🧮 algebra

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.

1. **Problem statement:** We are given the product term $$T = 1,5x \cdot (3x + y - 2)$$ which represents the area of the blue rectangle.

1. The problem is to analyze the set of points $\{(-7, -3), (-7, 2), (-6, 1), (-2, 6), (5, 3)\}$ and understand their properties. 2. Each ordered pair represents a point on the Car

1. The problem is to simplify the expression $1 - \frac{3}{4}$. 2. To subtract a fraction from a whole number, convert the whole number to a fraction with the same denominator: $1

1. **State the problem:** Simplify the expression $\frac{1}{5} \times 3 + \frac{7}{10} - \frac{1}{2}$. 2. **Recall the order of operations:** Multiplication and division come befor

1. Expand and Simplify each expression: 1.a) Expand and simplify $ (3x^2 - 4xy + 5y^2) - (5x^2 - 7xy - 4y^2) $.

1. **State the problem:** We need to add the fractions $\frac{4}{7}$ and $\frac{3}{2}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The formula

1. **Expand and Simplify:** a) Expand and simplify $ (3x^2 - 4xy + 5y^2) - (5x^2 - 7xy - 4y^2) $.

1. The problem is to simplify the expression $10^1 \times 10^{-2}$. 2. We use the rule of exponents that states when multiplying powers with the same base, we add the exponents: