🧮 algebra

1. **State the problem:** Simplify the expression $\sqrt{50} + 4\sqrt{18} - 6\sqrt{8}$.\n\n2. **Recall the rule:** $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ and simplify squar

1. **State the problem:** Solve the quadratic expression $x^2 + 3x + 2$ by factoring. 2. **Formula and rules:** To factor a quadratic $ax^2 + bx + c$, find two numbers that multipl

1. **State the problem:** We are given the system of linear equations: $$2y = x + 10$$

1. **State the problem:** We need to find the solution to the system of linear equations: $$-\frac{1}{2} y = \frac{1}{2} x + 5$$

1. The problem asks to find how much money was already in the account when Rachel started depositing money, i.e., the initial amount at time $0$ months. 2. We are given a table of

1. **Problem statement:** A metal cools at a constant rate. After 19 minutes, its temperature is 401 °C, and after 42 minutes, it is 148 °C. We need to find how time and temperatur

1. **State the problem:** Solve the equation $$2|x^2 - 2| + 5 = 6|2x^2 - 3|.$$\n\n2. **Understand the absolute value expressions:** The equation involves absolute values of quadrat

1. **State the problem:** Find 3 fractions between $\frac{1}{3}$ and $\frac{1}{4}$.\n\n2. **Recall the method:** To find fractions between two fractions, we can find equivalent fra

1. The problem asks to find 3 fractions between $\frac{1}{3}$ and $\frac{1}{4}$ using Method B, which involves scaling denominators and numerators. 2. First, note the fractions $\f

1. **State the problem:** We need to find the value of $c$ given the equation $c + 42 = 90$. 2. **Formula and rule:** To isolate $c$, subtract 42 from both sides of the equation. T

1. **State the problem:** Solve for $f$ in the equation $2f + 22 = 90$. 2. **Formula and rules:** This is a linear equation. To solve for $f$, isolate $f$ by performing inverse ope

1. Problem: Simplify the expression or concept as simply as possible. 2. Since no specific expression or problem was given, simplification means making something easier to understa

1. Stated problem: Izračunajte proizvod kompleksnih brojeva $ (2 + 3i)(4 - i) $. 2. Formula: Za množenje kompleksnih brojeva koristimo distributivnost:

1. The problem is to solve the equation $$\frac{2x+3}{x-1} = 4.$$\n\n2. We use the property that if $$\frac{a}{b} = c$$ and $$b \neq 0$$, then $$a = bc$$. Here, $$a = 2x+3$$, $$b =

1. Problem statement: Find the solution set of the inequality $2x^2+5x+2>0$. 2. Formula and rule: To solve a quadratic inequality $ax^2+bx+c>0$ we find its roots and determine the

1. **State the problem:** Simplify the expression $$(3 \times 6 \cdot 3 \times 6)^2 + (3 \times 6 + 3 \times 6)^2$$. 2. **Calculate each part inside the parentheses:**

1. Find the solution set of the following inequalities. (a) Solve $2x^2 + 5x + 2 > 0$.

1. **State the problem:** We want to find what fraction of 2 minutes is 6 seconds. 2. **Convert units to the same base:** Since 1 minute = 60 seconds, 2 minutes = $2 \times 60 = 12

1. **Find the 8th term of the GP 55, 11, 11/5, ...** The problem is to find the 8th term of a geometric progression (GP) where the first three terms are 55, 11, and 11/5.

1. Problem statement. Problem: Solve the inequality $2x^2+5x+2>0$.

1. **Find the common ratio $r$ for each GP:** (i) Sequence: $2, 8, 32, 128, \ldots$