Explanation

Given xy = 1 and x > 0:

y = 1/x

We want to minimize x + y = x + 1/x.

Let's find the minimum value:

Let f(x) = x + 1/x

f'(x) = 1 - 1/x² = 0 for minimum

x² = 1

x = 1 (since x > 0)

f(1) = 1 + 1/1 = 2

The minimum value of x + y is 2.

Explanation

Let the two consecutive odd numbers be x and x + 2.

Given x² + (x + 2)² = 394:

x² + x² + 4x + 4 = 394

2x² + 4x - 390 = 0

x² + 2x - 195 = 0

(x + 15)(x - 13) = 0

x = -15 or x = 13

For x = 13, the numbers are 13 and 15.

13² + 15² = 169 + 225 = 394

The sum of the numbers is 13 + 15 = 28.

Explanation

The given equation is:

5x - 10 = 35

Add 10 to both sides:

5x = 45

Divide by 5:

x = 9

Explanation

To evaluate the expression, follow the order of operations:

Multiply 3 and 3: 3 × 3 = 9

Divide 9 by 3: 9/3 = 3

Add 3 and 3: 3 + 3 = 6

Explanation

A regular polygon has all sides and angles equal.

Among triangles, only an equilateral triangle has all three sides and angles equal, making it a regular polygon.

Explanation

Explanation

Pythagoras was an ancient Greek mathematician and philosopher.

He is famous for the Pythagorean Theorem, which relates to right-angled triangles.

Explanation

The statement 3 < 0 is false, since 3 is greater than 0.

Therefore, it's a false sentence, as it has a definite truth value (false).

Explanation

At 45°, the sine and cosine of the angle are equal (sin 45° = cos 45° ≈ 0.707), so the x and y components of the force are equal.

This is because Fx = Fcosθ and Fy = Fsinθ; they are equal only when cosθ = sinθ.

Explanation

"Percent" means per hundred, so 1% = 1 ÷ 100

It can also be written as a decimal: 0.01.