🧮 algebra

1. **Problem:** Convert a fraction into a decimal. 2. **Formula and Explanation:** A fraction \( \frac{a}{b} \) represents division of the numerator \(a\) by the denominator \(b\).

1. The problem is to convert a fraction into a decimal. 2. A fraction is written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denominator.

1. **Problem Statement:** Find formulas for the compositions of the functions $f(x) = \sqrt{2x + 4}$ and $g(x) = x^{2} + 1$ for the following:

1. The problem is to simplify the expression given by the user. However, no specific expression was provided, so I will explain the general approach to simplification. 2. Simplific

1. **Problem Statement:** Solve the quadratic equation $x^2 - 5x + 6 = 0$. 2. **Formula Used:** The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $

1. **Problem statement:** We have a function $f$ defined for all real numbers such that $$f(x+y) = f\left(\frac{x}{2}\right) + f\left(\frac{y}{2}\right)$$ for all real $x,y$. We ar

1. **State the problem:** Simplify the expression $7 - 4 \times (3 - 8) + 2 \times (5 - 9)$.\n\n2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplicatio

1. **State the problem:** Evaluate the expression $7 - 4 \times (3 - 8) + 2 \times (5 - 9)$.\n\n2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplicatio

1. **State the problem:** We are given two functions: $$f(x) = \sqrt{2x + 4}$$

1. **State the problem:** Solve the linear equation $2x + 1 = 7x - 3$ for $x$. 2. **Write down the equation:**

1. The problem is to solve an algebraic expression or equation suitable for grade 9 CBSE level. Since no specific equation is given, let's consider a common example: Solve for $x$

1. The problem is to understand the applications of quadratic equations and inequalities. 2. Quadratic equations are equations of the form $ax^2 + bx + c = 0$ where $a \neq 0$.

1. The problem is not clearly stated, but since you mentioned "for senior 4," I assume you want a general algebra problem suitable for senior 4 level. 2. Let's solve a common algeb

1. The problem is to find the roots of the quadratic equation $ax^2 + bx + c = 0$ where $a \neq 0$. 2. The formula used is the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac

1. **Problem Statement:** Determine if the polynomial $12x^3 + 6x^2 - 1$ is factorable. 2. **Formula and Rules:** To factor a polynomial, first look for a greatest common factor (G

1. **Énoncé du problème :** Calculer la valeur de $$\frac{0,02 \times 10^{-3} + 0,8 \times 10^{-4}}{0,05 \times 0,2 \times 10^{-3}}$$

1. **Énoncé du problème :** Calculer la valeur de l'expression $$\frac{0,02 \times 10^{-3} + 0,8 \times 10^{-4}}{0,05 \times 0,2 \times 10^{-3}}$$

1. Let's clarify the problem: You mentioned an expression involving $e$ and $\sin$, and you want to know if it is a simple term. 2. The presence of $e$ (the base of natural logarit

1. The problem asks for the sum of integers from 1 to 15. 2. We use the formula for the sum of the first $n$ natural numbers: $$S = \frac{n(n+1)}{2}$$ where $n=15$.

1. **Problem Statement:** We have 400 students in 2015 with 180 females. The region-wise breakup of students is given by angles: North = 126°, South = 144°, East and West = 90°. 2.

1. **Problem Statement:** We have 400 students in Loyola College in 2015, with 180 females. We know 20 girls weigh less than 31 kg. We want to find the percentage of boys weighing