🧮 algebra

1. The problem is to find the greatest common divisor (GCD) or greatest common factor (GCF) of the terms in problem 294: $72a^3 b^2$, $18a^2 b^3 x^2$, and $15a^4 b^4 x$. 2. The for

1. **State the problem:** We have a composite figure made of two rectangles joined horizontally. We want to find two different expressions for the total area and then show they are

1. Calculer et simplifier : - $A = \sqrt{49} + \sqrt{25} = 7 + 5 = 12$

1. **State the problem:** We have 832 people surveyed about their birth month. \n\n2. **Given:** \n- $\frac{3}{13}$ of the people were born in May. \n- $\frac{5}{8}$ of the people

1. **State the problem:** Find the value of $a$ in the equation $$\frac{a}{6} - \frac{3}{8} = \frac{11}{24}.$$\n\n2. **Use the formula:** To solve for $a$, isolate $a$ by adding $\

1. **State the problem:** Solve the equation $2a + b = 10$ for one variable in terms of the other. 2. **Choose a variable to solve for:** Let's solve for $b$.

1. **State the problem:** Solve the equation $x^2 + 3y = 5$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we need to rearrange the equation by moving $x^2$ to

1. Let's start by stating the problem: solving simultaneous equations means finding values of variables that satisfy two or more equations at the same time. 2. Consider the system:

1. **State the problem:** Find the points of intersection between the line defined by the system $$\begin{cases} 2x - y + 2z - 12 = 0 \\ 2x - 4y - z + 6 = 0 \end{cases}$$

1. **State the problem:** Solve the equation $$9x^4 - 82x^2 + 9 = 0$$ for $x$. 2. **Use substitution:** Let $y = x^2$. Then the equation becomes a quadratic in $y$:

1. Problemi: Rishkruani shprehjet sipas udhëzimeve dhe thjeshtoni shprehjet algjebrike. 2. Formula dhe rregulla të rëndësishme: Në algjebër, shprehjet mund të thjeshtohen duke grup

1. **Problem:** Make $a$ the subject of the formula $2a + b = 10$. 2. **Formula and rules:** To isolate $a$, subtract $b$ from both sides, then divide both sides by 2.

1. **State the problem:** Solve the equation $$x^6 + 7x^3 - 8 = 0$$ for $x$. 2. **Use substitution:** Let $y = x^3$. Then the equation becomes $$y^2 + 7y - 8 = 0$$ because $x^6 = (

1. **State the problem:** Find the parametric equations of the line of intersection of the two planes given by: $$2x - y + 2z - 12 = 0$$

1. 题目是询问是否可以使用截距式来解决问题。 2. 截距式通常用于直线方程，形式为 $\frac{x}{a} + \frac{y}{b} = 1$，其中 $a$ 和 $b$ 分别是 $x$ 轴和 $y$ 轴的截距。

1. 题目要求求双曲线 $\frac{x^2}{4} - \frac{y^2}{5} = 1$ 的焦点坐标。 2. 双曲线标准形式为 $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$，其中焦点坐标为 $(\pm c, 0)$，且满足关系 $$c^2 = a^2 + b^2$$。

1. **State the problem:** We are given a rectangle with area 36 cm². The length is labeled as $x$ and the width as $x - 5$. We need to find the dimensions of the rectangle. 2. **Fo

1. نبدأ بحل التمرين الثاني وهو حساب قيمة الدالة $$g(x) = \sqrt{x} + \frac{2}{|x-1|} - 3$$ عند $$x=9$$. 2. نعوض $$x=9$$ في الدالة:

1. **بيان المسألة:** لدينا الدوال:

1. **Problem 1.1.1: Solve the quadratic equation** $$x^2 - 4x + 3 = 0$$ 2. **Formula:** For quadratic equations $$ax^2 + bx + c = 0$$, solutions are given by the quadratic formula:

1. **Problem:** Solve the equation $$x^2 - 4x + 3 = 0$$ 2. **Formula:** Use the quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $$a=1$$, $$b=-4$$, and $$c=3$$.