🧮 algebra

1. **Problem statement:** Given the equation $$0 = \frac{(ع س + ن)( س - 1)( س + 4)}{س - 1}$$, find the value of the variable \(ن\). 2. **Understanding the equation:** The expressio

1. El problema es factorizar una expresión algebraica usando el método de factor común por agrupamiento. 2. Este método consiste en agrupar términos que tengan un factor común y lu

1. El problema es factorizar una expresión usando el método de factor común. 2. La fórmula general para factorizar por factor común es extraer el término que se repite en todos los

1. **State the problem:** Ernie deposited a total of $4000 between two accounts, one with 4% simple interest and the other with 2% simple interest. After one year, the total intere

1. The problem asks us to find the value of the function $f(x) = 3x^3 + 7x^2 + 5x$ at $x = -3$. 2. To find $f(-3)$, substitute $-3$ into the function:

1. **State the problem:** We need to find the value of the function $f(x) = 20x^2 - 18x - 25$ at $x = -1$. 2. **Write the formula:** The function is given by

1. **State the problem:** Simplify the expression $4n + 1 + 4n$. 2. **Combine like terms:** The terms $4n$ and $4n$ are like terms because they both contain the variable $n$.

1. **State the problem:** Solve for $x$ in the equation $3x - 4 = 5$. 2. **Add 4 to both sides:**

1. **State the problem:** Add the fractions and mixed numbers $\frac{21}{4} + 3 \frac{3}{4}$. 2. **Convert mixed number to improper fraction:**

1. **State the problem:** Simplify the expression $3 - (-2 + 1) - (-7)$. 2. **Evaluate inside the parentheses:** Calculate $-2 + 1 = -1$. So the expression becomes $3 - (-1) - (-7)

1. The problem is to solve the equation labeled as #4 b. Since the exact equation is not provided, please provide the full equation or context for #4 b so I can assist you properly

1. **State the problem:** We need to find the number of generating sets $x$ that minimizes the cost function $$c[x] = 0.1x^2 - 0.7x + 2.425$$ where $c[x]$ is the cost in hundreds o

1. **Stating the problem:** Find the solution set of the equation $$x^2 = -9$$ where $$x \in \mathbb{R}$$. 2. **Formula and rules:** The equation $$x^2 = c$$ has real solutions onl

1. **State the problem:** Solve the two-step linear equation $$7k - 201 = 730$$ for the variable $k$. 2. **Add 201 to both sides:** To isolate the term with $k$, add 201 to both si

1. **State the problem:** Solve for $s$ in the equation $$\frac{s}{-15} + 215 = 240$$. 2. **Isolate the term with $s$:** Subtract 215 from both sides to get $$\frac{s}{-15} = 240 -

1. Let's solve a general algebra problem: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. The formula to isolate $x$ is to perform inverse operations to both sides of the equatio

1. **Problem statement:** Prove by mathematical induction that the harmonic series partial sum satisfies $$H_{2n} = 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{2n} \geq 1 + \

1. **State the problem:** A farmer wants to enclose two adjacent rectangular plots for sheep and one for cattle along a river, using 240 yards of fencing. The river forms one side,

1. **State the problem:** Solve the equation $ (x-1)^2 = 2(x-1) $. 2. **Rewrite the equation:** The equation is $ (x-1)^2 = 2(x-1) $.

1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}.$$\n\n2. **Use the given information:** We know

1. Let's start by understanding what percentage profit and loss mean. 2. Percentage profit occurs when the selling price (SP) of an item is more than its cost price (CP). The formu