🧮 algebra

1. **Stating the problem:** Solve the equation $|3x + 4| = |2x + 6|$. 2. **Formula and rules:** The absolute value equation $|A| = |B|$ implies either $A = B$ or $A = -B$.

1. **Problem:** Decide whether the given relations are functions or not and justify your answer. **a)** $y^2 = x - 3$

1. **Énoncé du problème :** Évaluez l’angle déterminé par les vecteurs ũ = [-1, 2] et ṽ = [-4, -3].

1. **State the problem:** Solve the system of linear equations: $$5x = 15 + 3y$$

1. The problem is to analyze the linear equation $y = -\frac{3}{4}x + 10$ and understand its graph. 2. This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is

1. The problem is to solve the quadratic equation $x^2 - 5x + 6 = 0$. 2. The formula to solve quadratic equations is the quadratic formula:

1. Problem 39: An automobile travels \(\frac{3}{5}\) of the total distance in 1 hour and the remaining \(\frac{2}{5}\) in 1.5 hours. Find how many times the first speed is greater

1. Problem: Katerning turg'un suvdagi tezligini toping, agar daryo oqimi bo'ylab va oqimga qarshi tezliklar yig'indisi 30 km/soat bo'lsa. Formulalar:

1. Problem 13: A dog starts chasing a fox 30 m away. The dog jumps 2 m per jump, the fox jumps 1 m per jump. If the dog jumps twice and the fox jumps three times, how far has the d

1. Masala 13: It va tulki masofani qancha bosib o'tishini topish. It 2 marta sakkaragа sakraydi, ya'ni $2 \times 2 = 4$ m.

1. Vamos analisar a função quadrática dada: $$g(x) = -3(x + h)^2 + k$$ com as condições $$h < 0$$ e $$k < 0$$. 2. A forma $$g(x) = a(x - h)^2 + k$$ é a forma canônica da função qua

1. Problém: Máte £12,8 a chcete si koupit jablečný koláč za £9. Chcete také dát spropitné ve výši 15–20 % ceny koláče. 2. Vzorec pro výpočet spropitného: $$\text{spropitné} = \text

1. Calculons $A = \frac{3}{4} + \frac{1}{4} \div \frac{8}{9}$. 2. Rappel : Diviser par une fraction revient à multiplier par son inverse. Donc

1. Calculons $A = \frac{3}{4} + \frac{1}{4} \div \frac{8}{9}$. 2. Rappelons que diviser par une fraction revient à multiplier par son inverse :

1. **State the problem:** Given the expression $$(\sqrt{a})^2 - 2\sqrt{3}a^2 + 3a = 4a,$$ prove that $$\frac{a^3 + a^2 + 1}{3a\sqrt{6a} + a^2} = 1.$$\n\n2. **Simplify the given exp

1. **State the problem:** Solve the linear equation $100x + 95 = 120$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inv

1. Let's clarify the problem: you want a brief explanation of the logic behind the solution to part d. 2. The key is to identify what the problem asks and the main principle or for

1. **State the problem:** Solve the linear equation $100x + 98 = 120$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 98

1. **State the problem:** Solve the linear equation $109x + 98 = 120$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 98

1. **Problemstellung:** Gegeben ist ein Rechteck mit den Seitenlängen $3y$ cm und $2y$ cm, wobei $y > 2$ gilt. Es gibt zwei blaue Flächen mit den Flächeninhalten (1) $6y^2 - 4y$ un

1. The problem is to solve the equation $307 = 0$. 2. This is a simple equation where the left side is a constant number 307 and the right side is 0.