🧮 algebra

1. **State the problem:** We have three functions:

1. مسئله: نوع عدد اعشاری مربوط به کسر 5/42 را مشخص کنید. 2. برای تعیین نوع عدد اعشاری کسر، باید مخرج کسر را تجزیه کنیم و ببینیم فقط شامل عوامل 2 و 5 است یا خیر.

1. **State the problem:** Simplify the expression $\frac{\sqrt{1}}{4 - x^2}$. 2. **Recall the properties:** The square root of 1 is 1 because $\sqrt{1} = 1$.

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{2\sqrt{8}}}{\sqrt[3]{\sqrt{2\sqrt{2}}}}$$. 2. **Recall the rules:**

1. **Problem statement:** Find (i) the domain and range of functions $f(x) = \sqrt{\frac{1}{4} - x^2}$ and $h(x) = \tan(x - 3)$.

1. **State the problem:** Solve the system of linear equations: $$8y = -x - 20$$

1. **State the problem:** Solve the linear equation $x + 8y = -20$ for $x$ in terms of $y$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by m

1. Masalah: Cari PBB (Pembagi Bersama Terbesar) dari 312 dan 70 menggunakan algoritma Euclidean dan ekspansi ke bentuk linear. 2. Rumus utama: Algoritma Euclidean untuk PBB menggun

1. Masalah: Nyatakan PBB(126, 35) = 7 sebagai kombinasi linear dari 126 dan 35. 2. PBB (Faktor Persekutuan Terbesar) dari dua nombor boleh dinyatakan sebagai kombinasi linear: $$\t

1. Le problème consiste à comprendre comment calculer les déterminants \(\Delta_1\), \(\Delta_2\) et \(\Delta_3\) d'une matrice donnée. 2. Rappel : Le déterminant d'une matrice car

1. **Énoncé du problème** : On veut vérifier si la matrice $A$ est symétrique et définie positive. 2. **Symétrie** : Une matrice est symétrique si elle est égale à sa transposée, c

1. **Problem:** Calculate the value of $2^5 \times 2^3$. **Solution:** Use the law of exponents: $a^m \times a^n = a^{m+n}$.

1. **Problem:** Calculate $2^3$. **Solution:** Use the power rule: $a^n$ means multiply $a$ by itself $n$ times.

1. **State the problem:** Solve the equation $$3\left(x+\frac{1}{x^2}\right)-7\left(1+\frac{1}{x}\right)=0$$ for $x$. 2. **Rewrite the equation:**

1. The problem is to find the function $H_4(x)$ defined by the formula $$H_4(x) = (-1)^4 e^{x^2} \frac{d^4}{dx^4} e^{-x^2}.$$ 2. This formula involves taking the fourth derivative

1. The problem is to order the given expressions from least to greatest. 2. The expressions are: $\sqrt{15}$, $2!$, $e^4$, $\frac{5}{9}$, $\int_1^8 x \, dx$, $\log_3(26)$, $\infty$

1. **Problem statement:** Find the population of the village in the beginning of 2079 BS given:

1. The problem is to verify or simplify the expression $2\sqrt{13} \times 3\sqrt{12} \times 4\sqrt{12}$ and compare it to $3^2 \times 4^3$. 2. First, recall that $a\sqrt{b} = a \ti

1. The problem asks us to determine which statements about the function $g(x)$ are true based on the graph. 2. From the graph description, the vertex is at approximately $(0, -1)$,

1. The problem asks to express the ordered pair from the table using function notation. 2. The table shows pairs $(x, f(x))$ as $(2,6)$, $(7,3)$, and $(9,5)$.

1. **Stating the problem:** Solve the equation $$x^r y^r = x^r + y^r$$ for variables $x$, $y$, and $r$. 2. **Rewrite the equation:** Move all terms to one side: