Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure
x1+4x2 =11
2x1+7x2=18
Find the solution to the system of equations.

Answers

Answer 1

Answer:

The solution of the Given matrix

  ( x₁ ,    x ₂ ) = ( - 5 , 4 )

Step-by-step explanation:

Step(i):-

Given equations are  x₁+4 x₂ = 11 ...(i)

                                 2 x₁ + 7 x₂= 18 ...(ii)

The matrix form

                                A X = B

            [tex]\left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right][/tex]

Step(ii):-

      [tex]\left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right][/tex]

The Augmented Matrix form is

[tex][AB] = \left[\begin{array}{ccc}1&4&11\\2&7&18\\\end{array}\right][/tex]

Apply Row operations,  R₂ → R₂-2 R₁

[tex][AB] = \left[\begin{array}{ccc}1&4&11\\0&-1&-4\\\end{array}\right][/tex]  

The matrix form

                   [tex]\left[\begin{array}{ccc}1&4\\0&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\-4\\\end{array}\right][/tex]

The equations are

                     x₁ + 4 x₂ = 11 ...(a)

                         - x ₂ = - 4

                            x ₂ = 4

Substitute   x ₂ = 4 in equation (a)

                      x₁ + 4 x₂ = 11

                      x₁ = 11 - 16

                        x₁ = -5

Final answer:-

The solution of the Given matrix

  ( x₁ ,    x ₂ ) = ( - 5 , 4 )


Related Questions

how do I get every number from 1-20 using only four four's. Please this is due Monday. I'll make it worth more points too just... help

Answers

Answer:

go 4+4+4+4+4       4x5 its a simple answer i took this 4 years ago

Step-by-step explanation:

4

4

4

4

4

4x5=20


Find the perimeter of the polygon with the vertices G(2, 4), H(2, – 3), J( – 2, – 3), and KC – 2,4).
The perimeter is units.

Answers

Answer:

22 units

Step-by-step explanation:

Add up all the units.

A news outlet reported that fifty million Americans visited online retail sites on Black Friday, representing an increase of 35 percent versus a year ago. How many Americans visited online retail sites on Black Friday last year?​

Answers

Answer:

37 million and 37037

Step-by-step explanation:

GivenCurrent year online retail site visitors = 50 millionPrevious year online retail site visitors = xThe difference = 35% increase from previous yearSolutionx + 35% = 50 millionx*1.35 = 50 millionx = 50 million /1.35 x = 37 million and 37037

37 million and 37037 Americans visited online retail sites on Black Friday last year

evaluate the 1/3 of 10.2​

Answers

Answer:

3.4

Step-by-step explanation:

The scatterplot shows the number of guests who visited a hotel pool and the temperature on those days. Estimate the location of the line of best fit. About how many guests will visit the pool when the temperature is 85°F?

Answers

Answer:

A) 26 guests

Step-by-step explanation:

I just took the quiz on edge

Melody weigh?
4. The bird flew 80 km in four hours. What was the bird's average speed in
km/hr?

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

20 km/h

▹ Step-by-Step Explanation

Amount of km - 80 km

Hours - 4 hours

km/h = 80/4

= 20 km/h

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

20 km/hr

Step-by-step explanation:

since she went 4 hours if we divide 80 km by 4 we should get our answer. 80/4 is 20 so the bird when 20 km/hr

Determine if the following relations represent y as a function of x.

Answers

Answers:A) No, it is not a function B) Yes it's a functionC) Not a functionD) Yes it's a functionE) Yes it's a function

================================================

Explanation:

If y has an exponent of 2, 4, 6, etc (basically any even number) then it leads to having inputs with multiple outputs.

Consider something like y^2 = x. If x = 100, then y = 10 or y = -10 are possible. A function can only have exactly one y output for any valid x input. Similar issues happen for things like y^4 = x and so on. So this is why A and C are not functions.

The other equations do not have y values with such exponents, so we can solve for y and have each x input lead to exactly one y output. Therefore, they are functions.

A function assigns the values. The only function that represents y as a function of x is D.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

For any relation to represent a function in terms of x that represents the value of y, the order of y in the function should be equal to 1, therefore, the power of y should be 1, also, the y variable should be alone(Isolated) on one side of the equal sign.

A.) x = y⁴

It represents x in terms of y, therefore, No.

B.) 6x² + y = 4

It represents constant in terms of x and y, therefore, No.

C.) 6x + y² = -1

It represents constant in terms of x and y, therefore, No.

D.) [tex]y = \sqrt{1-x^2}[/tex]

The given function represents y in terms of x, therefore, it is a function that represents y as a function of x.

E.)  -2xy = 1

It represents constant in terms of x and y, therefore, No.

Hence, the only function that represents y as a function of x is D.\

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D=ABC for A what is A​

Answers

Steps to solve:

d = abc for a

~Divide both sides by "bc"

d/bc = abc/bc

~Simplify

d/bc = a

Best of Luck!

The figures below are rectangles. Which polynomial represents the area of the shaded region? HAVE ALL MY POINTS but answer truthfully cause i have the answer choices

Answers

Answer:

[tex] 7x - 1 [/tex]

Step-by-step explanation:

Area of the shaded region = area of the large rectangular - area of the small rectangle

Area of rectangle is given as l*w

Area of the large rectangle = [tex] l*w = (x + 5)(x - 1) [/tex]

Expand

[tex] = x(x - 1) +5(x - 1) [/tex]

[tex] = x^2 - x + 5x - 5 [/tex]

Area of large rectangle [tex] = x^2 + 4x - 5 [/tex]

Area of small rectangle = [tex] l*w = (x + 1)(x - 4) [/tex]

[tex] = x(x - 4) +1(x - 4) [/tex]

[tex] = x^2 - 4x + x - 4 [/tex]

Area of small rectangle = [tex] = x^2 - 3x - 4 [/tex]

Area of shaded region = [tex] (x^2 + 4x - 5) - (x^2 - 3x - 4) [/tex]

[tex] = x^2 + 4x - 5 - x^2 + 3x + 4 [/tex]

Collect like terms

[tex] = x^2 - x^2 + 4x + 3x - 5 + 4 [/tex]

[tex] = 7x - 1 [/tex]

Predict the next number.
3. 256, 64, 16, 4, ...​

Answers

Answer:

1

Step-by-step explanation:

The pattern is always divide by 4. 256 divided by 4 equals 64, 64 divided by 4 equals 16, and 16 divided by 4. Continuing with the pattern, 4 divided by 4 equals 1.

Determine if the following relations represent y as a function of x.

Answers

Answers:

A) yesB) yesC) yesD) no

Each yes/no answer refers to the question "is this a function?"

==================================

Explanation:

The last equation is not a function because of the even exponent over the y term. If you apply the fourth root to both sides, you'll end up with y = |x| and y = -|x| as the two possibilities. For any nonzero x, there are multiple y outputs.

The first three equations are functions because we don't have the same issue as the last equation. All exponents for the y terms are odd. Something like y without an exponent really means y^1.

What is the runner’s average rate of change between the hours: 0.5 and 2? mph 1.5 and 2.5? mph Average Rate of Change

Answers

Answer:4mph

5mph

Slower

Step-by-step explanation:

The average rate of change for the runner is 0.667 miles per hour².

How to calculate the average rate of change?

To calculate the average rate of change, we follow the following formula:

[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],

where a is the average rate of change, v₂ is the final speed, v₁ is the initial speed, t₂ is the time for v₂, and t₁ is the time for v₁.

How to solve the given question?

In the question, we are asked to find the runner's average rate of change between the hours 0.5 and 2 with speeds of 1.5 mph and 2.5 mph.

So we take, the initial speed v₁ = 1.5 mph, the final speed v₂ = 2.5 mph, the time for v₁, t₁ = 0.5 hours, and the time for v₂, t₂ = 2 hours.

Thus, we can calculate the average rate of change a, using the formula:

[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],

or, a = (2.5 -1.5)/(2 - 0.5) = 1/1.5 = 0.667 miles per hour².

Therefore, the average rate of change for the runner is 0.667 miles per hour².

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Solve the inequality 14a/11>4/3, and write the solution in interval notation

Answers

Answer:

[tex]a > \frac{22}{21}[/tex]

Step-by-step explanation:

Given the inequality function [tex]\frac{14a}{11}>\frac{4}{3}[/tex], to write the inequality in interval notation, we need to first get the solution to the inequality as shown;

[tex]\frac{14a}{11}>\frac{4}{3}\\cross\ multiply\\14a \times 3 > 11 \times 4\\42a >44\\divide \ both \ sides \ by \ 42\\\frac{42a}{42} > \frac{44}{42}\\ a>\frac{22}{21}[/tex]

Hence the expression in interval notation is [tex]a > \frac{22}{21}[/tex]

If PQ = 8, QR = 7x, and PR
9x, what is PR?

Answers

Answer:

36

Step-by-step explanation:

PQ + QR = PR

substituting the values we have:

8 + 7x = 9x

8 + 7x - 7x = 9x - 7x

8 = 2x

8/2 = 2x/2

4 = x

Now, for the value of PR:

9 x 4

36

Write a story problem that will result to the problem -3+ -8

Answers

Jack was a bank loan manager. He checks everyone’s accounts and makes sure they are right. Once he was checking out an account and he saw that Mark was in dept of 8 dollars in his credit card. To add to that, he has just bought something worth of 3 dollars. In total, how much does Mark owe the bank?

Answer:

-11

I went to Starbucks today knowing that i had -3 dollars in my bank account, but i wanted this Frappe so bad and it was 8 dollars. Long story short i ended up leaving with -11 dollars in my account.


True or False? Natural Numbers are closed under division.

Answers

False because you can subtract your way out of the set of whole numbers

What is the value of 3 1/3 divided by 2/3

Answers

Answer: 5

Step-by-step explanation:

The required value of 3 1/3 divided by 2/3 is 5.

What is the division operation?

In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.

For example 4/2 = 2

We have to determine the value of 3 1/3 divided by 2/3.

As per the question,

⇒ 3 1/3 ÷ 2/3

Convert the mixed numbers to fractions,

⇒ 10/3 ÷ 2/3

⇒ (10/3)/(2/3)

⇒ 10/2

Apply the division operation, and we get

⇒ 5

Thus, the required value of 3 1/3 divided by 2/3 is 5.

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The figure below is a rectangular shipping box.
Name two different planes that contain AD.

Answers

Answer:

The planes that contain the line AD are

1) Plane represented by bounded area ABCD

2) Plane represented by bounded area ADHE

Step-by-step explanation:

The line AD is located at the boundary of the planes ABCD and ADHE and as such is contained in the two planes.

A plane is defined as a flat surface in two dimensional space that has a linear vector boundary on alternate sides

A plane can be specified by a letter written in capitals, or by use of the letters at three non collinear points on the plane, such as plane P or plane ABC.

X = 8 , m = 3 , EVAULATE !!!!
ILL GIVE YOU BRAINLIST SHOW WORK !!!

Answers

Answer:

2

Step-by-step explanation:

[tex]2(3x+6)\div(10m)\\\\x =8\\m =3\\\\2(3(8)+6)\div(10(3))\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(3\left(8\right)+6\right)\::\quad 30\\=2\times\:30\div \left(10\left(3\right)\right)\\\\\mathrm{Calculate\:within\:parentheses}\:\left(10\left(3\right)\right)\::\quad 30\\=2\times\:30\div \:30\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:2\times\:30\div \:30\:\\:\quad 2[/tex]

Answer:

2

Step-by-step explanation:

plug it in

2(3(8)+6)/(10(3))

pemdas

2(24+6)/(30)

2(30)/(30)

60/30

2

Simplify the expression.


5(2-j) + (2j-3)

Answers

Answer:

7-3j

Step-by-step explanation:

Answer:

7 - 3j

Step-by-step explanation:

5(2-j) + (2j-3)

Open the brackets. Take note of the signs.

10-5j + 2j-3

Rearrange.

10 - 3 -5 j + 2j

= 7 - 3j

Please thank, rate 5 stars, and give brainliest. Thank you.

Write the sentence as an inequality. 7 minus 5 times a number x is greater than 19. An inequality is​

Answers

7 - 5x > 19 is the answer.

Translate each phrase to an algebraic expression. (a) the product of 7 and d, decreased by 16 (b) the product of 7 and d decreased by 16

Answers

Answer:

a) 7d - 16b) 7(d - 16)

Step-by-step explanation:

Question A:

Step 1. The product of 7 and d is = 7d.

Step 2. Then the next part is separated by a comma.

Step 3. This leads to the influence of the idea that 7d is subtracted by 16.

Step 4. This concludes that the answer is 7d - 16.

Question B:

Step 1: The product of 7 concludes that 7 is alone.

Step 2: The separation of and shows that the part after and is together.

Step 3: If it is together, we can conclude it goes in parentheses.

Step 4: If it is in parentheses, it means the number 7 is being distributed.

Step 5: This concludes the answer is 7(d - 16).

Hope this helped,

Kavitha

Solve the equation for x. x3 = 64

Answers

Answer:

4 is correct answer

Step-by-step explanation:

kindly see attached picture

hope it helped you:)

thanks!

Answer:

[tex] \tt {x}^{3} \: = \: 64[/tex]

[tex]\tt x \: = \: \sqrt[3]{64} [/tex]

[tex]\tt x \: = \: \sqrt{4 \times 4 \times 4} [/tex]

[tex] \underline {\boxed{ \tt x \: = \: 4}}[/tex]

How far can you ride a bike if you ride for 10 min at speed of 150m/min

Answers

Answer:

250 meters/min = 15 km/hr

Step-by-step explanation:

The approximate number to divide from is 16.667. Divide the speed value by 16.667

Answer:

1500m

Step-by-step explanation:

If you ride 150 m every one min then you can ride 150 times 10 in 10 min.

150 times 10 = 1500m

Please Answer I will make you brainiest Could you please also explain I don't get it :(

Answers

Answer:

C, 2.15

Step-by-step explanation:

Arabian Plate: 1.29x10^-4 = .000129

African Plate: 6x10^-5 = .000006

Once you've converted both into standard form, divide them to find the difference.

.000129/.000006 = 2.15

Roslan had a total of $50 in 10-cent coins,20-cent coins and 50-cent coins. The value of his 10-cent coins was 30% of the total value of all his coins. The value of his 20-cent coins was 28% of the total value of all his coins.What was the value of his 50-cent coins?

Answers

Answer:

$21

Step-by-step explanation:

Provided total value = $50

$50 = 5,000 cents.

We are provided,

10 cent coins value = 30%  of total value

= 0.3 [tex]\times[/tex] 5,000 cents = 1,500 cents

Value of 20 cents coin = 28% of total value

= 0.28 [tex]\times[/tex] 5,000 cents = 1,400 cents

Therefore, remaining value of cents = Total value of 50 cents coins

5,000 cents - value of 10-cent coins - value of 20-cent coins = total value of 50 cents coins

5,000 - 1,500 - 1,400 = 2,100 cents = $21

Which means number of 50 cents coin = [tex]\frac{2,100}{50} = 42\ coins[/tex]

Alternatively,

To calculate value of 50 cent coins

Total value = 100%

Value in 10-cent coins + 20-cent coins = 30% + 28% = 58%

Value in 50-cent coins = 100 - 58 = 42%

= $50 [tex]\times[/tex] 42% = $21

Is the length and width of a square equal?

Answers

Answer:

Yes.

Step-by-step explanation:

Each side of a square must be congruent and parallel to its opposite side.

One number is 38 less than another number. If the sum of the two numbers is 108, find the two numbers.

Answers

Answer:

The two numbers are 35 and 73.

Step-by-step explanation:

We can solve this problem by creating two simultaneous equations using the information given.

Let number 1 = x

Let number 2 = y

x = y - 38 -> ( 1 )

x + y = 108 -> ( 2 )

We can solve simultaneous equations using substitution or elimination. For this question, we will use substitution as it is the easier and shorter option.

Substitute ( 1 ) into ( 2 ):

x + y = 108 -> ( 2 )

( y - 38 ) + y = 108

2y - 38 = 108

2y = 146

y = 146 / 2

y = 73 -> ( 3 )

Substitute ( 3 ) into ( 1 ):

x = y - 38 -> ( 1 )

x = ( 73 ) - 38

x = 35

Therefore:

x = 35 , y = 73

PLEASE HELP, THANK YOU! :)

Answers

Steps to solve:

-4z + 4 + 12z = 3z + 4 + 5z

~Combine like terms

8z + 4 = 8z + 4

~Subtract 4 to both sides

8z = 8z

~Divide 8 to both sides

0 = 0

All real numbers are solutions.

Set builder notation: {x | R}

This is an identity since every value can be a solution to the equation.

Best of Luck!

What is 6(x-1)-12= -5?

Answers

Answer:

x=[tex]\frac{13}{6}[/tex]

Step-by-step explanation:

[tex]6( x - 1) - 12 = - 5 \\ ⟹ 6x - 6 - 12 = - 5 \\ ⟹ 6x - 18 = - 5 \\ ⟹ 6x = - 5 + 18 \\ ⟹x = \frac{13}{6}[/tex]

Hi there! :)

Answer:

[tex]\huge\boxed{x = \frac{13}{6}}[/tex]

6(x - 1) - 12 = -5

Begin by adding 12 to both sides:

6(x - 1) = -5 + 12

6(x - 1) = 7

Divide both sides by 6:

6(x - 1)/ 6 = 7 / 6

x - 1 = 7/6

Add 1 to both sides:

x = 7/6 + 6/6

x = 13/6.

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