🧮 algebra

1. **State the problem:** We are given the matrix equation $$\begin{pmatrix}4 & 5 \\ 4 & 3\end{pmatrix} \begin{pmatrix}-4 \\ -2\end{pmatrix} = k \begin{pmatrix}26 \\ 22\end{pmatrix

1. **State the problem:** Simplify the expression $$(X^2 + 4)^2 - (X^2 - 2)^2$$. 2. **Formula used:** This is a difference of squares, which follows the rule $$a^2 - b^2 = (a - b)(

1. The problem is to find the equation of the line passing through the points $(-1, 2)$ and $(3, 4)$. 2. The formula for the slope $m$ of a line through two points $(x_1, y_1)$ and

1. **State the problem:** Simplify the expression $$(X - 4)^2 - (X - 2)^2$$. 2. **Recall the formula:** This is a difference of squares, which can be factored using the identity $$

1. **Problem Statement:** Given the equation $$\log(\sec A - \tan A) + \log(\sec A + \tan A) - \log(\sin^2 A + \cos^2 A) = \log k,$$ find the value of $k$. 2. **Formula and Importa

1. **State the problem:** A woman bought 210 oranges for 65 and sold them at a rate of 3 oranges for 2. We need to find the profit she made. 2. **Calculate the cost price (CP) per

1. Let's start by understanding the problem: you want an explanation using an example. 2. Suppose we want to solve the equation $2x + 3 = 7$.

1. **State the problem:** A tank contains 250 liters of water. If 96 liters are used, we need to find what percentage of the original quantity is left. 2. **Formula used:** To find

1. **State the problem:** Kofi is 2 years older than Ama, and the sum of their ages is 16. We need to find Ama's age. 2. **Define variables:** Let Ama's age be $x$ years.

1. **Problem statement:** Find the value of each expression for given values of variables. 2. **Formula and rules:** Substitute the given values into the expressions and perform ar

1. **Problem:** P varies directly as the square of Q and inversely as the cube of Z. Given P=5, Q=3, Z=1, find: (i) The relationship between P, Q, and Z.

1. The problem is to solve a quadratic equation, which generally has the form $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are constants and $a \neq 0$. 2. The formula to find the

1. **Problem statement:** Two warehouses A and B have the same workload. Alone, A takes 10 hours to move goods in warehouse A, B takes 12 hours in warehouse B, and C takes 15 hours

1. **Problem statement:** Solve the inequality $$3x^2 + 2x - 8 \leq 0$$ given that $$3x^2 + 2x - 8 = (x + 2)(3x - 4)$$. 2. **Formula and rules:** To solve quadratic inequalities, f

1. **State the problem:** Simplify the expression $$\frac{1}{2} \sqrt{2} - \sqrt{2}$$. 2. **Recall the rules:** When subtracting like terms involving square roots, treat the square

1. The problem is to understand the relationship between $-\sqrt{2}$ and $\sqrt{2}$. 2. Recall that $\sqrt{2}$ is the positive square root of 2, approximately 1.414.

1. The problem is to find the decimal value of the expression $\frac{1}{2} \sqrt{2} - \sqrt{2}$. 2. Recall that $\sqrt{2}$ is the square root of 2, approximately equal to 1.414.

1. **Problem:** Evaluate the expression without using a calculator or mathematical table: $$\frac{5}{6} \text{ of } (4 \times 1 \times 3 \times 5 \times 5 \times 6) \times \frac{5}

1. **State the problem:** Simplify the expression $$-27 + 18 - (10 - 14) - (-2)$$. 2. **Recall the rules:**

1. **State the problem:** We are given the product of three numbers is 1197, and two of the numbers are 3 and 19. We need to find the third number. 2. **Formula and rule:** The pro

1. **State the problem:** Simplify and substitute values into the expression $c = 4(x+2y) - 2x$ to find the total cost, where $x$ is the LCM of 6 and 8, and $y$ is the smallest cub