A triangle with sides 3 cm, 4 cm, and 5 cm satisfies the Pythagorean theorem (3² + 4² = 5²), thus it is a right-angled triangle.

Using the Pythagorean theorem, 7² + 24² = 49 + 576 = 625 = 25², thus it is a right triangle.

Speed = Distance / Time = 90 km / 1.5 hours = 60 km/h.

The leading zeros are not significant. Therefore, 0.050 kg has 2 significant figures.

'Barking up the wrong tree' means to pursue a mistaken or misguided course of action.

'On cloud nine' means to be in a state of blissful happiness.

'Under the weather' is an idiom that means someone is feeling ill or unwell.

'Under the weather' means feeling ill or unwell.

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

'Hit the nail on the head' means to describe exactly what is causing a situation or to be very accurate in one's assessment.

'Let the cat out of the bag' means to accidentally reveal a secret.

'Spill the beans' means to reveal confidential information or secrets.

'A chip on their shoulder' means to have a grudge or to be angry about something.

'On cloud nine' is an idiom that signifies being in a state of extreme happiness.

The area of a triangle is given by (1/2) * base * height. Thus, 60 = (1/2) * 10 * height. Solving for height gives height = 12 units.

Average = Total Sum / Number of Items. Therefore, Total Sum = Average × Number of Items = 20 × 5 = 100.

Circumference = 2πr. Setting 31.4 = 2 × 3.14 × r gives r = 5 units.

The circumference C = 2πr. Setting 31.4 = 2 * 3.14 * r gives r = 5.

Circumference = π * diameter = π * 10.0 cm ≈ 31.4 cm. Uncertainty in circumference = π * 0.1 cm ≈ 0.314 cm.

Perimeter P = 2(length + width). So, 20 = 2(6 + width). Solving gives width = 4 cm.

Perimeter P = 2(length + width). So, 30 = 2(10 + width). Dividing by 2 gives 15 = 10 + width. Thus, width = 15 - 10 = 5 cm.

The perimeter of a square is given by 4 times the length of one side. Therefore, if the perimeter is 36 cm, the length of one side is 36 cm / 4 = 9 cm.

Perimeter of a square = 4 × side. Therefore, 4 × side = 64 cm, giving side = 64/4 = 16 cm.

Let the original price be x. Then, x - 0.2x = 40, which gives 0.8x = 40. Thus, x = 40 / 0.8 = $50.

Circumference = 2πr = 2π × 7 cm = 14π cm.

Circumference = 2πr = 2 × 3.14 × 7 cm = 43.96 cm.

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 28, so 7x = 28, giving x = 4. Thus, A's age = 3x = 12.

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 70, giving 7x = 70, so x = 10. Thus, A's age = 3x = 30.

If the shorter side is 9 cm and the ratio is 3:4, then the longer side is (4/3) × 9 cm = 12 cm.

The third angle can be found by subtracting the sum of the other two angles from 180 degrees: 180 - (50 + 70) = 60 degrees.