🧮 algebra

1. Given the data points: $x-2$, $x+5$, $x+3$, $3x-4$, $2x+7$, the mean is given as 7. 2. The formula for the mean of $n$ data points $a_1, a_2, ..., a_n$ is:

1. **State the problem:** Simplify the expression $\frac{2}{3} + \frac{1}{6}$.\n\n2. **Formula and rules:** To add fractions, they must have a common denominator. The common denomi

1. **State the problem:** Calculate the value of the expression $2 \times 6 \div 1874 \times 2$. 2. **Recall the order of operations:** Multiplication and division are performed fr

1. **State the problem:** Simplify the expression $\left(4 \cdot 4^{3} \cdot 4^{-2}\right)^{3}$. 2. **Recall the properties of exponents:**

1. **State the problem:** Zion and Taylor together made 496 penalty kicks over 31 days. Taylor makes 7 penalty kicks each day. We need to find how many penalty kicks Zion makes eac

1. **State the problem:** Simplify the expression $$(3x^2 + 4x - 8) + 2(11 - 5x)$$ and find which equivalent expression it matches from the given options. 2. **Use the distributive

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)=(