Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)

[1 0 0 1]
[0 0 1 0]
[0 0 0 0]

(x1, x2, x3, x4) = _________

Answers

Answer 1

Answer:

[tex]x_1 = -t[/tex]

[tex]x_2 = s[/tex]

[tex]x_3 = 0[/tex]

[tex]x_4 = t[/tex]

Step-by-step explanation:

Given

[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]

Required

Determine x1 to x4

First, we write the augmented matrix

[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right] = \left[\begin{array}{c}0&0&0\end{array}\right][/tex]

Taking the position of each column, we have:

[tex]x_1 + 0 + 0 +x_4 = 0[/tex]

[tex]0 + 0 + x_3 +0 = 0[/tex]

[tex]0 + 0 + 0 + 0 = 0[/tex]

There is no explicit equation for [tex]x_2[/tex]

So: [tex]x_2 = s[/tex] ----- arbitrary variable

[tex]x_1 + 0 + 0 +x_4 = 0[/tex] implies that:

[tex]x_1 + x_4 = 0[/tex]

[tex]0 + 0 + x_3 +0 = 0[/tex] implies that

[tex]x_3 = 0[/tex]

[tex]0 + 0 + 0 + 0 = 0[/tex] implies that

[tex]0 = 0[/tex]

So, we have:

[tex]x_1 + x_4 = 0[/tex]

[tex]x_3 = 0[/tex]

[tex]x_1 + x_4 = 0[/tex] becomes

[tex]x_1 = -x_4[/tex]

Let

[tex]x_4 = t[/tex]

So:

[tex]x_1 = -x_4[/tex]

[tex]x_1 = -t[/tex]

Where t , s are real numbers


Related Questions

four times the difference of 15 and 6

Answers

Answer:

36

Step-by-step explanation:

9 is the difference

9 times 4 is 36

Subtraction is a mathematical operation. The statement "Four times the difference of 15 and 6" is equal to 36.

What is subtraction?

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The statement "Four times the difference of 15 and 6" can be expressed as,

= 4 × (15 - 6)

= 4 × (9)

= 36

Hence, The statement "Four times the difference of 15 and 6" is equal to 36.

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Which of the following represents the factorization of the trinomial below?
x2 - 14x + 49
O A. (x-7)
O B. (x-7)(x+7)
O C. (x+7)
O D. (x+2)(x+7)
ANSWER ASAP!!

Answers

the answer should be B!

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: ( {x - 7})^{2} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] {x}^{2} - 14x + 49[/tex]

[tex] = {x}^{2} - 7x - 7x + 49[/tex]

Taking "[tex]x[/tex]" as common from first two terms and "7" from last two terms, we have

[tex] = x \: ( \: x - 7 \: ) - 7 \: ( \: x - 7 \: )[/tex]

Taking the factor [tex](x-7)[/tex] as common,

[tex] = ( \: x - 7\:) \: (\: x - 7\: )[/tex]

[tex] =( {x - 7})^{2} [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Is 69 square routed a even number

Answers

No it is not, the square root is 8.3

Which expression can be modeled using the number line?

Answers

Answer:

7 x 1/10 = 7/10

Step-by-step explanation:

There are 7 "bumps" on the number line, and each "bump" moves the line 1/10.

This can also be modeled as

1/10 + 1/10 + 1/10 +1/10 +1/10 +1/10 +1/10 = 7/10

Please can you help me

Answers

Answer:

[tex]x = 24.75[/tex]

Step-by-step explanation:

Required

Find x

To find x, we have:

[tex]\angle PQR + \angle RPQ + \angle QRP = 180[/tex] -- angles in a triangle

Because [tex]\bar {PR}[/tex] is extended to S, then:

[tex]\angle QRS = \angle QRP[/tex]

So, we have:

[tex]2x + 6 + x - 7 + 5x -17 = 180[/tex]

Collect like terms

[tex]2x + x + 5x = 180 + 17 + 7-6[/tex]

[tex]8x = 198[/tex]

Divide by 8

[tex]x = 24.75[/tex]

Select all the correct answers.

These examples show the application of the negative exponent property. Which two examples correctly apply this property?

Answers

Answer:

First one and Third one

Step-by-step explanation:

Answer is correct from Plato

The correct expressions are:

[tex]17^{-1/4}[/tex] [tex]= \frac{1}{17^{1/4}}[/tex]

[tex]y^{1/2}[/tex] [tex]= \frac{1}{y^{-1/2}}[/tex]

In the given expression,

Since we know that the rule of exponent,

[tex]a^{-n} = \frac{1}{a^n}[/tex]

Therefore,

For the given expression,

[tex]17^{-1/4}[/tex]

Using the above property of exponent we can write it,

[tex]= \frac{1}{17^{1/4}}[/tex]

Hence this is the correct expression.

For the given expression,

[tex]y^{1/2}[/tex]

Using the above property of exponent we can write it,

[tex]= \frac{1}{y^{-1/2}}[/tex]

Hence this is the correct expression.

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Consider a species of bird that can be split into three age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years. The population is observed once a year. Given that the Leslie matrix is equal to

Answers

Answer: hello your question lacks some information attached below is the complete question

answer :

a) attached below

b) 65 students aged 1-2 years

Step-by-step explanation:

For a Leslie matrix ; there is a relation

Pn = L^n Po  where ; Pn = population vector after n years , Po = initial population vector .

a) Initial population vector

attached below

[tex]\left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]

b) Number of birds aged 1-2 years are available after 10 years

i.e. P10 = L^10 Po

note : Po = Xo

∴ P10 = [tex]\left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right][/tex]   [tex]\left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]

we will apply  MATLAB to resolve the above matrix

P10  = [tex]\left[\begin{array}{ccc}217.91\\65.24\\31.911\end{array}\right][/tex]

∴ Number of children between 1-2 years left after 10 years  = 65.24 ≈ 65

The total number of birds aged between 1-2 years which are available after 10 years is 65 and this can be determined by using the Leslie matrix relation.

Given :

Consider a species of bird that can be split into three age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years. [tex]\rm L = \left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right][/tex]

According to the given data, the initial population vector is given by:

[tex]x_0 = \left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]

Now, the total number of birds aged between 1-2 years which are available after 10 years is:

[tex]\rm P_{10} = \left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right] \left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]

Now, solve the above matrices in order to determine the value of [tex]\rm P_{10}[/tex].

[tex]\rm P_{10} = \left[\begin{array}{ccc}217.91\\65.24\\31.911\end{array}\right][/tex]

Therefore, the total number of birds aged between 1-2 years which are available after 10 years is 65.

For more information, refer to the link given below:

https://brainly.com/question/16823190

please help its urgent​

Answers

Answer:

Step-by-step explanation:

18x-6=120

18x=120+6

18x=126

    x=126÷18

    x=7

Simplify
x×x×x×у×у and
2×x×x×3×y×y×y​

Answers

Step-by-step explanation:

1.x³y²

2. 6x²y³

hope it helps

To solve the equation, Lorie applies the distributive property, combines like terms, then applies the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible coefficients of x after Lorie has completed these steps?

10 (one-half x + 2) minus 5 = 3 (x minus 6) + 1
–32 and 2
–2 and 32
–2 and 2
–32 and 32

Answers

Answer: -2 and 2

For this problem you really need to use algebraic skills. Coefficients refer to the number by the variable. So if you follow the steps it gives you then you’re fine.

Problem:
10(0.5x+2) - 5 = 3(x-6) + 1

Distribute:
5x +20 - 5 = 3x - 18 + 1

Combine like terms:
5x + 15 = 3x - 17

Addition and subtraction properties:
5x - 3x + 15 = -17
2x = -17 -15
2x = -32

OR:
5x + 15 = 3x - 17
15 + 17 = 3x - 5x
32 = -2x

Therefore your answer is -2 and 2 because coefficient is the number being multiplied by the variable. In this case it can be -2 or 2 depending where you move the variables (aka adding them or subtracting them from both sides)

Answer:

-2 and -2

Step-by-step explanation:

What is the volume in cubic centimeters of the figure below?

Answers

Answer:

so that you will multiply 15 * 4.

Step-by-step explanation:

15*4 = 60 now you divide 60 by 4 and the answer will be 15.

The interarrival time of nuclear particles in a Monte Carlo simulation of a reaction is designed to have a uniform distribution over an interval from 0 to 0.5 milliseconds. Determine the probability that the interarrival time between two particles will be:

Answers

Answer:

Incomplete question, but you can use the formulas given to solve it.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Uniform distribution over an interval from 0 to 0.5 milliseconds

This means that [tex]a = 0, b = 0.5[/tex]

Determine the probability that the interarrival time between two particles will be:

Considering [tex]a = 0, b = 0.5[/tex], and the question asked, you choose one of the three formulas above.

In mixture A of candy ingredients there are 3 parts of milk-chocolate for every Z parts peanut separate mixture B. there are 4 parts of nougat for every 3 parts of caramel equat parts of A and combined in one mixing bow what is the ratio of peanut butter to nougat in the bowl

Answers

3m=Z :A
4n=3c :B

If it’s a1:1 for A:B
z:4n

Feel like you left out something but this is what I got from info provided

Answer:

D. 7:10

Step-by-step explanation:

The Correct Answer

67 2/3% of the animals at an animal shelter are dogs. About what fraction of the animals at the shelter are dogs?

Answers

Answer:

2/3

Step-by-step explanation:

2/3 is 66 2/3%

subtract

a2-b2 from a2 +b2

Answers

Answer:

2b^2

Step-by-step explanation:

according to the question equation is

(a^2 + b^2 ) - (a^2 - b^2)

a^2 + b^2 - a^2 + b^2

plus a square and minus a square gets cancel

b^2 + b^2

since they are like terms they can be added

2b^2

Answer:

2b^2

Step-by-step explanation:

according to the question equation is

(a^2 + b^2 ) - (a^2 - b^2)

a^2 + b^2 - a^2 + b^2

= b^2 + b^2

like terms can be added

+2b^2

Find the length of side x

Answers

no no no no no no no no no no

Answer:

Step-by-step explanation:

tan(30) = x/1

sqrt(3) / 3 = x/1

x= sqrt(3) / 2

Diana is going to roll a 6-sided die. What's the probability she will role a 4 or
a 5? *

Answers

The probability of rolling any one number on a 6 sided die is 1/6

The probability of rolling a 4 is 1/6

The probability of rolling a 5 is 1/6

The probability of rolling a 4 or a 5 is the probability of rolling a 4 plus the probability of rolling a 5:

1/6 + 1/6 = 2/6 = 1/3

The answer is 1/3

ANYONE KNOW THE ANSWER TO THIS??

Answers

Answer:

x = 14 is your answer

Step-by-step explanation:

76 = 7x-22, so to figure it out, you first move -22 to the other side and get

76+22 = 7x.

add them together and you get 98 = 7x

7x would be your equation, so divide 98 by 7 and you get your solution

x = 14 is your answer

the answer is B: x=14

A box has three balls, one white and two red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:

a. Let F= the event of getting the white ball twice.
b. Let G= the event of getting two balls of different colors.
c. Let H= the event of getting white on the first pick.
d. Are F and G mutually exclusive?
e. Are G and H mutually exclusive?

Answers

Answer:

See explaation

Step-by-step explanation:

Given

Represent the balls with the first letters

[tex]W =1[/tex]

[tex]R =2[/tex]

Solving (a): P(F) --- White balls twice

The event of F is:

[tex]F = \{(W,W)\}[/tex]

So:

[tex]P(F) = P(W) * P(W)[/tex]

[tex]P(F) = \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(F) = \frac{1}{3} * \frac{1}{3}[/tex]

[tex]P(F) = \frac{1}{9}[/tex]

Solving (b): P(G) --- two different colors

The event of G is:

[tex]G = \{(W,R),(R,W)\}[/tex]

So:

[tex]P(G) = P(W) * P(R) + P(R) * P(W)[/tex]

[tex]P(G) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(R)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(G) = \frac{1}{3} * \frac{2}{3} + \frac{2}{3} * \frac{1}{3}[/tex]

[tex]P(G) = \frac{2}{9} + \frac{2}{9}[/tex]

[tex]P(G) = \frac{4}{9}[/tex]

Solving (c): P(H) --- White picked first

The event of H is:

[tex]H = \{(W,R),(W,W)\}[/tex]

So:

[tex]P(H) = P(W) * P(R) + P(W) * P(W)[/tex]

[tex]P(H) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(H) = \frac{1}{3} * \frac{2}{3} + \frac{1}{3} * \frac{1}{3}[/tex]

[tex]P(H) = \frac{2}{9} + \frac{1}{9}[/tex]

[tex]P(H) = \frac{3}{9}[/tex]

[tex]P(H) = \frac{1}{3}[/tex]

Solving (d): F and G, mutually exclusive?

We have:

[tex]F = \{(W,W)\}[/tex]

[tex]G = \{(W,R),(R,W)\}[/tex]

Check for common elements

[tex]n(F\ n\ G) = 0[/tex]

Hence, F and G are mutually exclusive

Solving (e): G and G, mutually exclusive?

We have:

[tex]G = \{(W,R),(R,W)\}[/tex]

[tex]H = \{(W,R),(W,W)\}[/tex]

Check for common elements

[tex]n(G\ n\ H) = 1[/tex]

Hence, F and G are not mutually exclusive

Find Length of x line OR

Answers

ATQ:-

Both figures r similar (given )

so :-

[tex] \frac{5}{2.5} = \frac{3}{1.5} = \frac{2}{1} = \frac{4}{x} \\ \frac{2}{1} = \frac{4}{x} \\ \frac{ \cancel{2}}{1} = \frac{ \cancel{4}^ { \tiny{2}}}{x} \\ x = 2 \: \: ans[/tex]

solve for x 7_3x=2x_3
[tex]7 - 3x = 2x - 3 = [/tex]

Answers

Answer:

x=2

Step-by-step explanation:

[tex]7 - 3x = 2x - 3 \\ 7 - 3x - 2x = - 3 \\ 7 - 5x = - 3 \\ - 5x = - 3 - 7 \\ - 5 = - 10 \\ x = \frac{ - 10}{ - 5} \\ x = 2[/tex]

HOPE IT HELPS!!!

I NEED BRAINLIEST ✌️ PLZ

WILL GIVE BRAINLIEST Solve for x

Answers

Answer:

Step-by-step explanation:

sin x° = [tex]\frac{17}{19}[/tex]

x° = [tex]sin^{-1}[/tex] [tex]\frac{17}{19}[/tex]

x° ≈ 63°

I need help please anyone

Answers

The answer is a or d u choose

Answer:

20

Step-by-step explanation:

l*w*h

4*5*1= 20

There is a bag filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?

Answers

Answer:

its a three in seven chance, since there are seven total outcomes and there is only one favorable outcome. Hope that helps.

Step-by-step explanation:

DO THIS FAST PLEASE I WILL GIVE BRAINLY CROWN



Use a model to divide. 5 ÷ 1/2 10 4 2 20

Answers

5 ÷ 1/2 => 5 x 2/1 => 10/1 => 10

Answer:

10

Step-by-step explanation:

In the pic, it shows ten half squares.  

Question 1 of 10
The number √3 goes on forever with no repeating pattern; therefore, it is
rational.
A. True
B. False
SUBMIT

Answers

the answer should be true

Answer:

False

Step-by-step explanation:

Rational number :

A rational number is a number which can be represent as p/q of two integers where q is not equal to zero

Example: 2/3

[tex]\sqrt{3}[/tex] = 17320508075........ and it keeps extending. Since it does not terminate or repeated after the decimal point.

Therefore [tex]\sqrt{3}[/tex] is an irritational number,

Hence given statement is FALSE

What is the answer. I need it ASAP u have to choose 3 answers

Answers

x= 5
y=1.25 :))))
If it is true, don't forget to click ”thanks♥️” for me

The ice cream man just ended his shift for the day. Let 1/2x^2 6/11x + 8 represent the amount of chocolate ice cream bars he sold. Let 5/9x^2 + 2/3 represent the amount of vanilla ice cream bars he sold. Finally let 1/3x^2 + 4x + 4/3 represent the amount of strawberry ice cream bars he sold. Select all the statements that are true

a. The total amount of ice cream bars sold can be represented by the expression 25/18x^2+ 50/11x +10
b. The total amount of ice cream bars sold can be represented by the expression 25/18x^2 + 172/33x +28/3
c. He sold 1/6x^2 + 50/11x + 28/3 more chocolate than strawberry ice cream bars.
d. He sold 1/6x^2 - 38/11x + 20/3 more chocolate than strawberry ice cream bars.

Answers

Answer:

A and D

Step-by-step explanation:

Total ice cream bars sold = sum of chocolate sold , vanilla and strawberry ice-creams sold.

=(1/2)x2 + (6/11)x + 8 + (5/9)x2 + (2/3) +(1/3)x2 + 4x +(4/3) (Given in the question)

=(25/18)x2 + (50/11)x + 10 (Adding terms corresponding to x2,x ,constant respectively)

Difference in chocolate and strawberry bars =[ (1/2)x2 + (6/11)x + 8] - [(1/3)x2 + 4x +(4/3)]

= (1/6)x2 - (38/11)x +(20/3)

So, the correct options are A and D

A TRIANGLE HAS SIDE LENGTH 3, 8 AND 9. FIND THE ANGLE MEASUREMENTFOR THE ANGLE CROSS FROM THE SIDE WITH LENGTH OF 8.

Answers

Answer:tu culo

Step-by-step explanation:

find the equation of straight line passing through each of the following pairs of points
a) (2,4) and (7,2)​

Answers

Answer:

The equation of the line is [tex]y = -\frac{2}{5}x + \frac{24}{5}[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

Slope:

Having two points, the slope is given by the change in y divided by the change in x. Points (2,4) and (7,2)​, so:

Change in y: 2 - 4 = -2

Change in x: 7 - 2 = 5

Slope: [tex]m = \frac{-2}{5} = -\frac{2}{5}[/tex]

So

[tex]y = -\frac{2}{5}x + b[/tex]

(2,4)

This means that when [tex]x = 2, y = 4[/tex]. So

[tex]y = -\frac{2}{5}x + b[/tex]

[tex]4 = -\frac{2}{5}(2) + b[/tex]

[tex]b = 4 + \frac{4}{5} = \frac{20}{5} + \frac{4}{5} = \frac{24}{5}[/tex]

The equation of the line is [tex]y = -\frac{2}{5}x + \frac{24}{5}[/tex]

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