🧮 algebra

Problem: Simplify the expression $5x^2 + 7x - 2x^2 + 9y + 8y^2 - 3x$. 1. Identify like terms.

1. **State the problem:** Simplify the given algebraic expressions and perform the indicated operations (multiplication and division) on the rational expressions. 2. **Expression 1

1. **State the problem:** Simplify the expression $a(\sinh(\frac{b}{a}) - \sinh(-\frac{b}{a}))$. 2. **Recall the property of hyperbolic sine:** $\sinh(-x) = -\sinh(x)$.

1. **State the problem:** We need to find the total money raised from selling 100 tickets, where adult tickets cost 18 and child tickets cost 12.5. 2. **Analyze the data:** The cum

1. **State the problem:** Simplify the expression $9x^2 - 16(2x - 3y)^2$. 2. **Expand the squared term:**

1. Problem: The perimeter of a rectangular plot is 860 m. Its length is 4 m more than its breadth. Find length and breadth. Step 1: Let breadth = $x$ m.

1. Zadání problému: Rozložte číslo na prvočísla. 2. Nejprve určete číslo, které chcete rozložit (uživatel neuvedl konkrétní číslo, proto uvedu příklad: 60).

1. Tentukan himpunan penyelesaian dari sistem persamaan: $$\begin{cases} x + y + z = -6 \\ x - y - z = 0 \\ x - y + z = -2 \end{cases}$$

1. Énonçons le problème : Simplifier l'expression $$\left( \frac{3a^2 b^3}{b^{-3}} \right)^{-1}$$ en utilisant les lois des exposants. 2. Simplifions l'intérieur de la parenthèse d

1. Énonçons le problème : Simplifier l'expression $$\left(\frac{3a^{2} b^{4}}{b^{-2}}\right)^{-1}$$ en utilisant les lois des exposants. 2. Appliquons la loi des exposants pour la

1. **Problem 1:** Given the hyperbola equation $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ and points $(4\sqrt{2}, 3)$ and $(8, 3\sqrt{3})$ lie on the locus, find $a$ and $b$. Also c

1. The problem is to simplify the expression $\frac{7}{4} - \frac{3}{2} : 2$. 2. Division by 2 can be rewritten as multiplication by $\frac{1}{2}$, so the expression becomes $\frac

1. সমস্যাটি হলো: আমাদের দেওয়া আছে দুটি সমীকরণ:

1. সমস্যাটি হলো: $f(x) = x - 1$ এবং $x \in \mathbb{R}$, আমাদের সমাধান করতে হবে অসমতা: $$-2 < 2 - f(x) < 8$$

1. The problem is to factor the expression $x^2$. 2. Notice that $x^2$ is a perfect square, which means it can be written as $(x)^2$.

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. Start by isolating the variable term $2x$ on one side. Subtract 3 from both sides:

1. **State the problem:** Simplify the expression $$(12x^2+17x-4)+(9x^2-13x+3)$$. 2. **Remove parentheses:** Since both groups are added, we can remove the parentheses directly:

1. **State the problem:** Given two functions $f(x) = 2x + 3$ and $g(x) = x - 1$, find the functions $f + g$, $f - g$, $fg$, and $\frac{f}{g}$, and determine the domain of each. 2.

1. Stating the problem: Simplify the expression $$B = [(+3) + (-5)](-3) \div (+2)$$. 2. Simplify inside the brackets: $$+3 + (-5) = 3 - 5 = -2$$.

1. **State the problem:** Given the set \{5-9, -4, 5, 0, 0.25, 23, 9.2, 21006\}, classify each number into the categories: a. natural numbers, b. whole numbers, c. integers, d. rat

1. Löse die Gleichungen: a) Gegeben: $-2x + 3 = -5(x - 15)$