🧮 algebra

1. The problem is to find the value of $x$ if $2|2x-1|=\frac{1}{4}$. 2. First, divide both sides of the equation by 2 to isolate the absolute value:

1. Here is a quadratic equation you can solve: $$x^2 - 5x + 6 = 0$$

1. The problem is to simplify the expression $\frac{1}{2} + \left( \frac{3}{5} - \frac{1}{3} \right)$ and verify which option matches the simplified result. 2. Start by simplifying

1. Énonçons le problème : On cherche le polynôme caractéristique de la matrice $A=\begin{pmatrix}1 & 0 & 0 \\ 1 & 0 & 3 \\ 1 & -1 & 3 \end{pmatrix}$. 2. Rappel : Le polynôme caract

1. The problem is about representing multiplication explicitly in STACK notation. 2. In mathematics, multiplication is often implied by writing variables and numbers side by side,

1. Let's consider a challenging O Level vectors problem involving geometry and vector algebra. 2. Problem: In triangle $ABC$, let $\vec{AB}=\mathbf{a}$ and $\vec{AC}=\mathbf{b}$. P

1. प्रश्न 25: वर्धन मासिककम् 4% के प्रभाव क्या होगी? यहाँ मासिक वर्धन दर 4% दी गई है। इसका मतलब है हर महीने मूल्य 4% बढ़ता है।

1. The problem states that \(\log x \log x\) is the same as the square of \(\log x\). 2. We start with the expression \(\log x \log x\).

1. The phrase "normal arithmetic expressions" typically means writing mathematical expressions using standard arithmetic operators such as addition (+), subtraction (-), multiplica

1. **Stating the problem:** Prove that for all integers $n \geq 1$, the sum of the series $$ 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots + \frac{1}{2^n} = \frac{2^n - 1}{2

1. Problem 24: Find the x- and y-intercepts of the given line. Given the graph description, the line passes through x-intercept roughly at $x=3$ and y-intercept roughly at $y=-2$.

1. Problem 18: Find matrix $X$ such that $$X + \begin{bmatrix}4 & 8 \\ 1 & -2\end{bmatrix} \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix} = \begin{bmatrix}6 & 7 \\ 1 & 2\end{bmatrix}$$

1. Problem: Find the unknown matrix $X$ if $$X + \begin{bmatrix}4 & 8 \\ 1 & -2

1. Find the vertical and horizontal asymptotes of the curve defined by $$xy - 5x - 2y + 3 = 0.$$ Step 1: Rearrange the equation to express $y$ in terms of $x$.

1. The problem is to solve the equation involving the absolute value: $|6-3X|=9$. 2. Recall that $|A|=B$ means $A=B$ or $A=-B$. So here, $6-3X=9$ or $6-3X=-9$.

1. Problem 10: Given ratios $x:y=2:3$ and $y:z=2:3$, find ratio $x:z$. Since $x:y=2:3$, we write $\frac{x}{y}=\frac{2}{3}$.

1. Problem statement: Calculate areas A1, A2, A3, total area, and perimeter of the composite shape formed by three rectangles with given dimensions. 2. Calculate area A1:

1. **সমস্যার বিবৃতি:** Cramer's Rule ব্যবহার করে নিম্নলিখিত সমীকরণগুলোর জন্য $x_1,x_2,x_3$ এর মান নির্ণয় করো: $$

1. Let's understand the problem: find the value of $0 \div \infty$ where $\infty$ denotes infinity. 2. Division by infinity is a limit concept; it isn't a standard arithmetic opera

1. The problem gives us two equations involving $x_1$ and $x_2$: $\begin{cases} x_1 + x_2 - x_1 x_2 = 7 \\ x_1 + x_2 + x_1 x_2 = -5 \end{cases}$

1. **Problem 1:** Given $y=12$ when $x=4$, find $y$ when $x=8$ assuming inverse variation. 2. In inverse variation, $y$ varies inversely with $x$ means $y=\frac{k}{x}$ for some con