🧮 algebra

1. **State the problem:** Divide the polynomial $3x^3 + 2x^2 - x + 4$ by the binomial $x - 1$. 2. **Formula and method:** We use polynomial long division or synthetic division to d

1. The problem is to understand the value of the probability expressed as $2.23 \times 10^{-7}$, which represents a very small number. 2. The expression $2.23 \times 10^{-7}$ is in

1. **State the problem:** We have 19 swans, 67 ducks, and 33 geese on a lake. We need to write the ratio of swans to ducks to geese in the form $1 : m : n$ where $m$ and $n$ are de

1. **State the problem:** We are given the fractions of black, silver, and blue cars in a garage as $\frac{1}{12}$, $\frac{7}{12}$, and $\frac{1}{3}$ respectively. We need to write

1. **State the problem:** Simplify the expression $$\frac{18u^{14}}{3u^2 \times 10u^6}$$. 2. **Write the expression clearly:** $$\frac{18u^{14}}{3u^2 \times 10u^6} = \frac{18u^{14}

1. **State the problem:** Simplify the expression $$\frac{18u^{14}}{3u^2} \times 10u^6$$. 2. **Recall the rules:**

1. **State the problem:** Expand and simplify the expression $4(3k + 4) - 2(k + 2)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor o

1. The problem involves calculating a percentage based on given quantities of ingredients. 2. We are given 25% g of butter, 500 g of sugar, 650 g of flour, and 425 g of rice.

1. The problem asks for the ratio of the amount Mr Sharma pays to the painter, simplified to its lowest terms. 2. Given the ratio of payments: painter : plumber : electrician = 245

1. **Problem Statement:** Suppose a company produces and sells $x$ units of a product. The cost to produce $x$ units is given by the cost function $$C(x) = 500 + 20x + 0.05x^2,$$ w

1. Diketahui matriks: $$A = \begin{bmatrix} 2 & -3 \\ -1 & 5 \end{bmatrix}, \quad B = \begin{bmatrix} -1 & 2 \\ 2 & 3 \end{bmatrix}$$

1. Masalah: Tentukan akar-akar dari persamaan kuadrat $x^2 - 5x + 6 = 0$. 2. Rumus yang digunakan adalah rumus kuadrat: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ di mana $a$, $b$,

1. **Problem statement:** The number of tigers in India in 2014 is approximately 30.48% greater than in 2010. We need to find the number of tigers in 2010, given the 2014 number. 2

1. **State the problem:** Simplify the expression $$\frac{y+1}{y^{2}-4} - \frac{5}{y+2}$$. 2. **Recall the formula and rules:**

1. The problem involves a fraction where the numerator is 5 and the denominator is an expression. 2. To solve or simplify such a fraction, we use the formula for division of expres

1. **State the problem:** Simplify the expression \[ \frac{y + 1}{y^2 - 4} - \frac{y + 2}{5} \]. 2. **Recall the formula and rules:**

1. Diketahui matriks $$A=\begin{bmatrix}-4 & 5 & 2 \\ 0 & -2 & 4 \\ -1 & -6 & 3\end{bmatrix}$$, tentukan nilai determinan $$\det(A)$$. 2. Rumus determinan matriks 3x3 adalah:

1. **Stating the problem:** The total number of students in a school is 1650. 70% of the pupils are boys. We need to find how many girls are there in the school. 2. **Formula and e

1. **Stating the problem:** Given the relation $$I = 1 + \frac{u}{f}$$

1. Problem: Find the domain and range of the function $f(x) = \sqrt{x^2 + 4}$. 2. Formula and rules: The domain of a function under a square root must satisfy the radicand $\geq 0$

1. সমস্যা: একটি সরল রৈখিক সমীকরণ সমাধান করুন, যেমন $2x + 3 = 7$। 2. সূত্র: সরল রৈখিক সমীকরণের সাধারণ রূপ হল $ax + b = c$, যেখানে $a$, $b$, এবং $c$ ধ্রুবক। সমাধানের জন্য, $x$ কে একপ