = $2.50

10 x 5 = $0.50

2.50 + 0.50 = $3.00

***I hope this helps

Step-by-step explanation:

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