🧮 algebra

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 $x > -2$.

1. The problem states that the function $f(x) = \cos(x)$ is transformed by stretching it horizontally by a factor of 4 and shifting it 1 unit up. 2. The formula for horizontal stre

1. **Problem statement:** We analyze Kiran's distance from home over time based on the piecewise graph. 2. **Given:**

1. **State the problem:** Emily spent 8 on snacks and bought movie tickets for herself and a friend. Each ticket costs 12. She spent a total of 32. We need to find how many movie t

1. **State the problem:** We want to find the price of a 1.8 kg cheese block given that a 2.3 kg cheese block costs 394.75. 2. **Formula used:** Price is proportional to weight, so

1. **Stating the problem:** We have a 2.3 kg block of mozzarella cheese that costs 394.75. We want to find the cost of 500 g of the same cheese. 2. **Formula used:** To find the co

1. **Problem Statement:** We are given a step graph showing the cost in dollars to mail a letter from the US to Canada in 2018 as a function of the letter's weight in ounces.

1. **State the problem:** We have a piecewise function $g(x)$ defined on several intervals with some missing parts. We need to:

1. The problem asks whether it is always, sometimes, or never true that two different patterns can look the same for the first few terms but differ later. 2. Let's clarify what a "

1. **Enunciado do problema:** Determine o valor aproximado do grau da amplitude do ângulo formado pelos vetores \(\vec{u} = (2, -3)\) e \(\vec{v} = (1, 4)\). 2. **Fórmula usada:**