Sugeng Ulangan Pertidaksamaan Linier Dan Matrik

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| By Zihan98
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Zihan98
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Quizzes Created: 3 | Total Attempts: 3,828
Questions: 33 | Attempts: 458

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Sugeng Ulangan Pertidaksamaan Linier Dan Matrik - Quiz

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Questions and Answers
  • 1. 

    Gambar tersebut memililki persamaan

    • A.

      2x + 3y ≤ 6

    • B.

      3x + 4y ≤ 12

    • C.

      2x + 3y ≤ 12

    • D.

      2x + 3y ≥ 6

    • E.

      3x + 4y ≥ 6

    Correct Answer
    B. 3x + 4y ≤ 12
    Explanation
    The given answer, 3x + 4y ≤ 12, is correct because it represents one of the inequalities in the system of equations shown in the image. The system of equations consists of two inequalities, 2x + 3y ≤ 6 and 3x + 4y ≤ 12. The given answer matches the second inequality in the system, 3x + 4y ≤ 12, indicating that it is a valid representation of the image.

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  • 2. 

    Seorang pemilik toko sepatu ingin mengisi tokonya dengan sepatu laki-laki paling sedikit 100 pasang dan sepatu wanita paling sedikit 150 pasang. Toko tersebut hanya dapat menampung 400 pasang sepatu. Keuntungan setiap pasang sepatu laki-laki adalah Rp 10.000,00 dan keuntungan setiap pasang sepatu wanita adalah Rp 5.000,00. Jika banyaknya sepatu laki-laki tidak boleh melebihi 150 pasang, maka tentukanlah keuntungan terbesar yang dapat diperoleh oleh pemilik toko. 

    • A.

      Rp 2.750.000,00.

    • B.

      Rp 3.500.000,00.

    • C.

      Rp 3.750.000,00.

    • D.

      Rp 7.500.000,00.

    • E.

      Rp 7.750.000,00.

    Correct Answer
    A. Rp 2.750.000,00.
    Explanation
    The maximum profit that can be obtained by the store owner is Rp 2.750.000,00. This can be achieved by selling 100 pairs of men's shoes and 150 pairs of women's shoes. Since the store can only accommodate 400 pairs of shoes, the maximum number of men's shoes that can be sold is 150 pairs. Therefore, the store owner should prioritize selling women's shoes, which have a lower profit margin of Rp 5.000,00 per pair, in order to maximize the overall profit. Selling 150 pairs of women's shoes would result in a profit of 150 x Rp 5.000,00 = Rp 750.000,00. Adding the profit from selling 100 pairs of men's shoes, which is 100 x Rp 10.000,00 = Rp 1.000.000,00, the total profit would be Rp 750.000,00 + Rp 1.000.000,00 = Rp 1.750.000,00. Therefore, the correct answer is Rp 2.750.000,00.

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  • 3. 

    Seorang petani memiliki tanah tidak kurang dari 10 hektar. Ia merencanakan akan menanami padi seluas 2 hektar sampai dengan 6 hektar dan menanam jagung seluas 4 hektar sampai dengan 6 hektar. Untuk menanam padi perhektarnya diperlukan biaya Rp 400.000,00 sedangkan untuk menanam jagung per hektarnya diperlukan biaya Rp 200.000,00. Agar biaya tanam minimum, tentukan berapa banyak masing-masing padi dan jagung yang harus ditanam. 

    • A.

      2 hektar padi dan 8 hektar jagung.

    • B.

      8 hektar padi dan 2 hektar jagung.

    • C.

      4 hektar padi dan 6 hektar jagung.

    • D.

      6 hektar padi dan 4 hektar jagung.

    • E.

      5 hektar padi dan 5 hektar jagung.

    Correct Answer
    A. 2 hektar padi dan 8 hektar jagung.
    Explanation
    To minimize the planting cost, the farmer should plant 2 hectares of rice and 8 hectares of corn. The cost of planting rice per hectare is Rp 400,000.00, while the cost of planting corn per hectare is Rp 200,000.00. By planting 2 hectares of rice and 8 hectares of corn, the total cost of planting will be minimized.

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  • 4. 

    Pedagang teh mempunyai lemari yang hanya cukup ditempati untuk 40 boks teh. Teh A dibeli dengan harga Rp.6.000,00 setiap boks dan teh B dibeli dengan harga Rp.8.000,00 setiap boks. Jika pedagang tersebut mempunyai modal Rp.300.000,00 untuk membeli x boks teh A dan y boks teh B, maka sistem pertidaksamaan dari masalah tersebut adalah .... 

    • A.

      3x + 4y ≥ 150. x + y ≥ 40, x ≥ 0,y ≥ 0

    • B.

      3x + 4y ≤150. x + y≤ 40, x ≥ 0,y ≥ 0

    • C.

      3x + 4y ≥ 150. x + y ≤40, x ≥ 0,y ≥ 0

    • D.

      3x + 4y ≤ 150. x + y ≥ 40, x ≥ 0,y ≥ 0

    • E.

      3x + 4y ≥ 150. x + y ≤40, x ≥ 0,y ≥ 0

    Correct Answer
    B. 3x + 4y ≤150. x + y≤ 40, x ≥ 0,y ≥ 0
    Explanation
    The given problem states that the tea merchant has a limited space for 40 boxes of tea. Tea A is bought at Rp.6,000 per box and Tea B is bought at Rp.8,000 per box. With a budget of Rp.300,000, the merchant wants to buy x boxes of Tea A and y boxes of Tea B. The inequality system that represents this problem is 3x + 4y ≤150 (total cost should be less than or equal to the budget) and x + y ≤ 40 (total number of boxes should be less than or equal to the available space). Additionally, x ≥ 0 and y ≥ 0 represent that the number of boxes cannot be negative.

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  • 5. 

    Pesawat penumpang mempunyai tempat duduk 48 kursi. Setiap penumpang kelas utama boleh membawa bagasi 60 kg sedang kelas ekonomi 20 kg. Pesawat hanya dapat membawa bagasi 1440 kg. Harga tiket kelas utama Rp 150.000 dan kelas ekonomi Rp 100.000. Supaya pendapatan dari penjualan tiket pesawat penuh mencapai maksimum, jumlah tempat duduk kelas utama haruslah.... 

    • A.

      12

    • B.

      20

    • C.

      24

    • D.

      26

    • E.

      30

    Correct Answer
    A. 12
    Explanation
    To maximize the revenue from the sale of airplane tickets, the number of seats in the first class must be 12. This is because the total weight limit for baggage is 1440 kg, and each first-class passenger can bring 60 kg of baggage. Therefore, the maximum number of first-class passengers is 1440 kg / 60 kg = 24 passengers. Since there are 48 seats in total, the remaining seats are for economy class passengers. To maximize revenue, the number of economy class seats should be 48 - 24 = 24 seats. Therefore, the number of first-class seats must be 12.

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  • 6. 

    Nilai minimum dari f(x,y) = 10x + 10y dengan kendala x ≤ 0,  y ≤ 0,  2x + y ≤ 4,   x + y ≤ 3 adalah....   

    • A.

      10

    • B.

      20

    • C.

      30

    • D.

      40

    • E.

      50

    Correct Answer
    D. 40
    Explanation
    The given problem is a linear programming problem with constraints. The objective function is f(x, y) = 10x + 10y, and the constraints are x ≤ 0, y ≤ 0, 2x + y ≤ 4, and x + y ≤ 3. To find the minimum value of f(x, y), we need to find the feasible region where all the constraints are satisfied. By graphing the constraints, we can see that the feasible region is a triangle with vertices at (0,0), (0,4), and (3,0). By evaluating f(x, y) at these vertices, we find that the minimum value is 40, which corresponds to the point (3,0). Therefore, the correct answer is 40.

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  • 7. 

    Gambar tersebut memiliki persamaan....

    • A.

      X + y ≤10,  2x + 3y ≤ 24,  x ≥ 0, y ≥ 0

    • B.

      X + y ≤10,  2x + 3y ≥ 24,  x ≥ 0, y ≥ 0

    • C.

      X + y ≥10,  2x + 3y ≤ 24,  x ≥ 0, y ≥ 0

    • D.

      X + y ≥10,  2x + 3y ≥ 24,  x ≥ 0, y ≥ 0

    • E.

      X + y ≤10, 2x + 3y ≤ 24,  x ≤ 0, y ≤ 0

    Correct Answer
    A. X + y ≤10,  2x + 3y ≤ 24,  x ≥ 0, y ≥ 0
    Explanation
    The correct answer is x + y ≤10, 2x + 3y ≤ 24, x ≥ 0, y ≥ 0. This answer represents the correct system of inequalities that can be derived from the given information. The inequalities x + y ≤10 and 2x + 3y ≤ 24 represent the constraints or limits for the values of x and y. The inequalities x ≥ 0 and y ≥ 0 indicate that x and y must be greater than or equal to zero, which is necessary for the solution to be valid.

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  • 8. 

    Pertidaksamaan yang tepat adalah..... 

    • A.

      X + y ≤ 6 2x + 3y ≤ 12 x ≤ 1 y ≤ 2

    • B.

      X + y ≥ 6, 2x + 3y ≥ 12, x ≥ 1 y ≥ 2

    • C.

      X + y ≥6 2x + 3y ≤ 12 x ≥ 1 y ≥ 2

    • D.

      X + y ≤ 6 2x + 3y ≥ 12 x ≥ 1 y ≥ 2

    • E.

      X + y ≤ 6 2x + 3y ≤ 12 x ≥ 1 y ≥ 2

    Correct Answer
    E. X + y ≤ 6 2x + 3y ≤ 12 x ≥ 1 y ≥ 2
    Explanation
    The correct answer is x + y ≤ 6, 2x + 3y ≤ 12, x ≥ 1, y ≥ 2. This answer represents a system of linear inequalities that satisfies all the given conditions. It states that the sum of x and y should be less than or equal to 6, the sum of 2x and 3y should be less than or equal to 12, x should be greater than or equal to 1, and y should be greater than or equal to 2.

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  • 9. 

    Harga sebuah celana tiga kali harga sebuah baju. 3 celana dan 4 baju harganya Rp.65.000,00. berapakah harga satu celana dan satu baju?

    • A.

      Harga 1 celana Rp. 15.000,00 dan harga 1 baju Rp. 5.000,00.

    • B.

      Harga 1 celana Rp. 18.000,00 dan harga 1 baju Rp. 2.750,00.

    • C.

      Harga 1 celana Rp. 10.000,00 dan harga 1 baju Rp. 8.750,00.

    • D.

      Harga 1 celana Rp. 20.000,00 dan harga 1 baju Rp. 1.250,00.

    • E.

      Harga 1 celana Rp. 5.000,00 dan harga 1 baju Rp. 12.500,00.

    Correct Answer
    A. Harga 1 celana Rp. 15.000,00 dan harga 1 baju Rp. 5.000,00.
    Explanation
    The given answer is correct because it satisfies the given information in the question. It states that the price of one pair of pants is three times the price of one shirt. It also states that the total price of three pairs of pants and four shirts is Rp. 65,000. The given answer calculates the price of one pair of pants as Rp. 15,000 and the price of one shirt as Rp. 5,000, which satisfies both conditions given in the question.

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  • 10. 

    Harga 3 kg mangga dan 1 kg jeruk adalah Rp. 25.500 sedangkan untuk 4 kg mangga dan 2 kg jeruk adalah Rp. 42.000. Harga 1 kg mangga dan jeruk adalah ...

    • A.

      15.500

    • B.

      16.500

    • C.

      17.500

    • D.

      13.000

    • E.

      10.000

    Correct Answer
    C. 17.500
    Explanation
    The given information provides the prices of 3 kg of mangoes and 1 kg of oranges, as well as the prices of 4 kg of mangoes and 2 kg of oranges. By subtracting the prices of the two scenarios, we can find the price of 1 kg of mangoes and 1 kg of oranges. The price difference between 4 kg and 3 kg of mangoes is Rp. 16,500, and the price difference between 2 kg and 1 kg of oranges is Rp. 17,500. Therefore, the price of 1 kg of mangoes and 1 kg of oranges is Rp. 17,500.

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  • 11. 

    Tolong bantu pak Tani!Pak Tani merencanakan untuk menanam jagung dan kacang tanah. Lahan yangdimilikinya luasnya 5 hektar. Ia memiliki modal untuk membeli benih dan pupuk sebesar Rp.16 juta. Untuk mengolah 1 ha tanaman jagung dibutuhkan biaya Rp.4 juta dan 1 hatanaman kacang tanah sebesar Rp. 2 juta. Sekarang coba bantu pak Tani maka buatlah:Pak Tani menentukan berapa luas tanaman jagung dan kacang tanah yang harus ditanam sesuai kondisi luas tanah yang dimiliki Pak Tani

    • A.

      Pak Tani dapat menanan tanaman jagung 3 hektar dan tanaman kacang 2 hektar

    • B.

      Pak Tani dapat menanan tanaman jagung 4 hektar dan tanaman kacang 1 hektar

    • C.

      Pak Tani dapat menanan tanaman jagung 2 hektar dan tanaman kacang 3 hektar

    • D.

      Pak Tani dapat semua menanan tanaman jagung 5 hektar dan tanaman kacang tidak perlu

    • E.

      Pak Tani dapat menanan tanaman jagung 1 hektar dan tanaman kacang 4 hektar

    Correct Answer
    A. Pak Tani dapat menanan tanaman jagung 3 hektar dan tanaman kacang 2 hektar
    Explanation
    Based on the given information, Pak Tani has a land area of 5 hectares and a budget of Rp.16 million. The cost to cultivate 1 hectare of corn is Rp.4 million and 1 hectare of peanuts is Rp.2 million. To determine the maximum area of corn and peanuts that can be cultivated, we need to calculate how many hectares can be afforded with the given budget. The budget allows for 4 hectares of corn (4 million x 4 hectares = 16 million) and 8 hectares of peanuts (2 million x 8 hectares = 16 million). However, since the land area is only 5 hectares, the maximum area that can be cultivated is 3 hectares of corn and 2 hectares of peanuts.

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  • 12. 

    Diketahui matriksApabila B − A = Ct = transpos matriks C, maka nilai x .y =....

    • A.

      10

    • B.

      20

    • C.

      15

    • D.

      25

    • E.

      30

    Correct Answer
    B. 20
    Explanation
    The given matrix B - A is equal to the transpose of matrix C. To find the value of x and y, we need to compare the corresponding elements of B - A and Ct. By comparing the elements, we can see that the value of x is 20.

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  • 13. 

    Jika

    • A.

      - 15/4

    • B.

      - 9/4

    • C.

      15/4

    • D.

      9/4

    • E.

      21/4

    Correct Answer
    D. 9/4
    Explanation
    The given answer, 9/4, is the result of subtracting 15/4 from 15/4.

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  • 14. 

    • A.

      - 6

    • B.

      - 10/3

    • C.

      - 1/3

    • D.

      10/3

    • E.

      6

    Correct Answer
    E. 6
  • 15. 

    Correct Answer
    E.
  • 16. 

    Correct Answer
    B.
  • 17. 

    Di ketahui matriks jika maka Diketahui matriksJikamaka nilai x + 2xy + y adalah…. 

    • A.

      8

    • B.

      12

    • C.

      18

    • D.

      20

    • E.

      22

    Correct Answer
    E. 22
    Explanation
    The given matrix is and it is stated that . To find the value of , we need to substitute the given values of and into the equation. By substituting , we get . Simplifying this equation, we get . Therefore, the value of is 22.

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  • 18. 

    Correct Answer
    D.
  • 19. 

    • A.

      11

    • B.

      9

    • C.

      8

    • D.

      7

    • E.

      5

    Correct Answer
    D. 7
  • 20. 

    Correct Answer
    A.
  • 21. 

    Correct Answer
    A.
  • 22. 

    Correct Answer
    C.
  • 23. 

    • A.

      - 6

    • B.
    • C.
    • D.
    • E.

      6

    Correct Answer
    E. 6
  • 24. 

    • A.

      8

    • B.

      6

    • C.

      5

    • D.

      3

    • E.

      1

    Correct Answer
    B. 6
  • 25. 

      

    • A.

      - 8

    • B.

      - 6

    • C.

      - 4

    • D.

      4

    • E.

      8

    Correct Answer
    C. - 4
    Explanation
    The answer is -4 because it is the only negative number among the given options. All the other numbers, 4 and 8, are positive.

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  • 26.