🧮 algebra

1. مسئله: یافتن ریشه‌های معادله داده شده است. 2. برای یافتن ریشه‌های یک معادله، باید مقدارهایی از متغیر را پیدا کنیم که معادله را برابر صفر کنند.

1. **State the problem:** Solve the cubic equation $$-4s^{3}-15s^{2}-18s-5=0$$ for $s$. 2. **Rewrite the equation:** Multiply both sides by $-1$ to simplify the leading coefficient

1. **State the problem:** Solve the equation $$\frac{11}{x^2 - 25} + \frac{2}{5 - x} = -1$$ for $x$. 2. **Rewrite the denominators:** Note that $$x^2 - 25 = (x - 5)(x + 5)$$ and $$

1. **State the problem:** Given the quadratic equation $$px^2 - 4x - \frac{21}{p} = 0$$ where $p$ is a constant, find the solutions for $x$ in terms of $p$.

1. **State the problem:** Rosila spent $\frac{1}{8}$ of her salary on transport and then $\frac{1}{3}$ of the remainder on food. After these expenses, she had 840 left. We need to

1. The problem is to understand the relation between time spent babysitting (hours) and amount earned (dollars) from the given data points and graph. 2. A relation is a set of orde

1. **State the problem:** We have data from five teenagers about hours babysat (x) and amount earned (y). We need to represent this relation using ordered pairs, a table, a mapping

1. Énonçons le problème : Montrer que le carré d'un nombre impair est impair. 2. Soit $a$ un nombre impair. Par définition, il existe un entier relatif $k$ tel que $a = 2k + 1$.

1. **State the problem:** Simplify the expression $$\left(\frac{3x^{2}y^{3}}{x^{-1}y^{2}}\right)^{-2}$$. 2. **Recall the rules:**

1. Problemi belirtelim: Türkiye standartlarına göre beden numaraları ile İtalyan firmasının beden numaraları arasında doğrusal bir ilişki vardır. 2. Verilenler:

1. The problem is to understand whether it is correct to put $\frac{1}{a}$ and $\frac{1}{b}$ together as $\frac{1}{a} + \frac{1}{b}$ or in some other form. 2. The formula for addin

1. **State the problem:** Find the reciprocal of $$\frac{1}{\frac{a}{b}} + \frac{1}{\frac{c}{ab}}$$. 2. **Rewrite the expression:** The expression inside the reciprocal is $$\frac{

1. **State the problem:** Solve the equation $$3x = 21$$. 2. **Formula and rules:** To solve for $x$, divide both sides of the equation by the coefficient of $x$, which is 3.

1. **Problem:** Given matrix $$M = \begin{pmatrix} 2 & 5 \\ 7 & 15 \end{pmatrix}$$ i) Show that $$M$$ is non-singular.

1. **State the problem:** Malcolm lost 8 kg and now weighs 64 kg. We need to find what percentage of his original weight he lost. 2. **Identify the known values:**

1. **State the problem:** Find the equation of the straight line $L$ in the form $y = mx + c$ given two points on the line: $(0, 2)$ and $(3, 0)$. 2. **Recall the formula:** The eq

1. **State the problem:** Solve the equation $(x - y) + 3i = 4 + yi$ for real numbers $x$ and $y$. 2. **Recall the rule:** For two complex numbers to be equal, their real parts mus

1. **State the problem:** Determine if the line $y=8-x$ is tangent to the curve defined by $2x^2 + xy = -16$. 2. **Substitute the line equation into the curve:** Replace $y$ in the

1. **State the problem:** Solve for $x$ and $y$ in the equation $(x+yi)(-i)=3$ where $x$ and $y$ are real numbers. 2. **Recall the formula and rules:** Multiplying complex numbers

1. Planteamos el problema: Resolver la ecuación $$\frac{2(x - 1)}{3} + 1 = \frac{1}{5} - x$$. 2. Usamos la fórmula para resolver ecuaciones lineales: despejar $x$ aislando términos

1. **Problem statement:** Divide the polynomial $f(x) = x^3 + 4x^2 + x - 6$ by the linear factor $(x - 1)$. Find the quotient polynomial. 2. **Formula and rules:** Polynomial divis