🧮 algebra

1. Let's start with understanding what a fraction is. A fraction represents a part of a whole and is written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denominator.

1. সমস্যাটি বোঝা যাক: একটি সান্ধ্যস্কুলের উচ্চতার ${3\over4}$ অংশ এবং ৩৬৩ কেন্দূবল আছে, এখানে উচ্চতা নির্ণয় করতে হবে। 2. ধরুন পুরো উচ্চতা $h$। তাহলে ${3\over4}h = 363$ সেমি।

1. Problem statement: Solve the quadratic equation $$Bx^2 - 13x + 52 = 0$$ using the quadratic formula. 2. Recall the quadratic formula for an equation $$ax^2 + bx + c = 0$$ is:

1. **Stating the problem:** We want to determine the type of solution a system of equations has if its two lines are parallel. 2. **Understanding parallel lines:** Parallel lines h

1. نبدأ بحل التعبير المعطى: $(1 - \sqrt{2})(2 - \sqrt{2}) - \sqrt{3}(\sqrt{3} - 1)$. 2. نفرّع الحد الأول باستخدام قانون التوزيع:

1. The problem asks to simplify $$(-2 + \sqrt{-4}) + (3 - \sqrt{-7})$$ in the form $$a + bi$$ where $$a$$ and $$b$$ are real numbers. 2. Recall that $$\sqrt{-1} = i$$, the imaginar

1. State the problem: Two kinds of oil, Oil A costing 40 per liter and Oil B costing 70 per liter, are mixed to form 100 liters of mixture costing 5500. 2. Define variables: Let $x

1. Let's understand the problem: "When solving a system by elimination, what is the main goal?" 2. A system of equations involves finding values for variables that satisfy all equa

**1. Stating the problem:** We are given a quadratic function $$y=2x^2 - 3$$ and a partially filled table of values for $$x = -3, -2, -1, 0, 1, 2, 3$$ with corresponding $$y$$ valu

1. **State the problem:** Solve the system of linear equations: $$x + y = 10$$

1. **Problem:** Solve the system of equations: $$x + y = 10$$

1. **Problem (01a):** Suman took a loan of 60000 at an 18% annual simple interest rate to be paid in 3 years. (i) Find the interest for 1 year.

1. Stating the problem: Simplify each logarithmic expression from a) to z). 2. a) $y = \log x$ is the basic common logarithm. No simplification needed.

1. We are given a monthly payment of $20.34 for a cell phone over a period of two years. 2. To find the total cost, we need to calculate the number of months in two years: $$2 \tex

1. **State the problem:** You bike 5 miles to campus and 5 miles back home, totaling 10 miles. You go faster going to campus (downhill) than returning by 9 miles per hour.

1. The problem asks to find the discount when the selling price (SP) is 841.50 and the discount rate (DR) is 15%. 2. The formula to find the discount (D) when we know the selling p

1. Stating the problem: We need to find the discount given the Original Price (OP) = 5610, Selling Price (SP) = 841.50, and Discount Rate (DR) = 15%. 2. The given discount rate see

1. نبدأ بقراءة السؤال: لدينا التغير في دالة 9(x) التي تمثل ص = 9(س) في الفترة من $-3$ إلى $5$ وتساوي 12، ونعلم أن 9(3) = 4. 2. المطلوب هو إيجاد قيمة 9(-1).

1. نبدأ بكتابة المعادلة المعطاة: $$هـ(s) + 1 هـ(s) - 4$$ 2. المعطى أيضاً:

1. Problema: Hitunglah nilai dari bentuk $3a^{\frac{3}{4}}$ dengan $a=16$. 2. Substitusi nilai $a=16$ ke dalam ekspresi:

1. Masalah: Susun bilangan $8^2$, $4^{32}$, $16^{18} \times 4^4$, $10$, dan $2^{81}$ dari yang kecil ke yang besar. 2. Ubah semua bilangan menjadi pangkat basis yang sama jika memu