🧮 algebra

1. **Zadanie:** Štyria kamaráti dostali za zber starého papiera peniaze takto: Fero dostal polovicu z toho, čo dostal Marek, Milan dostal o 10 eur viac ako Fero, Tibor dostal o 12

1. **State the problem:** Simplify the expression $$(3a+1)^2 - (3a+1)(2a-1)$$. 2. **Use the formula for expansion:**

1. **State the problem:** Factor the cubic polynomial $$x^3 - 3x^2 + 2$$. 2. **Recall the factoring approach:** To factor a cubic polynomial, first try to find rational roots using

1. **Problem statement:** Find the minimum point of the curve $y = x^2 - 2x - 4$.

1. **Problemstellung:** Gegeben sind die Rechnungen $A + B = L$ und $C = DA$ mit der Bedingung, dass gleiche Buchstaben gleiche Ziffern und unterschiedliche Buchstaben unterschiedl

1. **State the problem:** Simplify or analyze the function given by $$y=\frac{\ln\left(\frac{x}{m}-sa\right)}{r^2}$$ where $x$, $m$, $s$, $a$, and $r$ are variables or constants. 2

1. **State the problem:** Solve the equation $$\frac{\log_3 9 - 22}{\log_3 9 - 5} = 4$$. 2. **Recall the properties of logarithms:**

1. **State the problem:** Solve the simultaneous equations: $$y - 2x = 10$$

1. **State the problem:** Solve the equation $$\frac{x}{6.5} = 3$$ for $x$. 2. **Formula and rule:** To solve for $x$ when it is in the numerator of a fraction, multiply both sides

1. **Problem 14:** Find which algebraic expression is equivalent. Given expressions:

1. **State the problem:** We have a quadratic equation $$ax^2 + b = 181$$ where $$a$$ and $$b$$ are positive integers greater than 1. One solution is $$x=8$$. We need to find (a) t

1. **State the problem:** Determine if the relation given by the points (0, 3), (1, 4), (2, 3), (3, 0), and (5, 4) is a function. 2. **Recall the definition of a function:** A rela

1. **State the problem:** Solve the inequality $$2x - y \geq 1$$ graphically and find at least 6 ordered pairs that satisfy the inequality. 2. **Rewrite the inequality:** To graph

1. **State the problem:** We need to graph the linear equation $$y = 1 + \frac{4}{5}x$$ and fill in the table for given values of $x$. 2. **Formula and rules:** The equation is in

1. **State the problem:** Simplify the expression $$\frac{\log_2 x}{2} - \frac{\log_2 y}{3} - \frac{\log_2 z}{3}$$. 2. **Recall the logarithm power rule:** For any base $a$, $\log_

1. **State the problem:** We need to fill in the table for the equation $$y = -\frac{3}{4}x - 4$$ at the given values of $$x$$ and then graph the equation. 2. **Recall the formula:

1. **State the problem:** Find the equation and y-intercept of the line passing through points (2, -4) and (6, 8). 2. **Formula for slope:** The slope $m$ of a line through points

1. **State the problem:** We need to find the number of miles driven given a truck rental fee structure: a base fee plus a per-mile charge, and the total amount paid.

1. **State the problem:** Deon paid a $5 fee plus $0.09 per minute for a scooter ride, and the total bill was $16.16. We need to find the number of minutes, $x$, Deon rode the scoo

1. **State the problem:** Simplify the expression $(-2x+3y)^2-(y+x)^2$. 2. **Recall the formula:** Use the difference of squares formula: $$a^2 - b^2 = (a-b)(a+b)$$ where $a = -2x+

1. **State the problem:** We are given miles run and calories burned and asked if calories are proportional to miles, find calories burned for 7.5 miles, find the constant of propo