🧮 algebra

1. **State the problem:** Solve the quadratic inequality $$2x^2 \geq 5x - 3$$. 2. **Set one side to zero (standard form):**

1. The problem is to understand how to write a fraction bar in math expressions. 2. A fraction bar is used to represent division between two numbers or expressions.

1. Problem: Find the average rate of the plane in still air and the average rate of the wind given the airplane travels 450 miles with the wind in 3 hours and against the wind in 5

1. **Problem:** Solve the quadratic equation $x^2 - 7x + 12 = 0$ by factorising. 2. **Formula and rules:** To solve quadratic equations by factorising, express the quadratic in the

1. **Problem Statement:** Plot the given numbers $$\frac{13}{20}$$, $$-\frac{1}{7}$$, $$0.40$$, $$10\%$$, and $$2.25$$ on a number line and identify their positions as rational num

1. **State the problem:** We need to find the values of $k$ such that the x-axis ($y=0$) is tangent to the curve given by $$y = x^2 - (k+3)x + (3k + 4).$$ 2. **Understand the condi

1. **State the problem:** Find values of $k$ such that the line $y = kx + 1$ is tangent to the curve $y = x^2 - 7x + 2$. 2. **Formula and rules:** For tangency, the line and curve

1. Let's start with a math problem to solve. 2. Problem: Solve for $x$ in the equation $$2x + 3 = 11$$.

1. The problem is to understand the concept of distribution in mathematics. 2. Distribution often refers to the distributive property in algebra, which states that for any numbers

1. **समस्या:** एउटा घडी $4500$ मा बिक्री गर्दा $12\%$ नाफा भयो भने खरिद मूल्य कति हुन्छ? 2. **सूत्र:**

1. **Problem:** Multiply $(x-1)(x-2)$. 2. **Formula:** Use distributive property: $(a+b)(c+d) = ac + ad + bc + bd$.

1. **State the problem:** Find the equation of line N in the form $y = mx + c$ given it crosses the y-axis at $20$ and passes through the point $(1, 35)$. 2. **Recall the formula:*

1. **Problem Statement:** Given a linear function, find the equation of a line parallel or perpendicular to it passing through a specific point.

1. **State the problem:** Find the equation of the straight line passing through points $(0,4)$ and $(1,-1)$ in the form $y = mx + c$. 2. **Formula used:** The equation of a line i

1. Resolver la expresión $\dfrac{(2^3 \cdot x^{-2})^2}{x^4}$: $$\text{Primero, simplificamos el numerador:}$$

1. **Problem Statement:** A student saves money weekly starting with $50$ in the first week and increases the saving by $15$ each subsequent week. This forms an arithmetic sequence

1. **State the problem:** A student saves money weekly starting with $50$ in the first week and increases the amount saved by $15$ each subsequent week. This forms an arithmetic se

1. **State the problem:** Solve the inequality $$6x^2 + x - 2 \le 0$$. 2. **Identify the type of inequality:** This is a quadratic inequality of the form $$ax^2 + bx + c \le 0$$ wh

1. **State the problem:** Solve the inequality $$x^2 - 7x + 12 > 0$$. 2. **Recall the formula and rules:** This is a quadratic inequality. To solve it, first find the roots of the

1. **State the problem:** Solve the quadratic inequality $ax^2 + bx + c > 0$ (or $< 0$, $\geq 0$, $\leq 0$) where $a$, $b$, and $c$ are constants. 2. **Formula and rules:** The sol

1. **Problem 1: Find the sum of the first 20 terms of the sequence 21 + 16 + 11 + ...** 2. This is an arithmetic sequence where the first term $a_1 = 21$ and the common difference