Questions

Solve a number pyramid problem where each middle/top number is the sum of two below. Given top 40, bottom 7, ★, 9, find ★ + ♥ using addition and algebraic reasoning.

Step - by - step solution to solve the linear equation \( 5x - 3 = 2x + 9 \) for \( x \), using properties of equality to isolate the variable.

Step - by - step solution to completely factor the quadratic expression \( x^2 - 4x - 21 \) by finding two numbers that multiply to \( -21 \) and add to \( -4 \).

Step-by-step solution to the system of linear equations \( \\begin{cases} 2x + y = 8 \\\\ x - y = 1 \\end{cases} \) using the elimination method, resulting in the solution \( x = 3 \) and \( y = 2 \).

Solve for the hypotenuse of a right triangle with legs 5 cm and 12 cm using the Pythagorean theorem. Learn the steps to calculate the hypotenuse and apply geometric concepts in junior high mathematics.

Calculate the probability of choosing a non - blue ball from a bag with 4 red, 3 blue, and 5 green balls. Learn the steps to find total and favorable outcomes, apply the probability formula, and simplify fractions in junior high mathematics.

Learn how to simplify the polynomial expression (4x³ - 2x² + 5x - 1) - (x³ + 3x² - 2x + 4) by distributing the subtraction sign and combining like terms. Step-by-step solution included.

Learn how to solve the linear equation \( 3x + 7 = 22 \) for \( x \) using inverse operations (subtraction and division) while maintaining equation balance, typical of junior high school algebra.

This problem shows how to solve the linear equation \( 3x + 7 = 22 \) for \( x \). The solution involves using the properties of equality to isolate \( x \), resulting in \( x = 5 \). It covers concepts of linear equations in one variable, properties of equality, and algebraic manipulation.

Step-by-step solution to simplify the polynomial expression \((4x^3 - 2x^2 + 5x - 1) - (x^3 + 3x^2 - 2x + 4)\) using the distributive property (subtraction rule) and combining like terms, resulting in \(3x^3 - 5x^2 + 7x - 5\).

This problem requires balancing the chemical equation CH₄ + Cl₂ → CCl₄ + HCl. The solution uses element conservation (C, H, Cl) to determine coefficients: 1 CH₄, 4 Cl₂, 1 CCl₄, and 4 HCl, following the Law of Conservation of Mass.

This problem is about finding the slope of a line passing through the points (-2, 1) and (3, 1) in coordinate geometry. It is solved using the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \), and the resulting slope is 0.