🧮 algebra

1. **State the problem:** We need to factorize the quadratic expression $x^2 + 14x + 49$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b

1. Énoncer les définitions du cours : 1) Une valeur propre \(\lambda\) d'un endomorphisme \(f\) est un scalaire tel qu'il existe un vecteur non nul \(v\) vérifiant \(f(v) = \lambda

1. Muammoni tushuntirish: berilgan ifodalar ustida amallarni bajarish kerak: 28. $1 \tfrac{3}{7} (2.8a - 2.1) - 1 \tfrac{1}{9} (2.7a - 3.6)$ ni hisoblaymiz.

1. Let's start by writing the expression clearly: $$\sqrt{2 - \frac{\sqrt{3}}{2}} \times \sqrt{2 + \frac{\sqrt{3}}{2}}$$ 2. We can use the property of square roots that $$\sqrt{a}

1. **State the problem**: Simplify the expression $$\sqrt{2 - \frac{\sqrt{3}}{2}} \times \sqrt{2 + \frac{\sqrt{3}}{2}}.$$\n\n2. **Recall the property of radicals**: The product of

1. The problem involves calculating simple interest, which is given by the formula $$SI = \frac{P \times R \times T}{100}$$ where $P$ is the principal, $R$ is the rate per annum, a

1. Stating the problem: We have a geometric progression (GP) where the third term is $\frac{9}{2}$ and the fifth term is $\frac{81}{8}$. We need to find: A. The common ratio $r$

1. We are given a geometric progression with terms $2$, $x$, $y$, and $250$. 2. In a geometric progression, the ratio between consecutive terms is constant. Let this common ratio b

1. The problem asks to find the product of 1 and \(\pi\).\n2. Recall that multiplying any number by 1 results in the same number.\n3. Therefore, \(1 \times \pi = \pi\).\n\nFinal an

1. **Stating the problem:** Simplify and evaluate the expression $$\left(\frac{2\sqrt{2} - \sqrt{5}}{\sqrt{3}}\right)^{2023} \times \left(\frac{2\sqrt{2} + \sqrt{5}}{\sqrt{3}}\righ

1. Given the matrix equation: $$\begin{pmatrix} 3 & 2 \\ 7 & -2 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 12 \\ 8 \end{pmatrix}$$

1. The problem is to divide one polynomial by another using long division. 2. Start by dividing the leading term of the dividend by the leading term of the divisor to find the firs

1. The problem states that the $n^{th}$ term of a sequence is given by $$a_n=(-2)^{\frac{n}{2}}.$$ 2. We are asked to find the $2n^{th}$ term of the sequence, denoted as $a_{2n}$.

1. **Problem (a):** A hire tool firm's net return decreases by 10% annually. The current net gain is 400. Find the total of all future profits assuming the tool lasts forever. 2. S

1. Solve (a) $\frac{n}{3} x - 7 + 5 \le 6$. Simplify the left side: $\frac{n}{3} x - 2 \le 6$.

1. **Find the features of line A**. Line A passes through points (1,0) and (0,6).

1. **State the problem:** Simplify the expression $$\frac{xy}{x^2 - y^2} - \frac{y}{x + y}.$$\n\n2. **Factor the denominator:** Notice that $$x^2 - y^2$$ is a difference of squares

1. **Find the gradient between each pair of points given:** Gradient formula between points $(x_1,y_1)$ and $(x_2,y_2)$ is

1. Stating the problem: Simplify the expression $$\frac{2a + 5}{a + b} \times \frac{a - b}{xy} - \frac{y}{x^2 - y^2} \div \frac{x + y}{1}$$

1. The problem is to understand how the value of $m$ in linear equations of type $y = mx + c$ affects the graph. 2. We have two linear functions given:

1. Stating the problem: A car covers 180 kilometers in 3 hours. We want to find how many kilometers it covers in 5 hours. 2. Determine the speed of the car by dividing the distance