🧮 algebra

1. The problem is to simplify the expression $$\frac{1-(\frac{1}{2})x^n}{1-(\frac{1}{2})}$$. 2. Start by simplifying the denominator: $$1-\frac{1}{2} = \frac{2}{2} - \frac{1}{2} =

1. The problem is to simplify the expression $$\frac{1-\left(\frac{1}{2}\right)^n}{1-\frac{1}{2}}$$. 2. First, simplify the denominator:

1. The problem is to simplify the expression $$\frac{1-\left(\frac{1}{2}\right)x^n}{1-\left(\frac{1}{2}\right)}$$. 2. Start by simplifying the denominator:

1. **Stating the problem:** Understand that equivalent ratios are two ratios that express the same relationship between numbers. 2. **Example 1:** Is $\frac{2}{3}$ equivalent to $\

1. ප්‍රශ්නය අර්ථ දැක්වීම: සීමෝන්ට වැලි හා බඩුම කානම් වල අනුපාතය 2 : 13 ලෙස ඇත. 2. සීමෝන් මල් පෝවි සෑදිමට එක වාරයට බඩුම කානම් 60 ක් සන්ක් කරයි. එනම් $x+y=60$

1. **Convert 0.14 to a fraction and match options** 0.14 as a fraction is $$ \frac{14}{100} = \frac{7}{50} $$ which does not exactly match any option. Let's check each option by de

1. **State the problem:** A shopkeeper sells a table at a 20% discount and earns 60% profit. We need to find his new profit percentage if he sells the same table at a 40% discount.

1. The problem asks to solve an equation or expression using "tricks," which usually means simplifying, factoring, or using algebraic identities to make the problem easier. 2. Sinc

1. Restate the problem: A shopkeeper sells a table at a 20% discount and earns 60% profit. We need to find the new profit percent if the discount is increased to 40%. 2. Define var

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 $$X + \begin{bmatrix}4 & 8 \\ 1 & -2\end{bmatrix} \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix} = \begin{bmatrix}6 & 7 \\ 1 & 2\end{bmatrix}$$