🧮 algebra

1. The problem asks us to find the slope-intercept form of a line with slope $\frac{5}{6}$ passing through the point $(12,4)$. 2. Recall the slope-intercept form is $y = mx + b$, w

1. **Problem 1:** Solve the systems: \(x + y = -2ع\) and \(\frac{x}{4} = -\frac{y}{3}\).

1. **بين أصغر مجموعة تنتمي إليها الأعداد التالية:** - $C = 1 + \frac{1}{2 + \frac{1}{2 - \frac{1}{\frac{3}{5}}}}$

1. **بيان المشكلة:** لدينا الدالة $f(x)=\frac{2x}{1+|x|}$. نريد أن نثبت أن $f$ دالة متزايدة على مجال غير محدود.

1. We start with the expression \((3x - \sqrt{2})(3x + \sqrt{2}) - (x - \sqrt{5})^2\). 2. Recognize the first part as a difference of squares: \((a - b)(a + b) = a^2 - b^2\).

1. The problem is to find the time taken to travel the same distance at a different speed. 2. Given: original travel time $t_1 = 5$ hours, original speed $v_1 = 56$ km/hr.

1. First, state the problem: Solve the equation $1 - 2xx - y + 2 = 44$ for the variables. 2. Combine like terms on the left side: $1 + 2 = 3$, so the equation becomes $3 - 2xx - y

1. We are given the function $$h(x) = 2 \cdot (\ln x)^4 + 3$$. 2. To determine the domain $$D_h$$ of $$h(x)$$, note that the inside function involves $$\ln x$$.

1. **Simplify** $ (8m^{3})^{\frac{1}{3}} $ with positive powers. Step 1: Apply the power of a power rule: $$ (a^{m})^{n} = a^{m \times n} $$

1. Problem: Odrediti koeficijent uz $x^{36}$ u razvoju binoma $(1+x)^{-5}$ u red potencija. 2. Razumevanje: Binomski red za $(1+x)^n$ gde je $n$ realan broj je $$ (1+x)^n = \sum_{k

1. The problem asks us to develop (expand and simplify) the expression $$(\sqrt{7}-3)(\sqrt{7}+3)$$. 2. Notice this is a product of conjugates of the form $(a-b)(a+b)$ which equals

1. The problem statement is not fully provided, so I'll demonstrate how to find solutions for a generic algebraic equation, say $ax^2 + bx + c = 0$. 2. To solve the quadratic equat

1. We need to expand the expression $ (x + 2\sqrt{5})^2 $. 2. Use the algebraic identity for the square of a binomial:

1. The problem involves understanding the expression $x + 2\sqrt{5}$. 2. This expression consists of a variable term $x$ and a constant term $2\sqrt{5}$.

1. The problem asks to simplify the expression $$(3+2\sqrt{7})^2$$. 2. Use the formula for squaring a binomial: $$(a+b)^2 = a^2 + 2ab + b^2$$.

1. **Statement:** Simplify and evaluate the expressions A, B, C, D as given, and also simplify algebraic expressions involving variables a, b, c. ---

1. Let's start by stating the general approach: to solve an algebraic problem, we first identify the equation or expression, understand what's being asked, and then apply relevant

1. Simplify \(\frac{4-\frac{9}{x^2}}{2-\frac{3}{x}}\). Rewrite numerator: \(4-\frac{9}{x^2} = \frac{4x^2 - 9}{x^2} = \frac{(2x - 3)(2x + 3)}{x^2}\).

1. Simplify the expression $\frac{39.4 - \frac{9}{x^2}}{2 - \frac{3}{x}}$ by finding a common denominator for numerator and denominator. 2. For each choice (a), (b), (c), and (d),

1. Vous avez demandé un exemple de problème mathématique. 2. Voici un exemple simple en algèbre : Résoudre l'équation $2x + 3 = 7$.

1. The problem is to find a formula for the sum of squares from 1 to $n$, written as $$\sum_{i=1}^n i^2.$$\n\n2. This sum is the addition of all squared integers starting from 1 up