🧮 algebra

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:

1. **State the problem:** We need to list all elements in the set $B = \{x \in \mathbb{N} : x^3 \text{ is an odd number less than } 150\}$. This means we want natural numbers $x$ s

1. The problem is to write the equation $y=(x+2)^2+3$ in standard form. 2. The standard form of a quadratic equation is $y = ax^2 + bx + c$.

1. **State the problem:** List all elements in the set $A = \{x \in \mathbb{Z}^+ : (x^2 - 4) < 10\}$. 2. **Understand the set definition:** $A$ contains all positive integers $x$ s

1. **State the problem:** Evaluate the expression $$(2 \times 6 + 3 - 4) - 5 + \left(\frac{20}{5}\right) \times 3 + 50$$ using order of operations. 2. **Recall order of operations:

1. **State the problem:** Solve the equation $$\frac{9t+27}{9t+18} = 9$$ for $t$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both sides b

1. **State the problem:** Solve the equation $$\frac{9t+27}{9t+18} = 9$$ for $t$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both sides b

1. **State the problem:** Simplify the expression $\frac{7}{2x} + \frac{6}{2x}$. 2. **Identify the formula and rules:** When adding fractions with the same denominator, add the num

1. **State the problem:** Solve the quadratic equation $$4x^2 + 16x + 15 = 0$$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solutions

1. **Problem Statement:** We want to use Newton's forward interpolation formula to show that $$s = \sum n^3 = \left( \frac{n(n+1)}{2} \right)^2.$$

1. **State the problem:** Solve the equation $5x - 4(1 - 3x) = 4x - (x + 1)$ for $x$. 2. **Apply the distributive property:**