🧮 algebra

1. **State the problem:** Solve the quadratic equation $4x^2 - 1 = 0$ for $x$. 2. **Formula and rules:** This is a quadratic equation in the form $ax^2 + bx + c = 0$. Here, $a=4$,

1. Stated problem: Simplify and evaluate the expression $ (a - 1)^2 - (a + 1)(a - 1) $. 2. Use the formulas:

1. **State the problem:** Two classes, Class A and Class B, sell tickets for a movie night. Each ticket costs 5, and each class pays a 20 fee. Class B sells three times as many tic

1. **State the problem:** We need to divide the polynomial $x^3 - 2x^2 + 1$ by the binomial $x - 1$. 2. **Recall the formula:** Polynomial division can be done using long division

1. **Stating the problem:** Izračunajmo izraz $\left(\frac{1}{2} + a\right)^2$.

1. **Planteamiento del problema:** Se nos piden realizar operaciones de suma y resta entre matrices dadas. 2. **Reglas importantes:** Para sumar o restar matrices, deben tener las

1. **State the problem:** A store pays 18 for a teapot and marks up the price by 40%. We need to find the amount of the mark-up. 2. **Formula:** The mark-up amount is calculated by

1. **State the problem:** Juan's bill was 27 and he left a 20% tip. We need to find the amount of the tip. 2. **Formula:** Tip amount = (Percentage tip) \times (Bill amount)

1. **Problem:** Solve the equation $5 \cdot (x + 1) = 10 - 3 \cdot x$ for $x$. 2. **Formula and rules:** Use the distributive property $a(b+c) = ab + ac$ to expand expressions.

1. The problem asks if the ratios $\frac{11}{14}$ and $\frac{6}{7}$ form a proportion. 2. Two ratios form a proportion if they are equal, i.e., if

1. **State the problem:** Solve the equation $8 \div 2(4 - x) = 1$ for $x$. 2. **Recall the order of operations:** Division and multiplication have the same precedence and are eval

1. **State the problem:** Calculate the expression while keeping fractions in their fractional form. 2. **Formula and rules:** When performing arithmetic with fractions, use the fo

1. **State the problem:** Simplify the expression $$-3\begin{pmatrix}0 & 6 \\ -5 & 3\end{pmatrix} + \begin{pmatrix}-9 & 8 \\ 5 & 1\end{pmatrix} - 2\begin{pmatrix}4 & 6 \\ -4 & -7\e

1. **Problem Statement:** Find the LCM (Least Common Multiple) and HCF (Highest Common Factor) of the algebraic expressions given in part (a): $45xy$ and $135x^2y$. 2. **Formulas a

1. Το πρόβλημα ζητά να εξηγήσουμε τη συνάρτηση $f(x) = 1 - 1$ και τη συνάρτηση γινόμενο. 2. Αρχικά, εξετάζουμε τη συνάρτηση $f(x) = 1 - 1$.

1. Vamos fatorar a expressão 4.11: $$4x^2 + 4xy + y^2$$ 2. Observe que essa expressão é um trinômio quadrado perfeito, pois pode ser escrita como o quadrado de um binômio.

1. The problem is to resolve the expression or equation labeled as 4.11. Since the user did not provide the explicit expression, I will assume it is a typical algebraic problem inv

1. **State the problem:** We need to analyze and understand the function $$y = -6 |x - 5|$$ and describe its graph. 2. **Recall the formula and properties:** The absolute value fun

1. Vamos resolver a fatoração da expressão do exercício 4.10: $$ (2x + 1)^2 + 4(2x + 1) $$ 2. Primeiro, observe que a expressão tem um termo comum: $$ (2x + 1) $$.

1. **State the problem:** Simplify the expression $$\frac{4p^3 - p^2 + 2p}{3p - 1}$$ using synthetic division and write the result in standard form. 2. **Rewrite divisor:** The div

1. **State the problem:** Solve each equation for the variable and then arrange the solutions in numerical order from least to greatest. 2. **Equation 1:** $-5n - 8(1 + 7n) = -8$