Soal Latihan Matematika Kelas Xii

Explanation
To find the value of 2x + 3y, we need to solve the given system of equations. By solving the equations 4x + y = 9 and x + 4y = 6 simultaneously, we can find the values of x and y. After solving, we find that x = 2 and y = 1. Plugging these values into the expression 2x + 3y gives us 2(2) + 3(1) = 4 + 3 = 7. Therefore, the value of 2x + 3y is 7.

Explanation
The question provides the dimensions of a rectangular prism, specifically the lengths of AB, BC, and AE. To find the distance from D to F, we can use the Pythagorean theorem. We can consider the line segment DF as the hypotenuse of a right triangle, with DE as one leg and EF as the other leg. Using the given dimensions, we can calculate DE as 4 cm and EF as 3 cm. Applying the Pythagorean theorem, we find that DF is equal to the square root of 61 cm. Therefore, the correct answer is √61 cm.

Explanation
The given equation 2x - 3y + 8 = 0 represents a line in the form of Ax + By + C = 0. To find a line that is perpendicular to this line and passes through the point (-3, 2), we need to find the negative reciprocal of the slope of the given line. The slope of the given line is 2/3, so the negative reciprocal is -3/2. Using the point-slope form of a line, we can substitute the slope and the point into the equation y - y1 = m(x - x1) to find the equation of the perpendicular line. After simplifying, we get 3x + 2y + 5 = 0.

Explanation
The given information states that the price of a plate is twice the price of a glass. It also states that the total price of 6 plates and 14 glasses is Rp39,000. To find the price of 1 dozen glasses, we need to determine the price of 1 glass first. Let's assume the price of 1 glass is x. Therefore, the price of 1 plate would be 2x. According to the given information, 6 plates would cost 6*(2x) = 12x, and 14 glasses would cost 14*x. Since the total price of 6 plates and 14 glasses is Rp39,000, we can write the equation as 12x + 14x = 39,000. Simplifying the equation, we get 26x = 39,000. Dividing both sides by 26, we find x = 1,500. Therefore, the price of 1 dozen glasses (12 glasses) would be 12*x = 12*1,500 = Rp18,000.

Explanation
The given function h(t) represents the height of the bullet at time t. To find the maximum height, we need to find the vertex of the parabolic function. The vertex of a parabola in the form of h(t) = at^2 + bt + c is given by the formula t = -b/2a. In this case, a = -4 and b = 40. Plugging in these values, we get t = -40/(-8) = 5. Substituting t = 5 into the function, we get h(5) = 100 + 40(5) - 4(5^2) = 200. Therefore, the maximum height the bullet can reach is 200 m.

Explanation
The growth of the number of wereng follows a geometric sequence. To find the number of wereng on day 5, we can use the formula for the nth term of a geometric sequence: an = a1 * r^(n-1), where a1 is the first term, r is the common ratio, and n is the term number. In this case, a1 is 18, and the common ratio can be found by dividing the number of wereng on the last day (4,374) by the number of wereng on the second day (18). The common ratio is approximately 243, so the number of wereng on day 5 is 18 * 243^(5-1) = 486.

Explanation
The ability of a farmer to process waste into compost is increasing day by day. On the first day, the farmer was able to process 2m3 of waste, on the second day 5m3, and on the third day 8m3. Since the pattern is increasing by 3 each day, we can continue the pattern to find the amount of waste the farmer can process on the 10th day. By adding 3 to each previous day's amount, we get 11m3 on the fourth day, 14m3 on the fifth day, and so on. Continuing this pattern, on the 10th day, the farmer would be able to process 29m3 of waste. Therefore, the correct answer is 155m3.

Explanation
Based on the given diagram, the number of students who like green is 19. The diagram does not provide the exact number of students who like blue. However, based on the pattern in the diagram, the number of students who like blue appears to be one more than the number of students who like green. Therefore, the correct answer is 22.

Explanation
The correct answer is y = -x2 + 4x + 5. This is because the equation matches the given equation in the question.

Explanation
Based on the given information, we know that triangle ABC is an isosceles triangle with AB = BC. The length of AB is given as 6 cm. Since the triangle is isosceles, the angles opposite the equal sides are also equal. Therefore, angle ABC is also 120 degrees. To find the length of AC, we can use the sine rule which states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and angles in a triangle. Using the sine rule, we can find that AC = AB/sin(ABC) = 6/sin(120) = 6√3.