🧮 algebra

1. **State the problem:** Find the value of $$\left(\sqrt{\frac{6.231}{242.7}}\right)^3$$ using logarithm tables. 2. **Rewrite the expression:** Let $$x = \frac{6.231}{242.7}$$. Th

1. The problem is to find the square root of a number. 2. The square root of a number $x$ is a value $y$ such that $$y^2 = x$$.

1. **State the problem:** Calculate $\frac{6.231}{(242.7)^3}$ using logarithm tables. 2. **Formula and rules:** Using logarithms, division and powers can be transformed into subtra

1. **Problem statement:** The sum of the first two terms of an arithmetic series is 47, and the thirtieth term is -62. Find: a) The first term and the common difference.

1. **State the problem:** Factorize the expression $x^2 + 25y^2$. 2. **Recall the formula:** The sum of squares $a^2 + b^2$ generally cannot be factorized over the real numbers int

1. **State the problem:** Solve the quadratic equation $$3x - 15x + 18 = 0$$. 2. **Simplify the equation:** Combine like terms:

1. **State the problem:** We need to find which expression is equivalent to $ (xy)^{\frac{9}{5}} $, where $x$ and $y$ are positive. 2. **Recall the exponent and root rules:**

1. The problem is to understand and solve questions related to logarithms. 2. The logarithm function is defined as $\log_b(a) = c$ means $b^c = a$, where $b$ is the base, $a$ is th

1. Mari kita buktikan identitas pertama: $$12 - 22 + 32 - \cdots + (-1)^{n-1} n^2 = (-1)^{n-1} \frac{n(n+1)}{2}$$

1. Let's start by understanding what a logarithm is. A logarithm answers the question: to what power must we raise a base number to get another number? For example, $\log_b(a) = c$

1. Énoncé du problème : Résoudre les inéquations suivantes :

1. **State the problem:** We are given two equations: $$ (x + y)^6 = 64 $$

1. **State the problem:** Simplify the expression $ax^{3} + ax^{2}$ without factoring. 2. **Recall the expression:** The given expression is $ax^{3} + ax^{2}$.

1. **State the problem:** Simplify the expression $ax^3 + ax^2$. 2. **Formula and rules:** To simplify expressions like this, we use the distributive property: $a(b + c) = ab + ac$

1. **State the problem:** Factorise the expression $ab^2 + a^2b$. 2. **Identify common factors:** Both terms contain the variables $a$ and $b$.

1. **State the problem:** We need to simplify the expression $\frac{m-7}{3}$. 2. **Formula and rules:** Division of an expression by a number means dividing each term in the numera

1. **Problem statement:** Expand $$\sqrt{\frac{1+m}{1-m}}$$ in ascending powers of $m$ up to and including the term in $m^3$. State the values of $m$ for which the expansion is val

1. **State the problem:** We need to find which equation matches the line passing through points $(-8, -8)$ and $(8, 4)$.\n\n2. **Find the slope of the line:** The slope formula is

1. **Stating the problem:** We need to find the value of the expression $\frac{6!}{3!} + 4$. 2. **Recall the factorial definition:**

1. Masalah yang diberikan adalah menentukan nilai dari ekspresi $\frac{6!}{3!} + 4$. 2. Faktorial ($n!$) adalah hasil perkalian semua bilangan bulat positif dari 1 sampai $n$. Cont

1. **State the problem:** We have an element with an initial mass of 420 grams that decays by 11.8% per minute. We want to find how much of the element remains after 16 minutes, ro