🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{-20+V3-V1}{12}-\frac{\frac{2}{20+V3-V1}}{10}-\frac{V1}{10}$$. 2. **Rewrite the expression clearly:**

1. Problema afirmă că matricele nu comută neapărat, adică $AB \neq BA$ în general. 2. Se consideră matricele $A$ și $B$ și matricea identitate $I_n$ de dimensiune $n$.

1. Problema: Avem două matrice pătratice $A$ și $B$ de ordin $n$ cu elemente complexe, pentru care se știe că $$A^3 - B^3 = A(B - A)A$$ și $$\det(A + I_n) = \det(B + I_n).$$ Trebui

1. **State the problem:** Convert the mixed number percentages $3\ 7/8\%$ and $4\ 3/8\%$ into decimal form. 2. **Recall the formula:** To convert a mixed number percentage to a dec

1. We are asked to find the sum of the fractions: $\frac{2}{10} + \frac{5}{15} + \frac{2}{3} + \frac{1}{5} + \frac{2}{4}$.\n\n2. To add fractions, we need a common denominator. The

1. **State the problem:** Solve the equation exactly without rounding until the final answer. 2. **Identify the equation:** The user did not provide a specific equation, so I canno

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 $\sqrt{2} = 2^{\frac{1}{2}}$.