Sugeng Ulangan Pertidaksamaan Linier Dan Matrik

Umur Sani 7 tahun lebih tua dari umur Ari. Jika kita letakkan umur Ari sebagai X, maka umur Sani akan menjadi X + 7. Jumlah umur mereka adalah 43 tahun, jadi kita dapat membuat persamaan X + (X + 7) = 43. Menggabungkan X dan X + 7, kita dapatkan 2X + 7 = 43. Mengurangi 7 dari kedua sisi persamaan, kita dapatkan 2X = 36. Membagi kedua sisi dengan 2, kita dapatkan X = 18, yang merupakan umur Ari. Umur Sani adalah X + 7 = 18 + 7 = 25. Oleh karena itu, umur masing-masing adalah Sani 25 tahun dan Ari 18 tahun.

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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.

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.

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.

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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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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The answer is 16 because the given statement "Diketahui bahwa P = Q" implies that the values in matrix P and matrix Q are equal. Looking at the given matrix, we can see that the value of a is 24, b is 20, x is 18, and y is 16. Adding these values together, we get 24 + 20 + 18 + 16 = 78. Therefore, the correct answer is 78.

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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.

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

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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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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The correct answer is x + y ≤ 12, 2x + 5y ≥ 40, x ≥ 0, y ≥ 0. This answer correctly represents the system of inequalities given. The first inequality, x + y ≤ 12, indicates that the sum of x and y must be less than or equal to 12. The second inequality, 2x + 5y ≥ 40, states that twice the value of x plus five times the value of y must be greater than or equal to 40. The third and fourth inequalities, x ≥ 0 and y ≥ 0, specify that x and y must be greater than or equal to zero.

The given answer, 9/4, is the result of subtracting 15/4 from 15/4.

The given matrix represents a system of equations where the variables a, b, c, and d are being added together. The sum of these variables is equal to the number in the answer, which is 3. Therefore, the correct answer is 3.

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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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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.

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.

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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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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