🧮 algebra

1. সমস্যা: $R = \frac{2\sqrt{Q}}{\sqrt{3Q} - 4}$ এই সমীকরণটি বিশ্লেষণ করব। 2. সূত্র: এখানে মূলত একটি ভগ্নাংশের মধ্যে বর্গমূল রয়েছে। বর্গমূলের নিয়ম হলো $\sqrt{a} \times \sqrt{b} = \

1. **State the problem:** Solve the equation $6\sqrt{2x+1} = x^2 - 6x + 26$ for $x$. 2. **Recall the formula and rules:** To solve equations involving square roots, isolate the roo

1. **State the problem:** We need to find the y-intercept of the straight line passing through the points $(2, 15)$ and $(6, 39)$. 2. **Formula used:** The equation of a line in sl

1. **Énoncé du problème :** On considère les fonctions $g(x) = x^2 - 4x + 4$ et $f(x) = (x+2)(x+4)$. Il faut déterminer les domaines de définition de $f$, $g$ et de la composée $f

1. **State the problem:** Solve the linear equation $8x - 3 = 2x + 10$ for $x$. 2. **Formula and rules:** To solve for $x$, we use the properties of equality: we can add, subtract,

1. Masalah: Tentukan persamaan garis lurus yang melalui titik (5,3) dan (4,6). 2. Rumus yang digunakan: Persamaan garis lurus dapat ditentukan dengan rumus gradien $m$ dan persamaa

1. The problem is to calculate 2 multiplied by the square root of 11. 2. The square root function is denoted as $\sqrt{\cdot}$ and it means the number which when multiplied by itse

1. **State the problem:** Simplify the expression $2x\sqrt{11}$. 2. **Understand the components:** The expression consists of a coefficient 2, a variable $x$, and the square root o

1. مسئله: حل معادله $x^2 - 4 = 0$. 2. فرمول استفاده شده: معادله درجه دوم به شکل کلی $ax^2 + bx + c = 0$ است. در اینجا $a=1$, $b=0$, و $c=-4$.

1. **State the problem:** Solve the equation $$\frac{1-\sqrt{2}}{2-\sqrt{2}} = \frac{\sqrt{3}x}{3\sqrt{3}}$$ and express the answer in surd form. 2. **Simplify the right side:** Si

1. **State the problem:** Solve the equation $$\sqrt{2k+3} = k+2$$ and determine which of the statements I, II, and III are true. 2. **Solve the equation:**

1. **State the problem:** Solve the equation $7 - 2x = 5x + 14$ for $x$. 2. **Write down the formula and rules:** To solve linear equations, we isolate the variable on one side by

1. **State the problem:** Evaluate $\log_2 \log_2 \sqrt{2\sqrt{2\sqrt{2}}}$ and verify if the answer $\frac{7}{16}$ is correct. 2. **Simplify the innermost expression:**

1. The problem is to understand the fraction $\frac{7}{16}$.\n\n2. A fraction represents a part of a whole. Here, $7$ is the numerator (the number of parts we have), and $16$ is th

1. **State the problem:** Evaluate $\log_2 \log_2 \sqrt{2 \sqrt{2 \sqrt{2}}}$. 2. **Simplify the innermost expression:** Start with $\sqrt{2 \sqrt{2 \sqrt{2}}}$.

1. **State the problem:** Solve the equation $$\frac{1-\sqrt{2}}{2-\sqrt{2}} = \frac{\sqrt{3}x}{3\sqrt{3}}$$ and express the answer in surd form. 2. **Simplify the right side:** Si

1. The problem is to find the value of $A$ given the initial condition $y(1) = 2$. 2. We need the equation or function involving $A$ and $y(x)$ to proceed. Since it is not provided

1. **Stating the problem:** Find the largest integer $n$ such that

1. Masalah: Tentukan bilangan bulat terbesar $n$ sehingga $$\frac{3+9+18+30+\cdots+n}{n} < 2021.$$\n\n2. Perhatikan deret di pembilang: 3, 9, 18, 30, ...\nDeret ini bukan aritmatik

1. **State the problem:** Simplify the expression $$\frac{x^2 + 2x + 1}{x + 3}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor the numerator and d

1. **State the problem:** Given points P(3, 0), Q(-1, 6), R(k, -6), and S(4, -7), with PQ parallel to RS, find the value of $k$. 2. **Recall the formula for slope:** The slope $m$