🧮 algebra

1. **Problem statement:** Simplify the expression $$\frac{5^{m+3} + 125 \cdot 5^{m-1}}{5^{m+4} \div 25}$$. 2. **Recall important rules:**

1. **State the problem:** Solve the equation $$\sqrt{3} + 2x = -x$$ for $x$. 2. **Rewrite the equation:** Move all terms involving $x$ to one side:

1. The problem is to analyze the summation $$\sum_{i=1}^n iL(2)^{x+2} = (n-2)^{x+2} A$$ with the condition $$n > 0$$. 2. First, understand the summation notation: $$\sum_{i=1}^n iL

1. **Stating the problem:** We want to verify or understand the formula for the sum $$\sum_{i=1}^{n+1} i(2^i) = n \cdot 2^{n+2} + 2$$. 2. **Recall the formula for the sum of the fo

1. **State the problem:** Solve the quadratic equation $2x^2 - 13x + 20 = 0$. 2. **Formula used:** The quadratic formula is given by

1. **Problem:** Find the value of $32 \equiv \, ? \pmod{12}$. 2. **Formula:** To find $a \equiv r \pmod{m}$, compute the remainder $r$ when $a$ is divided by $m$.

1. The problem is to verify the factorization of the quadratic expression $$2x^2 - 13x + 20$$ given as $$(2x - 5)(x - 4)$$. 2. The formula for expanding two binomials is:

1. The problem is to simplify the expression where the first \(a\) is on the 2 and the second \(a\) is on the top with 3, which suggests the expression is \(a^{2a^3}\). 2. The expr

1. **State the problem:** Simplify the expression $$-\frac{1}{2}a + \frac{3}{2}a - 4$$. 2. **Identify like terms:** The terms $$-\frac{1}{2}a$$ and $$\frac{3}{2}a$$ are like terms

1. **State the problem:** Simplify the expression $\frac{5x}{5+x} + 17.5$. 2. **Understand the expression:** The expression consists of a rational term $\frac{5x}{5+x}$ and a const

1. The problem is to simplify the expression $\frac{5x}{5} + x + 17.5$. 2. Use the rule that $\frac{a \cdot b}{a} = b$ when $a \neq 0$.

1. **State the problem:** Find the value of $-32 \equiv ? \pmod{12}$. 2. **Recall the definition:** For integers $a$ and $m > 0$, $a \equiv r \pmod{m}$ means $r$ is the remainder w

1. **State the problem:** Find the equation of the line passing through points $(-8,7)$ and $(0,-1)$ in slope-intercept form $y=mx+b$. 2. **Formula:** The slope $m$ of a line throu

1. **Stating the problem:** Calculate the value of the expression $$\sqrt{16} \times 3 \times \sqrt{7} \times 1 \times \sqrt{25} \times 12 \times 7 \times \sqrt{36} \times 2 \times

1. Problema a resoldre: Calcula i simplifica l'expressió $$3 - 5 \times \frac{1}{4} - 2 \div 8$$. 2. Fórmules i regles importants:

1. The problem is to simplify the expression $+17 + (+1,7)$. 2. First, note that the expression contains a comma in $(+1,7)$ which is not standard notation for a number. Assuming i

1. The problem is to find the sum of $-8$ and $-27$. 2. We use the rule for adding integers with the same sign: add their absolute values and keep the common sign.

1. The problem is to find the sum of $-7$ and $-24$. 2. When adding two negative numbers, you add their absolute values and keep the negative sign.

1. The problem is to find the sum of $-5$ and $-61$. 2. We use the rule for adding integers: when adding two negative numbers, add their absolute values and keep the negative sign.

1. The problem is to find the sum of $-3$ and $-9$. 2. The formula for adding two numbers is simply $a + b$.

1. Diberikan pertidaksamaan: $$-3x - 5 \leq 7 + x$$ 2. Tujuan kita adalah mencari nilai $x$ yang memenuhi pertidaksamaan tersebut.