1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
xxTIMURxx [149]
3 years ago
6

2. Solve the following system of equations

Mathematics
1 answer:
notsponge [240]3 years ago
6 0

Answer:

The answer to your question is x = 2, y = -1, z = 3

Step-by-step explanation:

Data

          x  +  y  +  z =  4

          x  - 2y  -  z =   1

         2x  -  y  - 2z = -1

Solve the system of equations

          |  1   1   1  |

          |   1 -2 - 1 |

Δ =     |  2  -1  -2|    = (4 - 1 -2) - (-2 + 1 -4) = 1 + 5 = 6

          |  1    1   1  |

          |  1  -2  -1 |  

         | 4   1   1 |

         | 1   -2  -1 |

Δx =   |-1   -1   -2|   = (16 - 1 + 1) - (-2 + 4 + 2) = 16 + 4 = 12

         | 4   1    1 |

         |  1  -2  -1 |

         | 1   4   1  |

         | 1    1  -1  |

Δy =  | 2 - 1  -2 | = (-2 -1 -8) - (-8 + 1 + 2) = -11 - 5 = -6

         | 1   4    1 |

         | 1    1    -1|

         | 1   1   4|

         | 1 -2   1|

Δz =  | 2 -1   -1|   = (2 - 4 + 2) - (-1 -1 -16) = 0 + 18

         | 1   1    4|

         | 1  -2   1|

Find x, y and z

x = Δx/ Δ = 12/6 = 2

y = Δy/Δ = -6/6 = -1

z = Δz/Δ = 18/6 = 3

You might be interested in
A company manufactures and sells x television sets per month. The monthly cost and​ price-demand equations are ​C(x)equals72 com
solmaris [256]

Answer:

Part (A)

  • 1. Maximum revenue: $450,000

Part (B)

  • 2. Maximum protit: $192,500
  • 3. Production level: 2,300 television sets
  • 4. Price: $185 per television set

Part (C)

  • 5. Number of sets: 2,260 television sets.
  • 6. Maximum profit: $183,800
  • 7. Price: $187 per television set.

Explanation:

<u>0. Write the monthly cost and​ price-demand equations correctly:</u>

Cost:

      C(x)=72,000+70x

Price-demand:

     

      p(x)=300-\dfrac{x}{20}

Domain:

        0\leq x\leq 6000

<em>1. Part (A) Find the maximum revenue</em>

Revenue = price × quantity

Revenue = R(x)

           R(x)=\bigg(300-\dfrac{x}{20}\bigg)\cdot x

Simplify

      R(x)=300x-\dfrac{x^2}{20}

A local maximum (or minimum) is reached when the first derivative, R'(x), equals 0.

         R'(x)=300-\dfrac{x}{10}

Solve for R'(x)=0

      300-\dfrac{x}{10}=0

       3000-x=0\\\\x=3000

Is this a maximum or a minimum? Since the coefficient of the quadratic term of R(x) is negative, it is a parabola that opens downward, meaning that its vertex is a maximum.

Hence, the maximum revenue is obtained when the production level is 3,000 units.

And it is calculated by subsituting x = 3,000 in the equation for R(x):

  • R(3,000) = 300(3,000) - (3000)² / 20 = $450,000

Hence, the maximum revenue is $450,000

<em>2. Part ​(B) Find the maximum​ profit, the production level that will realize the maximum​ profit, and the price the company should charge for each television set. </em>

i) Profit(x) = Revenue(x) - Cost(x)

  • Profit (x) = R(x) - C(x)

       Profit(x)=300x-\dfrac{x^2}{20}-\big(72,000+70x\big)

       Profit(x)=230x-\dfrac{x^2}{20}-72,000\\\\\\Profit(x)=-\dfrac{x^2}{20}+230x-72,000

ii) Find the first derivative and equal to 0 (it will be a maximum because the quadratic function is a parabola that opens downward)

  • Profit' (x) = -x/10 + 230
  • -x/10 + 230 = 0
  • -x + 2,300 = 0
  • x = 2,300

Thus, the production level that will realize the maximum profit is 2,300 units.

iii) Find the maximum profit.

You must substitute x = 2,300 into the equation for the profit:

  • Profit(2,300) = - (2,300)²/20 + 230(2,300) - 72,000 = 192,500

Hence, the maximum profit is $192,500

iv) Find the price the company should charge for each television set:

Use the price-demand equation:

  • p(x) = 300 - x/20
  • p(2,300) = 300 - 2,300 / 20
  • p(2,300) = 185

Therefore, the company should charge a price os $185 for every television set.

<em>3. ​Part (C) If the government decides to tax the company ​$4 for each set it​ produces, how many sets should the company manufacture each month to maximize its​ profit? What is the maximum​ profit? What should the company charge for each​ set?</em>

i) Now you must subtract the $4  tax for each television set, this is 4x from the profit equation.

The new profit equation will be:

  • Profit(x) = -x² / 20 + 230x - 4x - 72,000

  • Profit(x) = -x² / 20 + 226x - 72,000

ii) Find the first derivative and make it equal to 0:

  • Profit'(x) = -x/10 + 226 = 0
  • -x/10 + 226 = 0
  • -x + 2,260 = 0
  • x = 2,260

Then, the new maximum profit is reached when the production level is 2,260 units.

iii) Find the maximum profit by substituting x = 2,260 into the profit equation:

  • Profit (2,260) = -(2,260)² / 20 + 226(2,260) - 72,000
  • Profit (2,260) = 183,800

Hence, the maximum profit, if the government decides to tax the company $4 for each set it produces would be $183,800

iv) Find the price the company should charge for each set.

Substitute the number of units, 2,260, into the equation for the price:

  • p(2,260) = 300 - 2,260/20
  • p(2,260) = 187.

That is, the company should charge $187 per television set.

7 0
3 years ago
Write an equation to make the number "24" using all the numbers 5,4,2,2 and +, -, x and ÷.
Snezhnost [94]

Answer: See explanation

Step-by-step explanation:

We are given the numbers 5,4,2, and 2 and told to make an equation from it and get a final answer as 24. This will be:

= 5 × 4 + 2 + 2

= 20 + 2 + 2

= 24.

Since we have gotten a final answer of 24, the equation is solved.

8 0
3 years ago
Everyone come view this question
N76 [4]

Answer:

provide an image please

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Which situation represents a proportional relationship?​
ozzi

Answer:

c.... i am just smart

5 0
3 years ago
Given the check digit is 3, find the missing X for the master card number 5164 2X13 2705 0183
Gekata [30.6K]

Answer:

9

Step-by-step explanation:

So there's 3 1's, 2 2's, 2 3's, 1 4, 2 5's, a 6, a 7, an 8, 2 0's, and no 9's.  

5 0
3 years ago
Read 2 more answers
Other questions:
  • You travel between these two mile markers and then find your average speed in miles per hour. Which equation does NOT represent
    13·2 answers
  • Ellie started work at 8
    9·2 answers
  • How does dividing the coins into equal groups help solve the problem
    9·1 answer
  • What is the next number in the sequence?
    12·1 answer
  • Write a number in which the digit 8 is ten times the value of the digit 8 in 4.381
    14·1 answer
  • If line L is parallel to plane P ,how many planes containing line L can be drawn parallel to plane P
    10·1 answer
  • *If diagonal of a square is of length 10√2 cm then the perimeter of square is ...............cm.*
    10·1 answer
  • ahmed is sitting on a dock watching a float plane in a harbour. At a certain time, the plane is 350 m above the water and 470 m
    5·1 answer
  • Lewis is saving for a down payment of $8,750 on a house. The initial amount of money he has saved is $250, and the amount of mon
    11·1 answer
  • Auto Needs has oil on sale at 3 quarts for
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!