🧮 algebra

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

1. The question is whether $x$ can be 0 in the context of the problem you are considering. 2. To determine if $x=0$ is valid, we need to check the conditions or domain restrictions

1. **State the problem:** Solve the equation $$(x - 2)^2 = (x + 7)^2 - 3x$$ 2. **Recall the formula:** The square of a binomial is $$(a \pm b)^2 = a^2 \pm 2ab + b^2$$

1. **State the problem:** Solve the quadratic equation $2x^2 - 8x + 8 = 4x - 8$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **Stating the problem:** Solve the first equation given: $$(X - 2)^2 = (X + 7)^2 - 3X$$

1. The problem asks to find the solution for the variable $w$ in the equation given, but the equation itself is missing from the message. 2. To solve for $w$, we need the explicit

1. **State the problem:** Solve the equation $3 \cdot 5^{0.2w} = 720$ for $w$. 2. **Isolate the exponential term:** Divide both sides by 3 to get

1. Let's start by understanding what "Case 3" means in the context of solving quadratic equations using the quadratic formula. 2. The quadratic formula is given by:

1. **State the problem:** We need to multiply the fraction $\frac{3}{5}$ by the mixed number $1 \frac{4}{7}$ and simplify the result. 2. **Convert the mixed number to an improper f

1. **State the problem:** Find the value of $\log \frac{1}{4}$. 2. **Recall the logarithm rule:** $\log \frac{a}{b} = \log a - \log b$.

1. The problem is to simplify the expression $\frac{1}{4} \log \frac{1}{4}$. 2. Recall the logarithm power rule: $a \log b = \log b^a$. We can rewrite the expression as $\log \left

1. The problem is to understand why when $u_n=1$, we assume $u_{n-1}$ and $u_{n-2}$ are also 1. 2. This situation often arises in sequences defined by recurrence relations, where e

1. **Énoncé du problème :** Résoudre l'équation $\frac{3}{2} = ... \times \frac{5}{2} \times ...$.