🧮 algebra

1. **State the problem:** Given $p=100000$ and the equation $p^2 + 2pq + q^2 = 1$, find the value of $q$. 2. **Recall the formula:** The equation $p^2 + 2pq + q^2 = 1$ can be recog

1. **State the problem:** Solve the equation $$(-4) + (-1) + 2 + 5 + \ldots + x = 437$$ where the terms form an arithmetic sequence. 2. **Identify the sequence:** The terms are $$-

1. The problem asks if $\log(7/5)$ divided by $\log(3/4)$ is the same as $\lg(7/5)/\lg(3/4)$. 2. Here, $\lg$ typically denotes the logarithm base 10, and $\log$ without a base ofte

1. **State the problem:** Simplify the expression $$5^{3 - \log_2 25} + 3^{2 - \log_3 3} - 4^{4 - \log_2 5}.$$\n\n2. **Recall logarithm and exponent rules:**\n- $a^{m-n} = \frac{a^

1. **State the problem:** Solve the equation $5 \cdot 6^x = 7 \cdot 8^x$ for $x$. 2. **Rewrite the equation:** We want to isolate $x$. Start by dividing both sides by $7 \cdot 6^x$

1. Het probleem is om gelijknamige breuken te rangschikken, dat wil zeggen breuken met dezelfde noemer. 2. Bij gelijknamige breuken vergelijken we alleen de tellers, omdat de noeme

1. **State the problem:** We want to understand how to go from the equation $$(\ln 3)(\ln 3 + \ln x) = (\ln 4)(\ln 4 + \ln x)$$

1. **Problem statement:** Löse die Gleichung $$ (x - 29)(-2x + 14) = 0 $$ und finde die Werte von $x_1$ und $x_2$. 2. **Formel und Regel:** Wenn das Produkt zweier Faktoren null is

1. Enunciado: Determine o valor de $$\log_a \left( \frac{a^2}{\sqrt[3]{b}} \right) \times \log_b \left( \frac{c^2 \sqrt{b}}{a^3} \right)$$

1. Das Problem scheint darin zu bestehen, verschiedene Werte bei bestimmten Nummern (5, 6, 7) zu vergleichen, möglicherweise aus einer Berechnung oder Messung. 2. Wir betrachten di

1. **State the problem:** Solve the equation $$|p-1| - |2-p| = -10$$. 2. **Recall the definition of absolute value:** For any real number $x$, $$|x| = \begin{cases} x & \text{if }

1. **Problem statement:** Simplify the expression $-4^5 + 11 \cdot 4^5$. 2. **Recall the distributive property:** For terms with the same base and exponent, $a \cdot x^n + b \cdot

1. The problem is to find the value of $x$. 2. Since no equation or context is given, we cannot solve for $x$ directly.

1. **State the problem:** Mrs. Mary Moolah invested a total of $20,000 in two types of bonds. One bond pays 5% interest, and the other pays 8%. The total interest earned from both

1. **State the problem:** Solve the equation $$\frac{5}{2x + 1} = \frac{3}{x + 3}$$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross products

1. The problem involves comparing the fractions $\frac{3}{6}$, $\frac{6}{10}$, and $\frac{9}{12}$.\n\n2. To compare fractions, we can simplify each fraction to its lowest terms or

1. Problem: Lag en veldig kort jukselapp om algebra. 2. Algebra handler om å bruke bokstaver (variabler) for å representere tall og løse likninger.

1. Let's start by understanding what algebra is: it's a way to use letters (called variables) to represent numbers in math problems. 2. A very important rule is that you can do the

1. Problema: Risolvi le equazioni esponenziali da 109 a 113. 2. Formula e regole importanti: Per risolvere equazioni esponenziali della forma $a^{f(x)} = b^{g(x)}$, se $a$ e $b$ po

1. Problem statement: Simplify the expression $5y^2 - 2y^3 - 7y^2 + 7y^3$. 2. Formula and rules: To combine like terms, add the coefficients of terms that have the same power of $y

1. Il problema riguarda le equazioni e disequazioni di grado superiore al primo. 2. Un'equazione di grado superiore al primo è un'equazione in cui la variabile compare con esponent