🧮 algebra

1. **Problem Statement:** Solve the simultaneous equations: $$2x^2 + xy + y^2 = 14$$

1. The problem is to simplify the expression $$\frac{-3x - 3}{3}$$. 2. The formula used here is the distributive property of division over addition/subtraction: $$\frac{a + b}{c} =

1. **Problem statement:** Given $\log_x 64 = 3$, find the value of $\log_x 8$. 2. **Recall the definition of logarithm:** If $\log_a b = c$, then $a^c = b$.

1. **State the problem:** Simplify the expression $-4(-3x - \frac{3}{3})$. 2. **Recall the distributive property:** $a(b + c) = ab + ac$. This means we multiply $-4$ by each term i

1. The problem asks to find the value of the expression $2n^2 - n + 4$ when $n = -3$. 2. The formula given is $2n^2 - n + 4$. We will substitute $n$ with $-3$ and simplify.

1. **Problema:** Hallar las raíces de la función $Y = 4x + 2$. 2. **Fórmula:** Para encontrar la raíz de una función lineal, igualamos la función a cero y despejamos $x$:

1. **Problem statement:** Factorize the given expression. Since no specific expression was provided, let's consider a general example: factorize $x^2 - 5x + 6$. 2. **Formula and ru

1. The problem asks for the product of 7 and 8 decreased by $x$, where $x=15$. 2. First, find the product of 7 and 8 using the multiplication formula: $$7 \times 8 = 56$$

1. The problem is to analyze the function $y = x^2$. 2. This is a quadratic function, which generally has the form $y = ax^2 + bx + c$. Here, $a=1$, $b=0$, and $c=0$.

1. The problem asks to find which function has a lesser rate of change (slope) than the function represented by the table. 2. First, find the slope of the function from the table.

1. **State the problem:** We are given a function graphed as a line passing through points (0,6) and (3,0) with slope approximately $-2$. We need to find which of the given options

1. The problem is to evaluate the expression $-\frac{4}{3} + 2 \times 3$. 2. According to the order of operations (PEMDAS/BODMAS), multiplication must be done before addition.

1. The problem is to understand and analyze the function $F(x) = x - \sqrt{x}$. 2. The function involves a linear term $x$ and a square root term $\sqrt{x}$. The domain of $F(x)$ i

1. The problem asks how to simplify a formula when using counts instead of probabilities. 2. Probabilities are often calculated as counts divided by total counts, i.e., $p = \frac{

1. The problem states that each side of a square is labeled as $3x + 2$. 2. We know that the perimeter $P$ of a square is given by the formula:

1. Vamos decompor o polinómio $3x^2 - 75 = 0$ em fatores. 2. Primeiro, podemos fatorar o termo comum 3:

1. المشكلة هي إيجاد الرقم التالي في المتتالية: 3, 11, 32, 71, 136, 229, ? 2. نلاحظ أن الأرقام لا تتبع زيادة ثابتة، لذا سنحسب الفروق بين الأعداد المتتالية:

1. **Problem Statement:** Analyze the polynomial graphs in parts (a) and (b) to determine:

1. Let's solve the first problem from the user's message: Simplify the expression $(x - 7y) \cdot 3(3x - 7)y \cdot (3x - 7) \cdot y$. 2. The problem involves multiplication of alge

1. The question asks whether the function is increasing (rastúca) or decreasing (klesajúca). 2. To determine this, we need the function or its graph to analyze its behavior.

1. **State the problem:** Solve the equation $2\ln(x) - 1 = 0$ for $x$. 2. **Recall the formula and rules:** The natural logarithm function $\ln(x)$ is defined for $x > 0$. To solv