🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{x^2 - 4}{2} + \frac{x^2 + 2x}{4}$$ as a single fraction in simplest form. 2. **Find a common denominator:** The denominato

1) Simplify the expression $m^{-6} \div m^{7} \times m^{2}$. 2) Simplify the expression $m^{-6} \times m^{7} \div m^{2}$.

1. **State the problem:** Solve the equation $$x = \sqrt{x-1} - 2$$ for $$x > 2$$. 2. **Rewrite the equation:** Add 2 to both sides to isolate the square root:

1. **State the problem:** Simplify the expression $$\sqrt[3]{250} + 3\sqrt[3]{54}$$. 2. **Recall the cube root properties:** The cube root of a product is the product of the cube r

1. **State the problem:** Simplify the expression $$\sqrt[3]{50} + \sqrt[3]{75}$$. 2. **Recall the cube root properties:** The cube root of a product is the product of the cube roo

1. The problem asks: "Twenty-four is .....% of 80." We need to find what percentage 24 is of 80. 2. The formula to find the percentage is:

1. The problem asks: What percentage is 24 of 80? 2. The formula to find what percent a number $a$ is of another number $b$ is:

1. **State the problem:** Solve for $x$ in the equation $x + 40 = 90$. 2. **Formula and rules:** To isolate $x$, subtract 40 from both sides of the equation.

1. **Problem:** Find the ratios between the number of pencils in Group A and Group B. Group A has 3 bundles with 6 pencils each, so total pencils in Group A = $3 \times 6 = 18$.

1. The problem states that the answer for part c is \(\frac{31}{105}\).\n2. To verify or understand this result, we would typically start by identifying the problem type (e.g., fra

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