🧮 algebra

1. **State the problem:** We need to list all elements in the set $B = \{x \in \mathbb{N} : x^3 \text{ is an odd number less than } 150\}$. This means we want natural numbers $x$ s

1. The problem is to write the equation $y=(x+2)^2+3$ in standard form. 2. The standard form of a quadratic equation is $y = ax^2 + bx + c$.

1. **State the problem:** List all elements in the set $A = \{x \in \mathbb{Z}^+ : (x^2 - 4) < 10\}$. 2. **Understand the set definition:** $A$ contains all positive integers $x$ s

1. **State the problem:** Evaluate the expression $$(2 \times 6 + 3 - 4) - 5 + \left(\frac{20}{5}\right) \times 3 + 50$$ using order of operations. 2. **Recall order of operations:

1. **State the problem:** Solve the equation $$\frac{9t+27}{9t+18} = 9$$ for $t$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both sides b

1. **State the problem:** Solve the equation $$\frac{9t+27}{9t+18} = 9$$ for $t$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both sides b

1. **State the problem:** Simplify the expression $\frac{7}{2x} + \frac{6}{2x}$. 2. **Identify the formula and rules:** When adding fractions with the same denominator, add the num

1. **State the problem:** Solve the quadratic equation $$4x^2 + 16x + 15 = 0$$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solutions

1. **Problem Statement:** We want to use Newton's forward interpolation formula to show that $$s = \sum n^3 = \left( \frac{n(n+1)}{2} \right)^2.$$

1. **State the problem:** Solve the equation $5x - 4(1 - 3x) = 4x - (x + 1)$ for $x$. 2. **Apply the distributive property:**

1. The problem is to provide a math question as requested. 2. Since the user asked "just give me the question," here is a simple algebra question:

1. **State the problem:** Simplify the expression $$\frac{4x}{3y} - \frac{5y}{6x}$$. 2. **Find a common denominator:** The denominators are $3y$ and $6x$. The least common denomina

1. **State the problem:** Solve the equation $z^2 - 1 = 0$ and represent the solutions on an Argand diagram. 2. **Formula and rules:** The equation is a quadratic in complex number

1. **State the problem:** Find the equation of the tangent line to the ellipse $$4x^2 + 9y^2 = 40$$ that has a slope of $$-\frac{2}{9}$$. 2. **Recall the ellipse equation and impli

1. **Stating the problem:** We have a sequence of patterns made from tiles, where the number of tiles increases by the same amount each time. We want to find the number of tiles in

1. Masalah yang diberikan adalah menyederhanakan persamaan dengan membuka tanda kurung, khususnya pada ekspresi $x+2$. 2. Aturan penting: ketika membuka tanda kurung, setiap suku d

1. The problem is to find $f^{-1}(3)$ given the function $f(x) = x^2 + 2x + 1$. 2. First, understand that $f^{-1}(3)$ means we want to find the value of $x$ such that $f(x) = 3$.

1. Das Problem lautet: Löse die Gleichung oder Aufgabe, die du gestellt hast. Da keine konkrete Aufgabe angegeben wurde, erkläre ich, wie man eine einfache lineare Gleichung löst.

1. Diketahui persamaan linear satu variabel: $$4x - 7(x+2) = -5$$ 2. Tujuan: Tentukan nilai dari $$x - 2$$.

1. The problem states that the population was 4 million in 1980 and increased by 0.041 million each year until 2007. 2. We need to find the population 10 years after 1980, which is

1. 题目要求对表达式 $8 - m (m^{3} + 2m^{2} + m - 2)$ 进行因式分解。 2. 首先，展开括号内的乘法：