curiouskids

Due: Jul 27th

Questions

  1. Solve the system of equations: 4x - 3y = 18 2x + 5y = 11
  2. Solve the equation for y: 7x - 3y = 21
  3. Solve the inequality: 4x - 7 < 3(x - 2) + 5
  4. If a bus uses 8 liters of fuel for 80 kilometers, how much fuel will it use for 600 kilometers?
  5. The sum of two numbers is 60 and their product is 671. What are the numbers?
  6. How much pure water should be added to 400 ml of a 60% alcohol solution to decrease its concentration to 40%?
  7. If you cycle at 10 km/h, how far can you go in 40 minutes?
  8. A plane travels at an average speed of 750 km/h. How long will it take to travel 2250 kilometers?
  9. Solve for x: 5x^2 - 36 = 0
  10. The sum of the angles in a polygon is 1800 degrees. How many sides does the polygon have?
  11. Simplify the expression: (5x^2 - 3x + 2) - (4x^2 - 2x + 3)
  12. You invested $10,000 between two accounts. The first account pays 4% annual interest and the second pays 6% annual interest. If you earned $520 in interest after one year, how much did you invest in each account?

Solutions

  1. The system of equations 4x - 3y = 18 2x + 5y = 11 can be solved using substitution or elimination methods to yield x = 3 and y = -1.

  2. To solve 7x - 3y = 21 for y, you rearrange it to get y = (7x - 21) / 3.

  3. Solving the inequality 4x - 7 < 3(x - 2) + 5 gives x < 4.

  4. If a bus uses 8 liters of fuel for 80 kilometers, it will use 8 * (600 / 80) = 60 liters for 600 kilometers.

  5. Let’s denote the two numbers as x and y. From x + y = 60 and xy = 671, solving these equations gives x = 31 and y = 29.

  6. Let’s denote the amount of pure water to add as x (in ml). The equation is 400 * 0.60 = (400 + x) * 0.40. Solving for x gives x = 200 ml.

  7. If you cycle at 10 km/h, in 40 minutes (or 2/3 hours) you can go 10 * 2/3 = 20/3 = 6.67 km.

  8. If a plane travels at an average speed of 750 km/h, it will take 2250 / 750 = 3 hours to travel 2250 kilometers.

  9. Solving for x in 5x^2 - 36 = 0 gives x = sqrt(36/5) and x = -sqrt(36/5).

  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) = 1800 gives n = 12, so the polygon has 12 sides.

  11. Simplifying the expression (5x^2 - 3x + 2) - (4x^2 - 2x + 3) gives x^2 - x - 1.

  12. Let’s denote the amount invested in the first account as x and in the second account as 10000 - x. The equation is 0.04x + 0.06(10000 - x) = 520. Solving for x gives x = 4000. Therefore, $4000 was invested in the first account and 10000 - 4000 = 6000 was invested in the second account.

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