🧮 algebra

1. **State the problem:** We are given the equation $-4(2n + 8) = -12$ and need to find the value of $n$. 2. **Write the equation:**

1. El problema nos da el foco $F = (2, -\frac{111}{16})$ y la directriz $y = -\frac{113}{16}$ de una parábola. 2. La fórmula estándar para una parábola con eje vertical es:

1. **State the problem:** Solve the exponential equations in Set 2 by expressing both sides with common bases and then equate the exponents. 2. **Recall the rule:** If $a^m = a^n$

1. **Stating the problem:** Solve the inequality $$\frac{1}{2}\left(x-\frac{2}{3}\right)^2 + x\left(x-\frac{2}{3}\right)\left(x+\frac{2}{3}\right) - x^3 \ge \frac{x}{2}\left(x-\fra

1. The problem asks to find the value of $f(7) + 9 \cdot g(-1)$.\n\n2. We need to find the values of $f(7)$ and $g(-1)$ from the given graphs.\n\n3. From the solid blue graph (whic

1. **State the problem:** We are given that the measure of an angle is five times the measure of its complementary angle. We need to find the measures of both angles. 2. **Recall d

1. **State the problem:** We are given that the measure of an angle is forty-four times the measure of its supplementary angle. We need to find the measure of each angle. 2. **Reca

1. **State the problem:** Solve the inequality $4 - 2x \leq 14$ for $x$. 2. **Write the inequality:**

1. **State the problem:** Solve the inequality $$2(x - 1) + 4x \leq 10$$. 2. **Expand and simplify:** Apply the distributive property to expand $$2(x - 1)$$:

1. Il problema è risolvere l'equazione fratta: $$\frac{x - 1}{x} = \frac{1}{x+1} + \frac{2 + x}{x^2 + x}$$

1. **Problem:** Divide the polynomial $x^3 - 7x - 17$ by $x - 8$. 2. **Formula and Rules:** Polynomial division is similar to long division with numbers. We divide the highest degr

1. **Stating the problem:** We are given a table showing the amount of a drug in a person's system over time and asked to determine if the relationship is linear or exponential, an

1. **State the problem:** Solve the equation $$\sqrt{3^x \sqrt{9^{x^2-1}}} = 3^{\frac{x+1}{4}}$$. 2. **Rewrite the equation using exponent rules:** Note that $$9 = 3^2$$, so $$9^{x

1. Problemet: Vi ska hitta fem heltal som har medelvärdet 11, medianen 10 och 9 som enda typvärde. 2. Definitioner och formler:

1. **State the problem:** Barbara orders twice as many hot dogs as pieces of cake for a group of girls. A hot dog costs 5 and a piece of cake costs 2. The total cost is 60. Each gi

1. **Stating the problem:** Solve the equation $$\frac{4}{x+1} - \frac{3}{x-1} = \frac{2}{x^2-1}$$ where $x^2-1 = (x+1)(x-1)$. 2. **Formula and rules:** To solve equations with fra

1. **Probleemstelling:** We moeten stukken verdelen in combinaties die passen bij lengtes van 15,2 m en 14,2 m met minimaal verlies. 2. **Formule en regels:** We zoeken combinaties

1. **Plantejament del problema:** Cal trobar el domini de la funci\'o irracional $f(x) = \sqrt{-x^2 + 6x - 8}$. 2. **F\'ormula i regla important:** El domini d'una funci\'o amb arr

1. **Problem statement:** Find the zeros (Nullstellen) of the polynomial function $$g(x) = -0.1(x - 2)(x - 4)(x - 3)$$ and mark them on the graph. 2. **Formula and rules:** The zer

1. **صورت مسئله:** چند تابعِ با ضابطه $y=x^2$ و بردِ $\{0,1,4\}$ می‌توان ساخت؟ 2. **فرمول و ایده اصلی:** چون ضابطه تابع ثابت است و فقط برد را داده‌اند، باید ببینیم برای کدام ورودی‌

1. **صورت مسئله را می‌نویسیم.** تابع $f(x)=|x+2|+1$ را 2 واحد به راست و 3 واحد به پایین منتقل می‌کنیم، سپس نمودار حاصل را نسبت به محور $x$ ها قرینه می‌کنیم.