MATH

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Front

How do you solve the equation 3x + 2(4x - 4) = 3?

Back

To solve for x, first distribute: 3x + 8x - 8 = 3. Combine like terms: 11x - 8 = 3. Add 8 to both sides: 11x = 11. Divide by 11: x = 1.

Front

What is the product of m⁵ and m²?

Back

The product of m⁵ and m² is m⁷, using the property of exponents that states a^m * a^n = a^(m+n).

Front

How do you solve the equation -8 = 3n + 4?

Back

To solve for n, first subtract 4 from both sides: -12 = 3n. Then divide by 3: n = -4.

Front

What is the process for adding fractions?

Back

To add fractions, find a common denominator, convert each fraction, and then add the numerators. Simplify if necessary.

Front

What is the definition of a cylinder in geometry?

Back

A cylinder is a three-dimensional shape with two parallel circular bases connected by a curved surface.

Front

What is the significance of π in calculations involving circles and cylinders?

Back

π (pi) is a mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter.

Front

How do you simplify the expression m⁵⋅m²?

Back

To simplify m⁵⋅m², use the property of exponents: m^(5+2) = m⁷.

Front

What is the method to isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean to express a fraction in lowest terms?

Back

Expressing a fraction in lowest terms means simplifying it so that the numerator and denominator have no common factors other than 1.