🧮 algebra

1. **State the problem:** We are given a recurrence relation with initial value $x_1 = 4$ and the recursive formula $x_{n+1} = 3x_n - 5$. 2. **Understand the formula:** This is a l

1. نبدأ بحل التمرين الأول: 1) لدينا كثير الحدود $p(x) = x^3 + 4x^2 + x + k$ ونريد إيجاد $k$ بحيث يكون $-3$ جذرًا لـ $p(x)$.

1. **State the problem:** Solve the equation $x - 3 = \sqrt{x - 1}$ and identify any extraneous roots. 2. **Recall the formula and rules:** To solve equations involving square root

1. The problem is to find the extraneous root of an equation, which typically arises when solving equations involving radicals or rational expressions. 2. An extraneous root is a s

1. **Problem:** Given the function $f(x) = 2x^2 - x + 5$, find $f(4)$. 2. **Formula:** To find $f(a)$, substitute $x = a$ into the function:

1. **Problem statement:** Given the function $f(x) = -2x^2 - x + 5$, solve the following: (1) Find $f(4)$.

1. 問題陳述：判斷下列不等式哪些與 $(x-1)(x-2)(x-3) < 0$ 有相同的解集。 2. 公式與規則：

1. The problem is to solve or analyze "number 5" but since the user did not specify the exact problem, I will assume it refers to a common algebraic problem involving the number 5.

1. **State the problem:** Simplify the expression given: $$4 + (x)(1 - x^2)(1 + x^2) + 5, 10x - x, 6, 5 + x - 4, 7, + 3c(2)$$ 2. **Identify and simplify each part step-by-step:**

1. **Énoncé du problème :** Nous avons la formule de la circonférence d'un cercle : $$C = \pi d$$ où $C$ est la circonférence et $d$ est le diamètre.

1. **State the problem:** We need to write an equation for the height $H$ of a plant in terms of time $t$ months after Scarlett bought it. 2. **Identify given information:** The pl

1. **State the problem:** We need to graph the linear function $y = -x + 5$. 2. **Formula and explanation:** This is a linear equation in slope-intercept form $y = mx + b$, where $

1. The problem asks to write an inequality for a graph showing a horizontal number line with an arrow pointing left from an open circle at -4. 2. An open circle at -4 means the val

1. The problem asks to write inequalities for given number line graphs. 2. For graph A: A closed dot at -4 with shading rightwards to 7 means $m \geq -4$.

1. The problem is to interpret the inequality $4 \geq m$ and identify the correct graph representation. 2. The inequality $4 \geq m$ means $m$ is less than or equal to 4.

1. The problem is to represent the inequality $-2 \leq b$ on a number line. 2. The inequality $-2 \leq b$ means that $b$ is greater than or equal to $-2$.

1. The problem is to graph the inequality $n < 5$. 2. The inequality $n < 5$ means all values of $n$ are less than 5, but not equal to 5.

1. The problem is to solve exercise n1, but since no specific details are given, let's assume it is a basic algebraic problem. 2. Typically, such exercises involve solving equation

1. The problem is to analyze the function $g(x) = x^2 + 5$. 2. This is a quadratic function in the form $g(x) = ax^2 + bx + c$ where $a=1$, $b=0$, and $c=5$.

1. **State the problem:** Solve the equation $x^2 - 5x + 6 = 0$. 2. **Formula and rules:** This is a quadratic equation of the form $ax^2 + bx + c = 0$. We can solve it by factorin

1. **State the problem:** Simplify the expression $$\sqrt{x}244 + (-19)x^2$$. 2. **Rewrite the expression:** The expression is $$244\sqrt{x} - 19x^2$$.