🧮 algebra

1. **State the problem:** We are given a rectangle with sides AG and NL. The length of side AG is $x^2$ and the length of side NL is $3x - 4$. Since opposite sides of a rectangle a

1. **Problem Statement:** We have several sequences and factorization problems to solve.

1. **Problem Statement:** We have a sequence of patterns made of matchsticks forming triangles. The first pattern has 3 matchsticks, the second 5, the third 7, and so on. We need t

1. The problem is to solve the inequality $\log x \leq -10$. 2. Recall that $\log x$ usually means the logarithm base 10, so the inequality is $\log_{10} x \leq -10$.

1. **State the problem:** Factor the expression $6a - 9$ by extraction. 2. **Formula and rule:** To factor by extraction, find the greatest common factor (GCF) of all terms and fac

1. **State the problem:** We need to solve the system of equations: $$x + y = 69$$

1. The problem is to evaluate the expression $e^{-\infty^2}$. 2. Recall that $\infty$ represents an infinitely large number, and squaring it, $\infty^2$, is still infinitely large.

1. **State the problem:** Solve the system of equations: $$X + Y = 0$$

1. **Problem Statement:** Solve the simultaneous equations from Q1 part a): $$4x + 6y = 16$$

1. **Problem Statement:** Find the number of pupils taking 10 to 30 minutes to travel to school on Monday, given that on Tuesday the number was 25% less than on Monday.

1. **State the problem:** Calculate the value of $$\sqrt{270(270-120)(270-170)(270-250)}$$. 2. **Simplify the terms inside the square root:**

1. The problem is to solve the equation $$\frac{\cap \times n + n}{\cap} = 10$$ for $n$. 2. First, recognize that $\cap$ is a variable (let's call it $c$ for clarity). The equation

1. **State the problem:** Solve the system of linear equations: $$2x + y = 7$$

1. **Problem statement:** We need to find how long 15 chickens and 4 ducks will take to eat 10 kg of grain, given that 10 chickens eat a 6 kg sack in 24 hours and 10 chickens eat i

1. **Problem Statement:** Given the functions: $$f(x) = x + 5, \quad g(x) = 2x - 1, \quad h(x) = 2x^2 + 9x - 5$$

1. **State the problem:** Simplify the expression $$\frac{3 \times 10^{-2}}{8 \times 10^{-1}}$$. 2. **Recall the rule for division of powers of 10:** When dividing terms with the s

1. **State the problem:** We need to simplify the expression $$\frac{3 \times 10^{-2}}{8 \times 10^{-1}}$$ and understand how to divide exponents. 2. **Recall the rule for dividing

1. **State the problem:** Simplify the expression $5\sqrt{7} + 3\sqrt{40}$. 2. **Recall the rule:** To simplify expressions with square roots, factor the radicand (number inside th

1. **Problem statement:** Simplify the expression $\left(V^3 V^{-1.5} V^2\right)^2$ using the laws of indices. 2. **Recall the laws of indices:**

1. **State the problem:** We need to list all positive integers $x$ such that $x^2 + 4$ is an even number less than 200. 2. **Analyze the condition:** The set $A = \{x \in \mathbb{

1. Problem 3: List all elements in $A = \{x \in \mathbb{Z}^+ : (x^2 - 4) < 10\}$. Step 1: Write the inequality: