Since 5² + 12² = 13², it is a right triangle.

Check using the Pythagorean theorem: 15² = 9² + 12², 225 = 81 + 144, 225 = 225. It is a right triangle.

In an isosceles right triangle, the angles opposite the equal legs are both 45 degrees.

If the lengths of two tangents from an external point are equal, the point must be outside the circle.

The report should be completed by Thursday to be ready for the meeting on Monday.

Shape A will appear when the paper is folded in half along the specified line.

The pattern increases by 2, so the next number is 10.

The concentration of hydrogen ions [H+] is 10^(-pH) = 10^(-3) = 0.001 M.

'Mock' is a synonym of 'tease', as both involve making fun of someone.

To joke is a synonym for teasing someone.

Being indecisive is synonymous with remaining neutral, as it implies not making a decision.

Percentage increase = ((25 - 20) / 20) * 100 = 25%

Percentage increase = ((60 - 50) / 50) * 100 = 20%

Let the original price be x. Then, x + 0.2x = 60, which gives x = 60/1.2 = $50.

New price after increase = 40 + 25% of 40 = 50; New price after decrease = 50 - 20% of 50 = 40.

ROI = ((Final price - Initial price) / Initial price) * 100 = ((75 - 50) / 50) * 100 = 50%

For no real roots, the discriminant must be less than zero: 2^2 - 4*1*k < 0, thus k > 1.

Using the tangent length formula: length = √(distance from center² - radius²) = √(10² - 7²) = √(100 - 49) = √51, which is approximately 7.14.

Using the tangent length formula: length = √(distance from center² - radius²) = √(10² - 7²) = √(100 - 49) = √51 ≈ 7.14.

Let the number of girls be 2x. Then, 3x = 15; x = 5. Number of girls = 2x = 10.

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 56, 7x = 56, x = 8. A's age = 3x = 24.

Let the length of the first rectangle = 5x and the second = 7x. Given 5x = 25, x = 5. Therefore, length of the second rectangle = 7x = 7*5 = 35.

Let the lengths be 7x and 4x. Given 7x = 28, x = 4. Therefore, the length of the second rectangle = 4x = 4*4 = 16.

Let the lengths be 5x and 7x. Given 5x + 7x = 72, 12x = 72, x = 6. Therefore, shorter rope = 5x = 5*6 = 30.

Let the sides be 3x and 5x. Then, 3x + 5x = 64, 8x = 64, x = 8. Therefore, the longer side = 5x = 5*8 = 40.

Let the shorter side be 7x and the longer side be 9x. Given 9x = 36, x = 4. Therefore, shorter side = 7x = 7*4 = 28.

Let apples = 7x and oranges = 3x. Given 7x = 42, x = 6. Therefore, oranges = 3x = 3*6 = 18.

Let speeds be 5x and 7x. Given 7x = 140, x = 20. Slower car's speed = 5x = 5*20 = 100 km.

Let the numbers be 7x and 9x. Then, 7x + 9x = 128, 16x = 128, x = 8. Therefore, the numbers are 7*8 = 56 and 9*8 = 72.

Let the numbers be 7x and 9x. Then, 7x + 9x = 128, 16x = 128, x = 8. Larger number = 9x = 9*8 = 72.