curiouskids

Due: Jul 29th

Questions

  1. Solve the system of equations: 2x - 5y = 15 4x + 3y = 21
  2. Solve the equation for y: 9x - 3y = 27
  3. Solve the inequality: 6x - 4 > 5(x - 2) + 1
  4. If a motorcycle uses 3 liters of fuel for 80 kilometers, how much fuel will it use for 360 kilometers?
  5. The sum of two numbers is 45 and their quotient is 5. What are the numbers?
  6. How much pure water should be added to 600 ml of a 40% alcohol solution to decrease its concentration to 30%?
  7. If you walk at 4 km/h, how far can you go in 45 minutes?
  8. A rocket travels at an average speed of 3000 km/h. How long will it take to travel 15000 kilometers?
  9. Solve for x: 7x^2 - 64 = 0
  10. The sum of the angles in a polygon is 1080 degrees. How many sides does the polygon have?
  11. Simplify the expression: (5x^2 - x + 4) - (3x^2 + 2x - 5)
  12. You invested $15,000 between two accounts. The first account pays 3.5% annual interest and the second pays 5.5% annual interest. If you earned $675 in interest after one year, how much did you invest in each account?

Solution

  1. The system of equations 2x - 5y = 15 4x + 3y = 21 can be solved using substitution or elimination methods to yield x = 3 and y = -1.

  2. To solve 9x - 3y = 27 for y, you rearrange it to get y = (9x - 27) / 3.

  3. Solving the inequality 6x - 4 > 5(x - 2) + 1 gives x > 7/6.

  4. If a motorcycle uses 3 liters of fuel for 80 kilometers, it will use 3 * (360 / 80) = 13.5 liters for 360 kilometers.

  5. Let’s denote the two numbers as x and y. From x + y = 45 and x / y = 5, solving these equations gives x = 40 and y = 5.

  6. Let’s denote the amount of pure water to add as x (in ml). The equation is 600 * 0.40 = (600 + x) * 0.30. Solving for x gives x = 200 ml.

  7. If you walk at 4 km/h, in 45 minutes (or 0.75 hours) you can go 4 * 0.75 = 3 km.

  8. If a rocket travels at an average speed of 3000 km/h, it will take 15000 / 3000 = 5 hours to travel 15000 kilometers.

  9. Solving for x in 7x^2 - 64 = 0 gives x = sqrt(64/7) and x = -sqrt(64/7).

  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) = 1080 gives n = 8, so the polygon has 8 sides.

  11. Simplifying the expression (5x^2 - x + 4) - (3x^2 + 2x - 5) gives 2x^2 - 3x + 9.

  12. Let’s denote the amount invested in the first account as x and in the second account as 15000 - x. The equation is 0.035x + 0.055(15000 - x) = 675. Solving for x gives x = 7500. Therefore, $7500 was invested in the first account and 15000 - 7500 = 7500 was invested in the second account.

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