🧮 algebra

1. **State the problem:** Solve the linear equation $11y + 20 = 64$ for $y$. 2. **Isolate the term with $y$:** Subtract 20 from both sides to get:

1. **Find the (n - 1)th term of the sequence $a_n = 2n + 1$.** The general term is given by $a_n = 2n + 1$.

1. **State the problem:** We have a rectangle with length $3x - 1$ cm and perimeter $10x$ cm. We need to find an expression for the area in the form $ax^2 + bx + c$. 2. **Recall th

1. The problem is to simplify the fraction $\frac{2}{24}$. 2. Find the greatest common divisor (GCD) of 2 and 24, which is 2.

1. The problem is to simplify the fraction $\frac{3}{24}$. 2. Find the greatest common divisor (GCD) of 3 and 24. The GCD is 3.

1. **State the problem:** Simplify the expression $$\frac{1}{(a+b)^{-1}} - (a^{0.5} - b^{0.5})^2$$. 2. **Simplify the first term:** Recall that $$x^{-1} = \frac{1}{x}$$, so

1. **State the problem:** Simplify the expression $$1\frac{1}{(a+b)^{-1}} - (a^{0.5} - b^{0.5})^2$$. 2. **Rewrite the mixed fraction:** The term $$1\frac{1}{(a+b)^{-1}}$$ means $$1

1. **State the problem:** Simplify the expression $$1\frac{a}{b}(a+b)^{-1} - (a^{0.5} - b^{0.5})^2$$. 2. **Rewrite the mixed fraction:** The term $$1\frac{a}{b}$$ means $$1 + \frac

1. **State the problem:** We need to find the values of $p$ such that the quadratic equation $2x^2 + px - 2p = 0$ has no real roots. 2. **Recall the condition for no real roots:**

1. **State the problem:** We are given the quadratic equation $kx^2 + 5x = -7$ and need to find all values of $k$ such that the equation has two distinct real solutions. 2. **Rewri

1. **State the problem:** We are given the quadratic equation $kx^2 + 5x = -7$ and need to find all values of $k$ such that the equation has two distinct real solutions. 2. **Rewri

1. The problem asks for the values of the constant $k$ such that the given equation has two distinct real solutions. 2. To determine this, we need to analyze the discriminant $\Del

1. ננסח את הבעיה: לפתור את המשוואה $$\log_3(3^x + 1) + x - 1 = \log_3 4$$. 2. נעביר את האיברים כך שנבודד את הלוגריתמים:

1. لنفترض أن المعادلة رقم 3 من التمرين الأول هي معادلة جبرية معينة. 2. ابدأ بكتابة المعادلة كما هي.

1. لنفترض أن الحد الثالث هو جزء من متتالية أو تعبير جبري. 2. أولاً، حدد صيغة الحد العام أو المتتالية التي تنتمي إليها الحد الثالث.

1. **State the problem:** Pedro drove from Toulouse to Montpellier in 2 hours 42 minutes at an average speed of 90 km/h. Janine drove the same route in 3 hours. We need to find Jan

1. **State the problem:** Solve the equation $\log_2(24 - 2^x) = x + 1$ for $x$. 2. **Rewrite the logarithmic equation in exponential form:**

1. **State the problem:** Solve the equation $\log_2(24 - 2^x) = x + 1$ for $x$.\n\n2. **Rewrite the logarithmic equation in exponential form:** Recall that $\log_b(a) = c$ means $

1. **State the problem:** We are given the quadratic equation $kx^2 + 5x = -7$ and need to find all values of $k$ such that the equation has two distinct real solutions. 2. **Rewri

1. **State the problem:** Simplify the expression $$2 - \frac{x + 2}{x - 3} - \frac{x - 6}{x + 3}$$ into a single fraction of the form $$\frac{ax + b}{x^2 - 9}$$ where $a$ and $b$

1. Énoncé : Trouver les coefficients $u$ et $v$ tels que $20u + 11v = 1$ en utilisant l'algorithme d'Euclide. 2. Appliquer l'algorithme d'Euclide pour calculer le PGCD de 20 et 11