🧮 algebra

1. Problem statement: Simplify the expressions (x + 10)^2 and (3 + z)^2 using the binomial formula. 2. Identify a and b:

1. The problem is to simplify an expression, but the exact expression is not provided. 2. To simplify an algebraic expression, we combine like terms, apply distributive property, a

1. Simplify $\frac{2}{9}$: The numerator and denominator have no common factors other than 1, so $\frac{2}{9}$ is already in simplest form. 2. Simplify $\frac{4}{60}$: Given as $\f

1. Énoncé du problème : Résoudre les équations suivantes pour $x$ : a) $e^{5x} = \frac{3}{2}$

1. Diketahui perbandingan senilai: $$8 : 10 = (y + 15) : 25$$ 2. Gunakan sifat perbandingan senilai, yaitu hasil kali silang sama:

1. **Stating the problem:** You want to solve a system of equations graphically by using substitution. 2. **Formula and rules:** Substitution involves solving one equation for one

1. The problem is to solve the quadratic equation $x^2 - 5x + 6 = 0$. 2. The formula used is the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$, and $

1. **Problem Statement:** Given the relation with pairs \((-2, -7), (-1, 0), (3, 0), (5, 4)\), find the domain (D), range (R), and determine if it is a function. 2. **Definitions:*

1. The problem asks to determine if values are to the left, right, middle, or out for two questions labeled a and b. 2. To solve this, we need the specific values or intervals for

1. **State the problem:** Calculate the value of the expression $2^3 + 3 imes 2$. 2. **Recall the order of operations:** According to PEMDAS/BODMAS, exponents are evaluated first,

1. **Problem Statement:** Sketch the graph of the function $$f(x) = (x - 1)^2 (x + 1)^3$$. 2. **Identify the roots and their multiplicities:**

1. **Stating the problem:** Given the ratios $x : y = 0.5 : 1$ and $z : y = 0.6 : 1$, find the combined ratio $x : y : z$ and the ratio $x : z$. 2. **Understanding ratios:** Ratios

1. **Problem Statement:** We need to sketch the graphs of two functions:

1. Problem: Find the domain of the functions given. 2. For function a) $$f(x) = \frac{1 + 2x + x^3}{2x - 8x^3}$$

1. **State the problem:** We need to find the value of $$\sqrt{2.307197196 \times 10^{-28}}$$. 2. **Recall the property of square roots:** The square root of a product is the produ

1. Simplify by combining like terms: $a + 3b - 5 + 3a - 4$ Step 1: Group like terms: $(a + 3a) + 3b + (-5 - 4)$

1. Simplifying expressions Simplify algebraic expressions by combining like terms and using distributive property.

1. Énoncé du problème : Pour tout réel $a > 0$, justifier que $$a - \frac{1}{a} = \frac{(a - 1)(a + 1)}{a}$$ 2. Justification :

1. **State the problem:** We have a geometric progression (GP) where the third term is 6 less than the second term, and the second term is 9 less than the first term. We need to fi

1. The problem states that the ratio $r$ is given by $r = \frac{a_3}{a_2} = \frac{a_2}{a_1}$ and that $a_2^2 = a_1 a_3$. 2. This implies a geometric progression where the middle te

1. **Stating the problem:** We are given two equations involving sequences: $a_3 = 6 + a_2$ and $a_1 = a_2 - 9$. We want to find the values of $a_1$, $a_2$, and $a_3$ if possible.