🧮 algebra

1. **Stating the problem:** We are given the equation $a + b = ax$ and asked to express $a$ in terms of $b$ and $x$. 2. **Rewrite the equation:** The equation is $a + b = ax$.

1. نبدأ بكتابة المعطى: طول نصف قطر الدائرة هو التعبير التالي: $$((و + ٣) س + ٢ + ص - ٣ ٤ س ص) + (٤ - ٢ س ص) + (م - و) ص + (ح - و) س - ٨$$

1. **State the problem:** Multiply the whole number 6 by the mixed number $6 \frac{5}{7}$. 2. **Convert the mixed number to an improper fraction:**

1. **State the problem:** Multiply the mixed numbers $7 \frac{4}{5}$ and $8 \frac{1}{2}$. Write the answer as a fraction or a mixed number. 2. **Convert mixed numbers to improper f

1. Masalah yang diberikan adalah mencari jumlah pembelian jagung pada tahun 1 jika pembelian selama 2 tahun mencapai 7.400 ton dan pembelian tahun 2 meningkat 25% dari tahun 1. 2.

1. **State the problem:** We are given the system of linear equations: $$50x + 49y = c$$

1. Uzdevums: Aprēķināt laukumu starp līknēm $$y = 4 - x^2$$ un $$y = x^2 - 2x$$. 2. Formulas un pieņēmumi: Laukumu starp divām funkcijām $$y = f(x)$$ un $$y = g(x)$$ intervālā $$[a

1. We are given the equation $2x + 7 = -15$ and need to solve for $x$. 2. The general form of a linear equation is $ax + b = c$, where $a$, $b$, and $c$ are constants.

1. **State the problem:** Solve the quadratic equation $$8x^2 - 29x - 12 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$,

1. **Stating the problem:** We are given zigzag diagrams with numbers at four points forming a 'W' shape. We need to find the relationship among these numbers based on the samples

1. **Problem Statement:** Find the relationship among the numbers in the zigzag line for Q1: points 9, 6, 18, 15. 2. **Observing the pattern:** The zigzag line has points arranged

1. Énonçons le problème : développer l'expression $J = (x + 2)(x - 2)$.\n\n2. La formule utilisée est la distributivité : $ (a + b)(c + d) = ac + ad + bc + bd $. Ici, on applique l

1. **State the problem:** Find the angle between the two lines given by the equations $$2x - y = 0$$ and $$3x + y = 0$$. 2. **Rewrite the lines in slope-intercept form:**

1. **State the problem:** Solve the equation $$-3(4x - \sqrt{2}) = -12x + \sqrt{4}.$$\n\n2. **Rewrite the equation:** Distribute the $-3$ on the left side:\n$$-3 \times 4x + (-3) \

1. **Énoncé du problème :** Résoudre dans $\mathbb{R}$ l'équation $$-3(4x - \sqrt{2}) = -12x + \sqrt{4}.$$ 2. **Formule et règles importantes :** Pour résoudre une équation, on che

1. **State the problem:** Solve the quadratic equation $x^2 - 6x + 5 = 0$. 2. **Formula and rules:** The quadratic formula to solve $ax^2 + bx + c = 0$ is:

1. **State the problem:** Simplify the expression $$\frac{\sqrt{2}}{\sqrt{3}+\sqrt{2}}$$ into the form $$a + \sqrt{b}$$ and find the values of $$a$$ and $$b$$. 2. **Formula and rul

1. Énoncé du problème : Développer les expressions algébriques données où les lettres minuscules représentent des nombres relatifs. 2. Rappel de la règle de développement : Pour dé

1. **Problem:** Given $x + y = 12$ and $xy = 27$, find the value of $x^3 + y^3$. 2. **Formula:** Recall the identity for the sum of cubes:

1. **State the problem:** We need to determine if the piecewise function $$h(x) = \begin{cases} x - 4 & \text{if } x < 2 \\ x^2 - 16 & \text{if } x \geq 2 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{\frac{1}{3} + \frac{1}{4}}{\frac{1}{5} + \frac{1}{6}}$$. 2. **Recall the formula:** To add fractions, use $$\frac{a}{b} +