🧮 algebra

1. **State the problem:** Simplify the expression $$-2(3g - 2) - (4g + 3)$$ and find which given option is equivalent. 2. **Use the distributive property:** Multiply $$-2$$ by each

1. Let's start by stating a complicated algebra problem: Solve the system of equations $$\begin{cases} 2x + 3y - z = 7 \\ 4x - y + 5z = 3 \\ -x + 2y + 4z = -1 \end{cases}$$ 2. The

1. **State the problem:** Expand and fully simplify the expression $$(2\sqrt{6} - 5\sqrt{2})^2$$. 2. **Formula used:** Use the formula for the square of a binomial: $$(a - b)^2 = a

1. Problem 25: A radiator has 4 liters of 20% antifreeze solution. Some amount $x$ liters is removed and replaced with 100% antifreeze to get a 30% solution. Formula: Concentration

1. **Problem Statement:** We are given a volume function $$V(x) = (16 - 2x)(30 - 2x)x$$ representing the volume of a box formed by cutting squares of side length $$x$$ from each co

1. **State the problem:** Simplify the expression $$\frac{2^3}{4} + \frac{3^2}{5} - 1 \frac{2}{3}$$. 2. **Evaluate powers:** Calculate the powers first.

1. **State the problem:** Solve the linear equation $2x - 3 = 7$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Additio

1. Statement of the problem: If $f(x)=5x+4$ and $g(x)=2-x$, compute $(f\circ g)(-2)+(g\circ f)(5)$. 2. Formula and rules: For composition the formula is $(f\circ g)(x)=f(g(x))$.

1. The problem is to simplify the expression or equation you have, but since you did not provide a specific expression, I will explain the general steps to simplify algebraic expre

1. The problem asks to find the slope of the graph passing through points approximately (3,0) and (-2,5). 2. The formula for slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)

1. **Énoncé du problème :** Calculer la dérivée de la fonction $f$ définie sur $\mathbb{R}$ par $f(x) = 2x^3 + x - 2$ et dresser son tableau de variation. 2. **Formule utilisée :**

1. State the problem: Given $f(x)=\frac{1}{x}$ and $g(x)=x^2-1$, find the domain of $f\circ g$. 2. Formula and rules: The composite is defined by $(f\circ g)(x)=f(g(x))$ and it is

1. We are asked to simplify the expression $$\frac{p^6q^2}{7r^3} \times \frac{-3p^2}{r}$$. 2. The formula for multiplying fractions is $$\frac{a}{b} \times \frac{c}{d} = \frac{a \t

1. State the problem. Problem: Given functions $f : R^+ → R$ defined by $$f(x)=x^2-7$$ and $g : [-3, 2] → R$ defined by $$g(x)=x^2+3$$, compute $(f-g)(-5)$.

1. Problem statement: We are given functions $f,g:\mathbb{R}\to\mathbb{R}$ with $f(x)=3x+1$ and $(f+g)(x)=x^3+2x-1$. 2. Formula and key rule: To find $g(x)$ use the formula $g(x)=(

1. Bài toán yêu cầu xác định số đường tiệm cận của hàm số $$y=\frac{x+1}{x-1}$$. 2. Hàm số dạng phân thức hữu tỉ có dạng $$\frac{P(x)}{Q(x)}$$, trong đó $P(x)$ và $Q(x)$ là đa thức

1. The problem asks to find the sum of the series \( \sum_{j=15}^{51} \frac{1}{j} \) with an increment of 2 in the index. 2. This means we sum the terms \( \frac{1}{15} + \frac{1}{

1. The problem asks to find the sum of the series $$\sum_{i=15}^{51} \frac{1}{i}$$ with $i$ increasing by 2 each step. 2. This is a finite sum of the reciprocals of odd integers st

1. Problem: If $f$ and $g$ are real functions with $f(x)=\frac{x-2}{x^2-3x+2}$ and $g(x)=x-3$, find $(f/g)(3)$. 2. Formula and rule: The quotient of two functions is given by $(f/g

1. Problem: Determine the domain of the function $f(x)=\sqrt{x-1}+\sqrt{x+2}$. 2. Formula and rules: For a real square root $\sqrt{A}$ to be defined we require $A\ge 0$.

1. Problem statement: Determine the domain of the function $f(x)=\sqrt{\frac{x-3}{\sqrt{5-x}}}$. 2. Condition 1: The expression under the outer square root must be nonnegative, so