🧮 algebra

1. **State the problem:** We are given a proportional relationship between variables $a$ and $b$ with values $a = 0.6, 1.0, 1.5, 2$ and $b = 20.8, 34, 56, 92$. We need to write the

1. **State the problem:** Find the square root of the complex number $8 - 6i$. 2. **Formula and approach:** To find the square root of a complex number $z = a + bi$, we look for $x

1. **State the problem:** We are given a table showing a proportional relationship between $x$ and $y$:

1. **State the problem:** Simplify the expression $-5(3p - 2n + 6m^2)$. 2. **Recall the distributive property:** For any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This means

1. Énonçons le problème : Trouver le domaine de la fonction définie par morceaux $$f(x) = \begin{cases} 6x - 1 & \text{si } x \geq 6 \\ \frac{1}{x - 3} & \text{si } 3 \leq x < 6 \\

1. **State the problem:** We have the function $f(x) = 6x - 50$ which represents the profit in dollars when selling $x$ shirts. We need to find $f(-2)$, $f(7)$, and $f(12.5)$ and i

1. The problem is to simplify the expression $5^4 \cdot 5^2$. 2. We use the rule of exponents that states when multiplying powers with the same base, we add the exponents: $$a^m \c

1. **State the problem:** We have the function $f(x) = 10000 + 1000x$ which represents financial aid amount based on the number of siblings $x$ in the household.

1. Énoncé du problème : On effectue le changement de variable $X = \cos x$ pour transformer une équation trigonométrique en une équation polynomiale du second degré $L_1$ équivalen

1. **State the problem:** Simplify the expression $$\frac{-3 - \sqrt{80}}{6}$$. 2. **Recall the rules:** To simplify, first simplify the square root if possible, then simplify the

1. **State the problem:** Solve the quadratic equation $$2x^2 + 3x - 20 = 0$$. 2. **Formula and rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we can use

1. The problem is to simplify the expression $$\sqrt{18x^3y^2z}$$ assuming all variables are positive. 2. Recall the property of square roots: $$\sqrt{a \cdot b} = \sqrt{a} \cdot \

1. **بيان المشكلة:** لدينا دالتان ممثلتان بيانياً في السؤالين (د) و (هـ). المطلوب:

1. **State the problem:** Factorise the quadratic expression $6x^2 + 11x + 4$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that mu

1. **State the problem:** Simplify the expression $3(-3)-4-5(-3)2^2$. 2. **Recall order of operations:** Calculate exponents first, then multiplication and division from left to ri

1. **State the problem:** Solve the inequality $$|2x - 7| < 1$$ and identify the correct graph for the solution. 2. **Recall the definition of absolute value inequality:** For $$|A

1. **Problem Statement:** Solve the equation $2x + 3 = 11$ for $x$. 2. **Formula and Rules:** To solve a linear equation, isolate the variable on one side by performing inverse ope

1. **Problem 1: Simplify the polynomial expression** Given: $$P(x) = (3x - 2)(2x^2 + 2x + 3) + 7$$

1. **State the problem:** Solve the inequality $$|2x - 7| < 1$$ and graph the solution. 2. **Recall the definition of absolute value inequality:** For $$|A| < B$$ where $$B > 0$$,

1. The problem asks whether "all real solutions" is ever an option when solving an absolute value equation or inequality. 2. Recall that an absolute value equation or inequality in

1. The problem asks whether the solution $x < 4$ or $x > -2$ has no solution. 2. Let's analyze the inequality $x < 4$ or $x > -2$.