🧮 algebra

1. **State the problem:** The original price of the shirt is 27. It is reduced by 15% in a sale. We need to find the new price after the reduction. 2. **Formula used:** To find the

1. **Stel het probleem vast:** Los de irrationale vergelijking $$2x - x^2 - \sqrt{6x^2 - 12x + 7} = 0$$ algebraïsch op in $$\mathbb{R}$$. 2. **Schrijf de vergelijking op:**

1. The problem asks to find the value of $p$ that satisfies the equation $4p - 5p = 14$. 2. Combine like terms on the left side: $4p - 5p = (4 - 5)p = -1p = -p$.

1. The problem states that the lowest wind speed recorded is 5 mph and the highest is 14 mph. 2. We want to find an inequality that is true for all wind speeds $w$ recorded that da

1. El problema es simplificar la expresión: $$\sqrt{2} \cdot \sqrt{a}\sqrt{8} \cdot \sqrt{3}\sqrt{a}\sqrt{24} \cdot \sqrt{6}\sqrt{a}\sqrt{12}\sqrt{2}\sqrt{a}12\sqrt{2}$$ 2. Recorde

1. **Stating the problem:** We are given the system of equations:

1. We are asked to find the equations of the horizontal and vertical asymptotes of the given irrational functions. 2. Recall that vertical asymptotes occur where the denominator of

1. **Stel het probleem vast:** Los algebraïsch de irrationale vergelijking op in ℝ: $$2\sqrt{2x + 1} = x - 2$$ 2. **Beperkingen bepalen:** Omdat er een wortel staat, moet de uitdru

1. **State the problem:** Solve the equation $$3x^4 - 4x^2 + 3x = -2$$ and explain why it has two solutions. 2. **Rewrite the equation:** Move all terms to one side to set the equa

1. مسئله: مقدار $$\sqrt[3]{8}$$ را پیدا کنید. 2. فرمول: ریشه سوم عدد $$a$$ برابر است با عددی که وقتی سه بار در خودش ضرب شود، برابر $$a$$ شود. یعنی اگر $$x=\sqrt[3]{a}$$، آنگاه $$x^

1. Problemet är att hitta talet som ligger mitt emellan $\frac{1}{3}$ och $\frac{1}{4}$.\n\n2. Formeln för talet mitt emellan två tal $a$ och $b$ är medelvärdet: $$\frac{a+b}{2}$$\

1. **State the problem:** Write the expression $$\frac{5x - 2}{3} + \frac{2}{5x + 2}$$ as a single fraction in simplest form. 2. **Find a common denominator:** The denominators are

1. **State the problem:** We are given two linear functions, Function A and Function B, and need to determine which has the greater slope. 2. **Recall the slope formula:** For any

1. **State the problem:** We have two linear functions, Function A given by the equation $y=4x-2$ and Function B given by a table of points: $(-4,-9)$, $(-3,-7)$, and $(8,15)$. We

1. **Stating the problem:** We have a sequence defined by the initial term $u_0 = 6$ and the recurrence relation $u_{n+1} = 3 u_n$. We want to express $u_n$ explicitly as a functio

1. **Énoncé du problème** : On considère la suite $(u_n)$ définie explicitement par $u_0 = 2$ et $u_n = u_0 \times 7^n$. 2. **Objectif** : Déterminer la relation de récurrence qui

1. المشكلة: تبسيط التعبير الجبري أو حل المعادلة بطريقة سهلة وبسيطة. 2. القاعدة الأساسية: عند تبسيط التعبيرات الجبرية، نستخدم قواعد الجمع والطرح والضرب والقسمة، ونحاول دائماً تبسيط

1. **State the problem:** Solve the system of equations using elimination: $$9x + 6y = -12$$

1. **Problem statement:** Given the quadratic equation $\alpha x^2 + \beta x + \gamma = 0$ with $\alpha \neq 0$, prove that the sum of the roots $x_1 + x_2 = -\frac{\beta}{\alpha}$

1. **Stating the problem:** We want to understand the fundamental properties of fractions. 2. **Definition:** A fraction represents a part of a whole and is written as $\frac{a}{b}

1. **State the problem:** Simplify the expression $$\frac{x^2 - 2x}{x^2 + 2x}$$ given that $$x \neq -2$$ and compare it to $$\frac{-2}{x+2}$$. 2. **Recall the formula and rules:**