curiouskids

Due: Jul 28th

Questions

  1. Solve the system of equations: 5x + 2y = 25 3x - 4y = 14
  2. Solve the equation for y: 8x - 4y = 24
  3. Solve the inequality: 5x - 6 > 4(x - 1) + 3
  4. If a truck uses 12 liters of fuel for 100 kilometers, how much fuel will it use for 750 kilometers?
  5. The difference of two numbers is 25 and their product is 780. What are the numbers?
  6. How much pure alcohol should be added to 500 ml of a 30% alcohol solution to increase its concentration to 50%?
  7. If you swim at 5 km/h, how far can you go in 30 minutes?
  8. A ship travels at an average speed of 30 km/h. How long will it take to travel 450 kilometers?
  9. Solve for x: 6x^2 - 49 = 0
  10. The sum of the angles in a polygon is 1440 degrees. How many sides does the polygon have?
  11. Simplify the expression: (4x^2 + 2x - 3) - (3x^2 - x + 4)
  12. You invested $12,000 between two accounts. The first account pays 2.5% annual interest and the second pays 4.5% annual interest. If you earned $430 in interest after one year, how much did you invest in each account?

Solutions

  1. The system of equations 5x + 2y = 25 3x - 4y = 14 can be solved using substitution or elimination methods to yield x = 5 and y = 0.

  2. To solve 8x - 4y = 24 for y, you rearrange it to get y = (8x - 24) / 4.

  3. Solving the inequality 5x - 6 > 4(x - 1) + 3 gives x > 5/2.

  4. If a truck uses 12 liters of fuel for 100 kilometers, it will use 12 * (750 / 100) = 90 liters for 750 kilometers.

  5. Let’s denote the two numbers as x and y. From x - y = 25 and xy = 780, solving these equations gives x = 45 and y = 20.

  6. Let’s denote the amount of pure alcohol to add as x (in ml). The equation is 500 * 0.30 + x = (500 + x) * 0.50. Solving for x gives x = 250 ml.

  7. If you swim at 5 km/h, in 30 minutes (or 0.5 hours) you can go 5 * 0.5 = 2.5 km.

  8. If a ship travels at an average speed of 30 km/h, it will take 450 / 30 = 15 hours to travel 450 kilometers.

  9. Solving for x in 6x^2 - 49 = 0 gives x = sqrt(49/6) and x = -sqrt(49/6).

  10. The sum of the angles in a polygon is 180(n - 2) degrees, where n is the number of sides. Solving 180(n - 2) = 1440 gives n = 10, so the polygon has 10 sides.

  11. Simplifying the expression (4x^2 + 2x - 3) - (3x^2 - x + 4) gives x^2 + 3x - 7.

  12. Let’s denote the amount invested in the first account as x and in the second account as 12000 - x. The equation is 0.025x + 0.045(12000 - x) = 430. Solving for x gives x = 4000. Therefore, $4000 was invested in the first account and 12000 - 4000 = 8000 was invested in the second account.

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