transfer transfer the system of equations by forming a matrix equation.

2x - 3y = 19
x + 2y = -1
he multiplies the left side of the coefficient matrix by the inverse matrix.

how does he proceed to the solution?​

Transfer Transfer The System Of Equations By Forming A Matrix Equation.2x - 3y = 19x + 2y = -1 He Multiplies

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]\begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}^{-1}\times \begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}\times \begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7} \begin{bmatrix}2 & 3 \\ -1 & 2\end{bmatrix}\times \begin{bmatrix}19\\ -1\end{bmatrix}[/tex]  

Since, [tex]\begin{bmatrix}2 & -3\\ 1 & 2\end{bmatrix}^{-1}=\frac{1}{7}\begin{bmatrix}2 & 3\\ -1 & 2\end{bmatrix}[/tex]

And [tex]A^{-1}A=I[/tex]

[tex]\begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7}\begin{bmatrix}2 & 3\\ -1 & 2\end{bmatrix}\times \begin{bmatrix}19\\-1 \end{bmatrix}[/tex]

[tex]\begin{bmatrix}x\\y \end{bmatrix}=\frac{1}{7}\begin{bmatrix}35\\ -21\end{bmatrix}[/tex]

[tex]\begin{bmatrix}x\\y \end{bmatrix}=\begin{bmatrix}5\\ -3\end{bmatrix}[/tex]                

Therefore, x = 5 and y = -3 will be the value of variables.


Related Questions

In a high school of 1000 students, 355 are playing sports and 233 are in a school band. If there are 175 students playing sports and are in a school band, how many are in neither activity?

Answers

Answer:

237

Step-by-step explanation:

1000 minus 355= 645

645 minus 233= 412

412 minus 175= 237

Answer:

237 students

Step-by-step explanation:

355 are playing sports

233 are in a school band.

175 in both

355 + 233 + 175 = 763

763 students are in sports, band or both

1000 - 763 = 237

237 students aren't participating in neither.

hope this helps :)

Find the product of (4c-5)(7x^2m- 3x + 3)

Answers

Answer:
28cx2m−12cx+12c−35x2m+15x−15

Step-by-step explanation:

A relation contains the points {(1, -4), (3, 2), (4, -3), (x, 7), (-4, 6)}.For which values of x will the relation be a function? Select ALL that apply.
A . -4
B. -3
C. 0
D. 3
E. 4

Answers

Answer:

th e answer is E. 4

Step-by-step explanation:

Which statement correctly describes the relationship between the graph of f(x)=x and the graph of g(x)=f(x)−7 ?

The graph of g(x) is the graph of​​​ f(x) translated 7 units down.

The graph of g(x) is the graph of​ f(x)​ vertically stretched by a factor of 7.

The graph of g(x) is the graph of​​ f(x)​ vertically compressed by a factor of 7.

The graph of g(x) is the graph of f(x) translated 7 units left.

help please

Answers

Answer:

translated down 7 units

Step-by-step explanation:

whenever it is written like this I'm pretty sure it's just translated down it would have to be in parentheses to go left and right

Select all the true statements. Triangle A B C where the measure of angle A is 2 x plus 1 degree, angle B is x degrees, and angle C is x plus 15 degrees. Group of answer choices m∠C = 56 From smallest to largest: ∠B, ∠C, ∠A m∠A = 99 x = 49 (4x + 16) = 180

Answers

Answer:

[tex]B= 41[/tex]; [tex]C = 56[/tex]; [tex]A = 83[/tex]

Step-by-step explanation:

Given

[tex]A = 2x + 1[/tex]

[tex]B = x[/tex]

[tex]C = x + 15[/tex]

Required

Arrange the angles from smallest to largest

First, we need to determine the value of x.

Since, it is a triangle:

[tex]A + B + C = 180[/tex]

Substitute values for A, B and C

[tex]2x + 1+ x + x + 15 = 180[/tex]

Collect Like Terms

[tex]2x + x + x = 180 - 15 -1[/tex]

[tex]4x = 164[/tex]

Solve for x

[tex]x= 164/4[/tex]

[tex]x= 41[/tex]

Solve for A, B and C

[tex]A = 2x + 1[/tex]

[tex]A = 2 * 41 + 1[/tex]

[tex]A = 82 + 1[/tex]

[tex]A = 83[/tex]

[tex]B = x[/tex]

[tex]B= 41[/tex]

[tex]C = x + 15[/tex]

[tex]C = 41 + 15[/tex]

[tex]C = 56[/tex]

From Smallest to Largest, we have:

[tex]B= 41[/tex]; [tex]C = 56[/tex]; [tex]A = 83[/tex]

Convert 12/25 to percent

Answers

Answer:

48%

Step-by-step explanation: multiply 4 with the numerator and denominator

a=-13y solve for y
This is all the question says so idk

Answers

I think that y=-1/13x

Gm!!! everyone (who see's this)

Answers

Answer:

GOODMORNING!!!

Step-by-step explanation:

I pray you, have a wonderful day!!  


Line t passes through points (9, 10) and (3, 3). Line u is parallel to line t. What is the slope of
line u?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Step-by-step explanation:

a parallel line has the same slope. that is the actual meaning of "parallel".

so we need to find the slope of line t to get our answer.

remember, the slope is the ratio " y coordinate change / x coordinate change" when going from one point on the line to another.

so, here we have 2 points (9, 10) and (3, 3).

going from the first to the second we see

x changes by -6 (from 9 to 3).

y changes by -7 (from 10 to 3).

the slope is then -7/-6 = 7/6.

and therefore, the slope of u is also 7/6.

Use the grouping method to factor the polynomial below completely.
x3 + 2x2 + 5x + 10
O A. (x2 + 5)(x+5)
O B. (x2 + 5)(x+2)
O C. (x2 + 5)(x+5)
O D. (x2 + 5)(x+2)

Answers

Answer:

(x²+5)(x+2)

simple find the common factor between x³ and 2x² and the cf of 5x and 10

u will end up with these results then^

PLZ HELP....!

A pair of parallel lines is cut by a transversal: A pair of parallel lines is cut by a transversal. The interior angle made on the left by the intersection of the upper parallel line and the transversal is divided into 2 parts by a slanting line. One part of this angle is labeled as x, and the other part is labeled as 35 degrees. The interior angle made on the right by the intersection of the lower parallel line and the transversal is labeled as 85 degrees. What is the measure of angle x?

A) 50 degrees

B) 55 degrees

C) 85 degrees

D) 125 degrees

Answers

Answer:

the answer is a)50 degree

Step-by-step explanation:

as alternate angle so

x+35=85

so x=85-35

x=50 degree

thanks

Answer:

50

Step-by-step explanation:

ʕ•ᴥ•ʔ hope this helps


If you claim a dependent and have to pay for child
care while you're at work, you can claim a tax credit of
$780. If you owed $5,638 in federal income taxes, how
much do you owe after claiming that credit?

Answers

Answer:

4858

Step-by-step explanation:

5,638-780=4,858


please answer and show work asap !! due in 30 mins !!

Answers

Answeri got u my boy

Step-by-step explanation:

it is

implifying

4x + 6y + -3 = 0

Reorder the terms:

-3 + 4x + 6y = 0

Solving

-3 + 4x + 6y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 4x + 3 + 6y = 0 + 3

Reorder the terms:

-3 + 3 + 4x + 6y = 0 + 3

Combine like terms: -3 + 3 = 0

0 + 4x + 6y = 0 + 3

4x + 6y = 0 + 3

Combine like terms: 0 + 3 = 3

4x + 6y = 3

Add '-6y' to each side of the equation.

4x + 6y + -6y = 3 + -6y

Combine like terms: 6y + -6y = 0

4x + 0 = 3 + -6y

4x = 3 + -6y

Divide each side by '4'.

x = 0.75 + -1.5y

Simplifying

x = 0.75 + -1.5y

Kilani and Adrian are starting a nutrition program. Kilani currently consumes 1200 calories a day and will increase that number by 100 calories each day. Adrian currently consumes 3230 calories a day and will decrease that number by 190 each day. They will continue this pattern until they are both consuming the same number of calories per day. In how many days will that be? Be sure to define your variables, write an equation, and answer the question in context.

Answers

Answer:

7 days

Step-by-step explanation:

Let us represent the number of days = a

Kilani currently consumes 1200 calories a day and will increase that number by 100 calories each day.

1200 calories + 100 calories × a

1200 + 100a

Adrian currently consumes 3230 calories a day and will decrease that number by 190 each day.

3230 calories - 190 calories × a

3230 - 190a

The number of days that they would be consuming the same number of calories =

Kilani = Adrian

1200 + 100a = 3230 - 190a

Collect like terms

190a + 100a = 3230 - 1200

290a = 2030

a = 2030/290

a = 7 days

Therefore, the would be consuming the same number of calories in 7 days

Jasmin is getting a new phone. It is $50 to activate and $15 monthly to keep on.

Please represent this word problem in all other ways. Explain if this is linear or not. Why or why not( HELP!!)

Answers

Answer:

y=15x+50

Step-by-step explanation:

yes this is linear because you are paying 15 dollars every month, with 50 dollars too

please help me!!

solve each of the equations below for the given variable

a.
[tex] \frac{ 2n - 1}{19} = \frac{m}{10} [/tex]
b.
[tex] \sqrt{x + 2 = 5} [/tex]

Answers

Step-by-step explanation:

b.

[tex]( \sqrt{x + 2} ) { }^{2} =( 5) { }^{2} \\ \\x + 2 = 25 \\ x = 25 - 2 \\ x = 23 [/tex]

The volume of a cone is 1967 cubic feet. Its
radius is 7 feet. Find the height.

Answers

Answer:

38.33 feet.

Step-by-step explanation:

Answer: 38.33ft

Explanation: I looked it up :)

Find the range of the data. 133,117,152,127,168,000,000

Answers

Answer:

168

Step-by-step explanation:

168  would be the range because the range is the highest number - the lowest number so 168=highest and 000=lowest

so 168-000 or just0=168

here's some extra answers.


The mean=100 rounded up to nearest 100

Mean= the average of the data set.

Median=127

The median is the middle number when the numbers in the data set are sorted least to greatest.

Mode=000 or just 0

The mode is the number that appear the most in the data set and 000 or just 0 appears twice rather than,all the other numbers only appear once.

Minimum=000 or just

The minimum is the lowest number in the data set and as for this one is is 0.

Maximum=168

The maximum is the highest number and the data set and 168 is the highest in this one.

Hope it helps have a great day:)

Need help with geometric series'!
Please include a step by step explanation.

Answers

Answer:

[tex] - 13107[/tex]

Step-by-step explanation:

We would like to evaluate the following Geometric Series ,

[tex]\displaystyle\longrightarrow \sum _{n=1}^8 (-4)^{n-1 }[/tex]

In a geometric series, a common number is multiplied to the previous term in order to find the next term . And that common number is called common ratio (r) .

As we know that ,

[tex]\displaystyle\longrightarrow \sum_{x = 1}^n f(x) = f(1) + f(2) + \dots + f(n) [/tex]

So , we can write the series as ,

[tex]\displaystyle\longrightarrow (-4)^{1-1}+(-4)^{2-1}+\dots +(-4)^{8-1} [/tex]

Simplify,

[tex]\displaystyle\longrightarrow (-4)^0 + (-4)^1+(-4)^2+\dots +(-4)^7 [/tex]

We can find the common ratio by dividing and successive term by its preceding term , as ;

[tex]\displaystyle\longrightarrow r =\dfrac{-4}{1}=-4 [/tex]

Again , here ;

First term = a = [tex](-4)^0=1[/tex]Common ratio = [tex]-4[/tex]number of terms (n) = 8

And we can find the sum of geometric series using the formula , ( this is used when the value of r is less than 1 , here it is -4 ) .

[tex]\displaystyle\longrightarrow \Bigg[ Sum = \dfrac{a(1-r^n)}{1-r}\Bigg] [/tex]

where the symbols have their usual meaning.

On substituting the respective values, we have;

[tex]\displaystyle \longrightarrow\rm{ Sum }=\dfrac{ 1\{1-(-4)^8\}}{1-(-4)}\\ [/tex]

Simplify ,

[tex]\displaystyle\longrightarrow \rm{Sum} = \dfrac{1-65536}{1+4}\\[/tex]

[tex]\displaystyle\longrightarrow \rm{Sum} = \dfrac{-65535}{5} [/tex]

Simplify by dividing ,

[tex]\displaystyle\longrightarrow \underline{\underline{ \rm{Sum} = -13107}} [/tex]

And we are done !

Which of these numbers is irrational?
O A. v3
OB. 0.25
O C. 1
O D. V9

Answers

Answer:

A

Step-by-step explanation:

the square root of 3 is an irrational number.

Which statement below best applies to the following expression?

Answers

Answer:

A.

Step-by-step explanation:

Radical expressions can only be simplified if their radicands are identical.

What is the slope for the equation of the line passing through the points (20,-32) and (10, -15)?​

Answers

Answer:

-17/10

Step-by-step Explanation :

Please answer :) much appreciated

Answers

29+m=41
m=12
He received $12

Which expression is equivalent to 3^0x3

Answers

Hey there!

3^0 * 3

= 1 * 3

= 1 + 1 + 1

= 2 + 1

= 3


Therefore, your answer is: 3


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

what is the constant of posprtainality in the equation y=0.41

Answers

Answer:

The constant of proportionality in the equation y=0.41 is 0.41

Step-by-step explanation:

bobby's cat runs x mph. bobby's dog runs twice as fast as his cat. if the cat and the dog start running away from each other, how far away from each other will they be after 30 minutes

Answers

Answer:

They will be 0.5x miles away from each other.

Calculation of the distance:

Since Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.

So here the speed of the dog should be 2x

Now we know that

Here distance of cat should be x of 30 minutes or half hour = 0.5x miles

And, Distance of dog should be 2x of 0.5 = x miles

So, the difference should be

= x - 0.5

= 0.5x miles

hence, They will be 0.5x miles away from each other.

Step-by-step explanation:

Answer:

1.5x miles, because you already know that the cat's speed is 0.5x miles, and the dog is x miles, so when you add it together, you get 1.5x miles

Find the missing side lengths. Leave your answers as radicals in simpler form. Please explain it

Answers

Answer:

Step-by-step explanation:

todd Has a collection of 8cds and sally has a collection of 18 cds Todd is adding 9cds a month to his collection while sally is adding 7 cds a month to her collection when will they have the same number of cds and how many will they have

Answers

Answer:

Step-by-step explanation:

Let's create some equations first.

Say M = number of months, T = Todd and S = Sally.

We know that Todd starts with 8 cds and sally starts with 18 cds.

This means when M= 0,  T = 8 and S = 18

After one month (M = 1), Todd adds 9 cds.

This means can write the following equation:

T = 8 + 9M

So after the first month (where M = 1), we can find out that Todd has

T = 8 + 9 x 1 = 8 + 9 = 17 cds

For Sally, we know she adds 7 cds per month.

S = 18 + 7M

After one month (M = 1),

S = 18 + 7 x 1 = 25 cds.

Now we are trying to find when they will have the same number of cds and how many.

This means we are trying to figure out what M = ? when Todd and Sally are equal.

So we want to find when T = S

Remember, earlier we wrote :

T = 8 + 9M

S = 18 + 7M

If T = S, this means:

8 + 9M = 18 + 7M

Gather the like terms and solve for M.

Subtract 8 from both sides.

9M = 10 + 7M

Subtract 7M from both sides

2M = 10

Divide both sides by 2

M = 5.

So in 5 months, we are saying T = S (Todd and Sally will have the same number of cds).

Put M = 5 back into our earlier equations to find out how many cds they have after 5 months.

T = 8 + 9M

T = 8 + 9 x 5

T = 53

Therefore, after 5 months Todd and Sally will have 53 cds each :)

ConnectMe phone service charges Deva $29.95 per month for cellular data. Endless Data phone company is offering the same service for 20% less. How much will Deva save per month if she switches to Endless Data?

Answers

Answer:

5.99

Step-by-step explanation:

How wide is each annual ring (springwood and summerwood combined)? Disregard the bark and pith in your calculations. Show your work. Write your answer in inches

Answers

The width of each ring in the redwood trees of coastal California is 0.06 inches.

How to estimate the width of a ring in a tree

According to the statement, we know that age of a tree and base diameter are directly proportional to the number of rings. The width of the ring is estimated by dividing the radius of the tree base by the age of the tree:

[tex]w = \frac{10\,ft \times 12\,\frac{in}{ft} }{2000}[/tex]

[tex]w = 0.06\,in[/tex]

The width of each ring in the redwood trees of coastal California is 0.06 inches. [tex]\blacksquare[/tex]

Remark

The statement in incomplete, correct form is shown below:

Each year of its life, a tree grows a new ring just under the outside bark. The new ring consists of two parts, light-colored springwood, when the tree grows the fastest, and a darker-colored summerwood, when growth slows. When conditions are good and there is lots of sun and rain, the new ring is thicker than the rings formed when there is drought or excessive cold. At the center of the tree is a dark circle called pith that is not connected to the age of the tree.

The redwood trees of coastal California are the tallest living things on earth. On redwood is 350 feet tall, 20 feet in diameter at its base, and around 2000 years old. Assume that the lower 50 feet of the tree form of the tree form a cylinder 20 feet in diameter and that all of the rings grew at the same rate.

How wide is each annual ring (springwood and summerwood combined)? Disregard the bark and pith in your calculations. Show your work. Write your answer in inches.

To learn more on trees, we kindly invite to check this verified question: https://brainly.com/question/13604529

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