Let the two-digit number be 10a + b, where a is the tens digit and b is the units digit. We have a + b = 9 and 10a + b = 4(a + b). Solving these gives a = 4 and b = 5, so the number is 45.

The sum of the first n natural numbers is given by the formula n(n + 1)/2 = 255. Solving n(n + 1) = 510, we find n = 16.

The sum of the first n natural numbers is given by the formula n(n + 1)/2. Setting this equal to 2550, we have n(n + 1) = 5100. Solving the quadratic equation n^2 + n - 5100 = 0 gives n = 50.

Let the integers be n, n+1, n+2. Then n + (n+1) + (n+2) = 72. Solving gives 3n + 3 = 72, so n = 24.

Let the other number be x. Then, 9 + x = 15. Thus, x = 15 - 9 = 6.

Let the two numbers be x and y. We have x + y = 15 and xy = 50. Solving these equations gives the larger number as 10.

Let the other number be x. Then, x + 12 = 20. So, x = 20 - 12 = 8.

Let the numbers be x and y. We have x + y = 30 and x - y = 10. Solving these gives x = 20 and y = 10.

Relative error = (Uncertainty / Measured value) * 100 = (0.5 / 50.0) * 100 = 1%.

Substituting x = 3 into the expression: 2(3^2) + 3(3) - 5 = 2(9) + 9 - 5 = 18 + 9 - 5 = 22.

Maximum possible mass = Measured mass + Uncertainty = 2.50 kg + 0.05 kg = 2.55 kg.

In a triangle, the sum of angles is 180 degrees. If one angle is 90 degrees, the other two angles must sum to 90 degrees. Therefore, each of the equal angles is 45 degrees.

The number 100.0 has 1 decimal place, so the answer should also be rounded to 1 decimal place.

The number with the least decimal places is 0.3 (1 decimal place), so the answer should be rounded to 1 decimal place.

The result of 3.4567 + 2.1 is 5.5567. However, since 2.1 has only 2 significant figures after the decimal, the result should be rounded to 5.6, which has 3 significant figures.

The number 3.4567 has 4 significant figures. The leading digit is not counted as significant.

To find x, subtract 5 from both sides: 3x = 20 - 5 = 15. Then divide by 3: x = 15 / 3 = 5.

To solve for x, subtract 2x from both sides: 3x - 2x = 10 - 5, which simplifies to x = 5.

The term 2.1 × 10^2 has 2 significant figures, so the final answer should be rounded to 2 significant figures.

Substituting x = 2 into the equation gives 5(2) + 3y = 15, which simplifies to 10 + 3y = 15. Thus, 3y = 5, and y = 5/3.

Substituting x = 2 into the equation gives 5(2) + 3y = 20. This simplifies to 10 + 3y = 20, leading to 3y = 10, thus y = 10/3, which is approximately 3.33. The closest integer option is 4.

Area = (1/2) * base * height. Thus, 60 = (1/2) * 10 * height, giving height = 12 cm.

Let the integers be n and n+1. Then n(n+1) = 240. Solving the quadratic equation n^2 + n - 240 = 0 gives n = 14, so the integers are 14 and 15.

If A's age is 12, then B's age = (4/3) * 12 = 16 years.

'Burn the midnight oil' means to work late into the night, usually to study or complete a task.

'Burning the midnight oil' means to stay up late working or studying.

'Cost an arm and a leg' means to be very expensive.

'Costs an arm and a leg' means something is very expensive.

'Costs an arm and a leg' means that something is very expensive.

'Hit the nail on the head' means to describe exactly what is causing a situation or problem.