🧮 algebra

1. **State the problem:** The Pharaoh kept 1020 white goats, which represent 17% of the total flock. We need to find the total number of goats in the flock.

1. Énonçons le problème : Vérifier si les expressions $\log(5x^3) + \log 2 - 2 \log(8x^2)$ et $\log(2x) + \log 5 - 3 \log(4x)$ sont équivalentes.

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 5x + 3}{2x^2 - x - 3}$$. 2. **Factor numerator and denominator:**

1. **State the problem:** Simplify the expression $$\frac{1}{x-2} - \frac{2}{x-1} + \frac{1}{x-3}$$. 2. **Find a common denominator:** The denominators are $x-2$, $x-1$, and $x-3$.

1. We are given the function $f(x) = x^3 - 3x$ and points $a = 1$ and $b = -\frac{1}{2}$. We want to find the slope of the secant line between these points. 2. The formula for the

1. **State the problem:** Identify the like terms in the expression $$-3x^{3} + 2^{4} + x^{5} - x^{3} + x^{4} - 4x^{5} + 5x - 5x^{5}$$. 2. **Recall the definition of like terms:**

1. **State the problem:** Simplify the expression $$5x + 8(2x - 3) - 14x + x^{2}$$ and then determine how many terms it has and identify the constant term. 2. **Apply the distribut

1. **State the problem:** Rewrite the rational function $$\frac{x^2 + x + 4}{x (x - 2)^2}$$ as partial fractions.

1. **State the problem:** TechWiz Electronics makes a profit of 35 for each MP3 player sold and 136 for each DVD player sold. Last week, they sold a combined total of MP3 and DVD p

1. **State the problem:** Simplify the expression $$\frac{x^{-3} y^{3} x^{4}}{x^{-2} x^{5} y^{3}}$$. 2. **Recall the exponent rules:**

1. **State the problem:** Evaluate the expression $-2^2 + \left(-\frac{1}{3}\right)^{-3}$.\n\n2. **Recall order of operations and exponent rules:** Exponents are evaluated before n

1. **State the problem:** Deon drove to the mountains in 8 hours with heavy traffic and returned in 6 hours without traffic, driving 16 mph faster on the way back. We need to find

1. The problem is to simplify the fraction $\frac{7}{15}$ or understand why it might "not be working" in a certain context. 2. The formula for simplifying fractions is to divide th

1. **State the problem:** Evaluate $\frac{1}{2} \left( \frac{3}{5} + \frac{1}{3} \right)$ and simplify the result. 2. **Use the formula:** To add fractions, find a common denominat

1. Problem: Przedstaw liczbę $\sqrt{2\sqrt{2}}$ jako potęgę liczby 2. 2. Zapisz wyrażenie pod pierwiastkiem jako potęgę liczby 2. Wiemy, że $\sqrt{2} = 2^{\frac{1}{2}}$.

1. Problema cere să calculăm suma divizorilor naturali ai numărului $a + 22$, unde $$a = \sqrt{2024} + 6\sqrt{2015} - \sqrt{2024} - 6\sqrt{2015}.$$\n\n2. Observăm că termenii $\sqr

1. Problema cere să calculăm suma divizorilor naturali ai numărului $22 + a$, unde $a$ este definit prin ecuația $$2015^6 - 2024^6 + 2015^6 - 2024^6 = a.$$ 2. Mai întâi, calculăm v

1. **State the problem:** Find the equation of the straight line passing through the points $(5, 10)$ and $(9, 24)$ in the form $y = mx + c$. 2. **Formula for slope:** The slope $m

1. Planteamos el problema: Evaluar la expresión del ejercicio 46: $$2\cdot[8 - 3(4 + 2)] - 3$$. 2. Primero, resolvemos dentro del paréntesis interior: $$4 + 2 = 6$$.

1. **Stating the problem:** We start with the exponential growth function $$y=1\cdot 2^x$$ where $x$ is the day number and $y$ is the number of people who know the information. The

1. Problema: Resolver la operación con monomios $(-5x^5 y^2)(-3x^6 y^4)$. 2. Fórmula y reglas: Para multiplicar monomios, multiplicamos los coeficientes y sumamos los exponentes de