Explanation

To evaluate the expression:

2/3 × 1/2 ÷ 1/3

First, multiply 2/3 and 1/2:

(2/3) × (1/2) = 2/6 = 1/3

Then, divide the result by 1/3:

(1/3) ÷ (1/3) = 1

Explanation

To divide (3x³ - 19x² + 10x + 50) by (x - 5), let's perform polynomial division:

1. Divide 3x³ by x: 3x²

2. Multiply (x - 5) by 3x²: 3x³ - 15x²

3. Subtract: -19x² + 15x² = -4x², bring down 10x

4. Divide -4x² by x: -4x

5. Multiply (x - 5) by -4x: -4x² + 20x

6. Subtract: 10x - 20x = -10x, bring down 50

7. Divide -10x by x: -10

8. Multiply (x - 5) by -10: -10x + 50

9. Subtract: 0

The quotient is:

3x² - 4x - 10

Explanation

To find 50% of 55:

50% of 55 = 0.5 * 55

= 27.5

Explanation

Expanded form is writing a number as the sum of the place values of its digits.

For example, 345 would be written as 300 + 40 + 5 in expanded form.

Explanation

An open sentence contains a variable (like x) and becomes either true or false only when a value is assigned.

x < 3 is open because its truth depends on the value of x.

Explanation

Given:

a + b = 4

ab = 3

The formula for a^3 + b^3 is:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

However, a simpler approach uses the identity:

a^3 + b^3 = (a + b)^3 - 3ab(a + b)

Plugging in the values:

a^3 + b^3 = (4)^3 - 3(3)(4)

= 64 - 36

= 28

Explanation

The expression (x^2 + 2) / (x^2 + 2x + 2) is an improper fraction.

Because the degree of the numerator is equal to the degree of the denominator.

Explanation

Area of a pizza (circle) = π × r², where r = b

With crust thickness a, and using π ≈ n,

Value (volume-like expression) becomes:

n × b² × a = nb²a

Explanation

The first five positive odd integers are:

1, 3, 5, 7, 9

Let's calculate their sum:

1 + 3 = 4

4 + 5 = 9

9 + 7 = 16

16 + 9 = 25

The sum is:

25

Explanation

Prime factors of 6 = 2 × 3

Prime factors of 14 = 2 × 7

LCM = 2 × 3 × 7 = 42