🧮 algebra

1. **State the problem:** We need to multiply and simplify the expression for total weight growth per basket given by $$W(x) = D(x) \times R(x)$$ where $$D(x) = \frac{4}{x+2}$$ and

1. The problem asks to simplify $\sqrt{32}$ and enter the simplified numerical coefficient only. 2. Recall the property of square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{

1. The problem asks us to find the values of $x$ that make the rational expression $$\frac{4}{x(x - 3)}$$ undefined. 2. A rational expression is undefined when its denominator equa

1. **State the problem:** Multiply the expressions $$\frac{x}{x+3} \cdot \frac{x+3}{4}$$. 2. **Recall the multiplication rule for fractions:** When multiplying fractions, multiply

1. The problem asks for the domain of the function $f(x) = \sqrt{x - 4}$.\n\n2. The domain of a square root function is all values of $x$ for which the expression inside the square

1. **Factorise the expression 9p^2 - q^2** This is a difference of squares, which follows the formula:

1. **State the problem:** We need to find a rational expression for the total amount of food per fasting person, given: - Rice per person: $\frac{2}{x}$ kilograms

1. The problem asks us to analyze the behavior of the graphs of the functions $f(x) = x^3 - 1$ and $g(x) = -x^3 + 1$ for large values of $x$. 2. The key idea is to understand the e

1. **State the problem:** Find real numbers $a$ and $b$ such that $a + bi = -9 + 4i$. 2. **Recall the rule:** Two complex numbers are equal if and only if their real parts are equa

1. **Stating the problem:** Understand the concept of Ratio and solve typical ratio problems seen in competitive exams like GMAT or bank job exams. 2. **Concept of Ratio:** A ratio

1. **State the problem:** Solve the system of equations using substitution: $$y = 4x - 9$$

1. **State the problem:** Solve the system of equations using the substitution method: $$-12x - 2y = -6$$

1. **State the problem:** Write the expression $$\frac{3 + i}{2 - i} + \frac{4 + 10i}{-9 + 7i}$$ in the form $$a + ib$$ where $$a$$ and $$b$$ are real numbers. 2. **Recall the form

1. **Problem statement:** We have a relation $f = \{(5nm, 3m + 3n) : m,n \in \mathbb{Z}\}$. We want to find two pairs $(m_1, n_1)$ and $(m_2, n_2)$ such that they have the same dom

1. **Problem:** Solve the rational equation $$\frac{1}{x - 1} + 5 = \frac{11}{x - 1}$$ and find restrictions on $x$. 2. **Restrictions:** The denominator $x - 1$ cannot be zero bec

1. Problem: Solve a quadratic equation of the form $ax^2 + bx + c = 0$. 2. Formula: The solutions are given by the quadratic formula:

1. **State the problem:** Solve the quadratic equation $$x^2 - 5x - 14 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where the equ

1. **State the problem:** We need to find the number of 1-peso coins and 25-centavo coins that total 20 coins and amount to 9.50 pesos.

1. The problem asks to create a graph similar to the described stepwise curve but different in values. 2. The original graph has three segments: an orange curve rising steeply from

1. Stating the problem: Solve the equation $$\frac{2}{3} + \frac{1}{a - b} = \frac{2}{3}a$$ for $a$. 2. Write down the equation:

1. **State the problem:** Simplify the expression $$\frac{a}{2x+2y} = \frac{3x+3y - b}{3x+3y}$$ and understand the relationship between the terms. 2. **Rewrite the denominators:**