🧮 algebra

1. সমস্যাটি হলো, একজন ব্যবসায়ী প্রতিদিন ২০ কেজি ৪০০ গ্রাম ডাল বিক্রয় করলে, মাসে মোট কত ডাল বিক্রয় করতে পারবেন তা নির্ণয় করা। 2. প্রথমে, ২০ কেজি ৪০০ গ্রাম কে কেজিতে রূপান্তর করতে হব

1. **Stating the problem:** We need to find the missing numbers in the equivalent fractions given: a) $\frac{3}{5} = \frac{12}{\square}$

1. The problem is to verify the correctness of the given geometric sequence terms expressed as $a_n = a_m \cdot q$ for various indices $n$ and $m$. 2. Recall the formula for the $n

1. সমস্যাটি হলো: একটি সরলরেখার সমীকরণ নির্ণয় করা যা বিন্দু (2,3) দিয়ে যায় এবং ঢাল $m=4$। 2. সরলরেখার সমীকরণ সাধারণত হয়: $$y = mx + c$$ যেখানে $m$ ঢাল এবং $c$ $y$-অক্ষের ছেদ।

1. نبدأ بكتابة الدالة المعطاة: $$k(x) = \frac{(x \times x) - 4}{x - 1} = \frac{x^2 - 4}{x - 1}$$. 2. نلاحظ أن البسط هو فرق بين مربعين، يمكننا تفكيكه باستخدام قاعدة الفرق بين مربعين

1. **Stating the problem:** We are given the equation $$z^{50} - 1 = 0$$ and asked to analyze it.

1. المشكلة: حل الدوال هو إيجاد قيمة الدالة عند نقاط معينة أو تبسيطها. 2. القاعدة الأساسية: الدالة هي علاقة تربط كل عنصر من مجموعة معينة بعنصر واحد فقط من مجموعة أخرى.

1. The problem asks whether we should substitute values for all terms and the order to evaluate the sum of differences. 2. When evaluating expressions involving sums and difference

1. The problem is to understand the identity involving terms with powers of $R$ and how they relate to the value 1. 2. The identity given is: $$1 = \frac{1}{2} \times R \times R \t

1. **Problem Statement:** Show that $$\sum_{r=15}^n (6r^2 + 2) = n^3 + (n+1)^3 - k$$ where $k$ is a constant.

1. **State the problem:** We need to find the equation of a line parallel to line A that passes through point P. 2. **Identify the slope of line A:** Line A passes through points (

1. **Problem statement:** Find the values of $x$ for which $W = \frac{\sqrt{x+2}}{2x}$ is non-real. 2. **Recall the rules:**

1. **State the problem:** We need to determine the values of $x$ for which the expression $$M = \frac{1}{\sqrt{2x - 1}}$$ is real. 2. **Understand the formula and rules:** For $M$

1. **State the problem:** We are given that $b$ is inversely proportional to the cube of $a$, and we need to find the constant of proportionality $k$ when $b=60$ and $a=5$. 2. **Wr

1. The problem is to evaluate $$\left(\frac{81}{16}\right)^{\frac{1}{4}} + \left(\frac{81}{16}\right)^0$$. 2. Recall the rules:

1. The problem is to convert a mixed fraction into an improper fraction or a whole number. 2. A mixed fraction consists of a whole number and a proper fraction, for example, $2 \fr

1. The problem is to calculate $15^{14}$, which means multiplying 15 by itself 14 times. 2. The formula for exponentiation is $a^n = a \times a \times \cdots \times a$ ($n$ times).

1. **State the problem:** Evaluate the expression $-3^2 + 2(-3) + 1$. 2. **Recall order of operations:** Exponents are evaluated before multiplication and addition/subtraction.

1. Let's first state the problem: You have expressions $X = \text{belamder}x$ and $T = \text{be}(\lamder + 1)t$ and you want to check if they are correct. 2. To analyze this, we ne

1. **Problem:** Solve the equation $$|4x - 1| = |x - 3|$$. 2. **Formula and rules:** The absolute value equation $$|A| = |B|$$ implies either $$A = B$$ or $$A = -B$$.

1. **State the problem:** Solve the equation $$9^{x+3} = \frac{3\sqrt{3}}{27^x}$$ for $x$. 2. **Rewrite bases as powers of 3:**