🧮 algebra

1. Stating the problem: Solve the equation $$\left(\frac{1}{2}\right)^x \cdot 8 - 4^{x-1} = 0$$ for $x$. 2. Rewrite the terms with base 2:

1. Let's clarify the method being discussed, likely completing the square. 2. The standard form of a quadratic equation is $ax^2 + bx + c = 0$.

1. Solve the quadratic equation $ax^2 + bx + c = 0$ by completing the square. Step 1: Divide all terms by $a$ (assuming $a \neq 0$) to get $x^2 + \frac{b}{a}x + \frac{c}{a} = 0$.

1. Let's clarify what "adding and subtracting half of the coefficient" usually refers to. It often comes up in the process of completing the square in algebra. 2. Consider a quadra

1. **Enunciado:** Dado o sistema com incógnitas $x,y,z$ e parâmetros reais $a,b$: $$\begin{cases} x - 4y + 3z = 2b \\ ay + z = b \\ x - y + (a+1)z = -b \end{cases}$$

1. **أوجد ناتج التعبير التالي في صيغة ترميز علمي:** المطلوب جمع العددين $98.6 \times 10^4$ و $7.24 \times 10^5$ بصيغة علمية.

1. **أوجد ناتج التعبير في صيغة ترميز علمي:** المعطى: $$ (98.6 \times 10^4) + (7.24 \times 10^5) $$

1. The problem is to complete the square for a quadratic expression such as $ax^2 + bx + c$. 2. Start with the quadratic expression in the form $x^2 + bx + c$ (assume $a=1$ for sim

1. **সমস্যা বর্ণনা**: g(t) = $\frac{t^4 + t^2 + 1}{t^2}$ এবং আমাদের $g(-3^{-1})$ নির্ণয় করতে হবে। 2. প্রথমে $-3^{-1}$ মানে $-\frac{1}{3}$, অর্থাৎ আমরা $t = -\frac{1}{3}$ বসাব।

1. Stating the problem: Simplify the expression $$\frac{12 w^{12}}{2 w^2}$$. 2. Simplify the numeric coefficients: $$\frac{12}{2} = 6$$.

1. State the problem: Evaluate the function $$f(x) = \frac{1 - x}{(x + 1)^2}$$ at $$a = -1$$. 2. Substitute $$x = -1$$ into the function:

1. Given the equation $5^x = 27$, we want to find the value of $k$ and the equation of the variation. 2. Taking the natural logarithm on both sides to solve for $x$, we get:

1. **Problem statement:** We are given a rectangle whose length is twice its width and its perimeter is 54 cm.

1. The nature of roots of a quadratic equation $ax^2+bx+c=0$ depends on the discriminant $\Delta=b^2-4ac$. 2. If $\Delta>0$, there are two distinct real roots.

1. **State the problem:** Differentiate between rational and irrational numbers. 2. **Explanation:**

1. **Énoncé du problème**: Montrer que l'ensemble $$F = \{(x,y,z) \in \mathbb{R}^3 \mid x + 2y = 0\}$$ est un sous-espace vectoriel de $$\mathbb{R}^3$$ et donner une base de $$F$$.

1. Let's start by stating the general form of a quadratic equation: $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are constants and $a \neq 0$. 2. To solve this quadratic equation,

1. Problem: Simplify $\frac{\sqrt{2}}{\sqrt{3}}$. Work: Multiply numerator and denominator by $\sqrt{3}$ to rationalize the denominator.

1. Let's start by clearly stating the problem: Solve the equation like a student. 2. Since the user did not specify an equation, assume a simple example: Solve for $x$ in the equat

1. সমস্যা বর্ণনা: গ) y^4 - 1 \over y^3 + y কে সবচেয়ে সরল রূপে প্রকাশ করতে হবে।

1. Problemi: Sa është 4% e 5600? Zgjidhje: