🧮 algebra

1. Állítsuk fel a problémát: Egy új autó ára 12000 euró, és az éves fenntartási költségek az autó korától függenek az adott táblázat szerint. 2. A cél az, hogy az 5 év alatt a nett

1. **Problem statement:** A roll of crimson ribbon is $5 \frac{2}{5}$ meters long. The length of a roll of crimson silk strip woven from this ribbon is $\frac{2}{3}$ of the length

1. **State the problem:** We need to find the length and width of a rectangular room where the length is 5 yards more than the width, and the area is 150 square yards. 2. **Define

1. **State the problem:** We want to find the partial fraction decomposition of the rational expression $$\frac{9x^2 - x + 14}{(x+1)(x^2+5)}.$$\n\n2. **Formula and setup:** Since t

1. **State the problem:** Simplify the rational expression $$\frac{x^2}{(x-5)^2 (x+1)}$$. 2. **Understand the expression:** The numerator is $$x^2$$ and the denominator is the prod

1. **State the problem:** Find the partial fraction decomposition of the rational expression $$\frac{10}{5x^2 - 11x + 2}$$. 2. **Factor the denominator:** We need to factor the qua

1. The problem asks for the correct form of the partial fraction decomposition of the rational expression with denominator $(x - 8)(x^2 + 8)$. 2. When decomposing a rational functi

1. **State the problem:** We need to find the cost of a snack-size bag of chips, a bottle of water, and a gallon of milk given the total cost and relationships between their prices

1. **State the problem:** We have 3 gallons of milk, 6 bottles of water, and 5 snack-size bags of chips. The total cost is 25.50 before tax. 2. **Define variables:** Let $c$ be the

1. **State the problem:** Simplify the expression $$\frac{y^2}{3} - \frac{2}{y}$$. 2. **Identify the common denominator:** To combine the terms, find a common denominator. The deno

1. **State the problem:** Solve the equation $\frac{Y}{4} = -16$ for $Y$. 2. **Formula and rule:** To isolate $Y$, multiply both sides of the equation by 4 because dividing by 4 is

1. **State the problem:** Find the general term (nth term) of the sequence 3, 8, 13, 18, ... 2. **Identify the pattern:** The sequence increases by 5 each time (8 - 3 = 5, 13 - 8 =

1. **State the problem:** Solve for $w$ in the equation $$-\frac{5}{w+2} = -8 - \frac{7}{w-1}.$$\n\n2. **Rewrite the equation:** Move all terms to one side to isolate fractions:\n$

1. **State the problem:** Solve the equation $10\log(x-4) + 10\log(x-2) = \log 3^3$ using algebraic methods. 2. **Recall logarithm properties:**

1. **State the problem:** Solve for $x$ in the equation $$1 = \sqrt{2x - 6} - 1.$$ 2. **Isolate the square root:** Add 1 to both sides to get $$1 + 1 = \sqrt{2x - 6}$$ which simpli

1. Énoncé du problème : Déterminer quelle affirmation parmi les propositions données est vraie concernant les propriétés des logarithmes. 2. Rappel des propriétés importantes des l

1. **State the problem:** We are given the function $F(x) = 3x^4 - 2x^2 + 7$ and we want to analyze or work with it. 2. **Identify the type of function:** This is a polynomial func

1. Let's start by stating the problem: We want to understand how to find the domain of a function. 2. The domain of a function is the set of all possible input values ($x$) for whi

1. **State the problem:** Kimberly wants to find the number of bus rides where the total cost of paying per ride equals the total cost of buying a bus pass plus a reduced per-ride

1. **State the problem:** We need to find Jada's rate of change (slope) of her weekly profit as a function of the amount of paprika sold. 2. **Recall the formula for slope:** The s

1. **State the problem:** We need to find the slope of the line representing Riley's distance over time during the first 5 minutes of the race and write an equation for distance $y