🧮 algebra

1. **State the problem:** We want to analyze the rational function $$y = \frac{2x^2 - 4}{2x^4 - 5x^2 + 2}$$ to find points of exclusion (POEs), vertical asymptotes (VAs), zeros (x-

1. **State the problem:** Solve the equation $$(z+1)(z+3)=0$$ for $z$. 2. **Formula and rule:** The zero product property states that if the product of two factors is zero, then at

1. **State the problem:** We are given a cost of 176 for 11 hours and want to find the cost for 374 hours using proportions. 2. **Formula used:** The unit rate is calculated as cos

1. **State the problem:** Solve the system of equations: $$A + B = 2$$

1. **State the problem:** Solve the equation $30 = (2x + 9) + 5$. 2. **Simplify the right side:** Combine like terms inside the parentheses and constants.

1. **Énoncé du problème** : On considère la fonction définie sur l'intervalle $I = ]-1;0[$ par $$g(x) = \frac{1}{x(1+x)^2}.$$

1. **State the problem:** We need to analyze the function $$y = \frac{2x^2 - 4}{2x^4 - 5x^2 + 2}$$ by factoring it, finding points of exclusion (POE), vertical asymptotes (VA), zer

1. **State the problem:** Rewrite the expression by factoring out $ (y - 6) $ from the expression $$5 y^2 (y - 6) - 3 (y - 6)$$.

1. **State the problem:** Simplify the expression $ (x+3)(x-4) $. 2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term in th

1. **State the problem:** Simplify the expression $ (x+3)(x-4) $. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL method):

1. **Express the partial fraction decomposition of** $\frac{3x}{(x+1)(x-2)}$. 2. **State the problem:** Decompose $\frac{3x}{(x+1)(x-2)}$ into partial fractions.

1. لنبدأ بتحديد السلسلة التي تريد حلها. 2. السلسلة هي مجموع متتالي من الأعداد أو التعبيرات الرياضية.

1. **Stating the problem:** We want to understand the power laws and laws of exponents, which are rules that help us simplify expressions involving powers. 2. **Key exponent laws:*

1. The problem asks to determine which of the given relations define functions from set E to set F. 2. Recall that a relation $R$ from $E$ to $F$ defines a function if and only if

1. The problem: Understand and apply the power laws in algebra. 2. Power laws are rules for simplifying expressions involving exponents. The main power laws are:

1. The problem states that out of 456 students, 130 prefer pizza over tacos. We need to find the percentage of students who prefer tacos. 2. First, find the number of students who

1. **State the problem:** We need to find which store offers the best price per box of cereal given the prices and quantities from Kroger, Food Lion, and Martins. 2. **Formula:** P

1. **Problem Statement:** Understand the laws of exponents, which are rules for simplifying expressions involving powers of numbers or variables. 2. **Basic Laws of Exponents:**

1. **State the problem:** We are given the equation $$x^2 - x - y^2 - 4y - 5 = 0$$ and want to identify the graph and its key features. 2. **Rewrite the equation by completing the

1. **Problem Statement:** Find the domain of the function

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 2x - 4y = -3 \\ x - 2y = 1 \end{cases}$$