🧮 algebra

1. **State the problem:** Solve the quadratic equation $x^2 - 7x + 6 = 0$. 2. **Formula and rules:** To solve a quadratic equation of the form $ax^2 + bx + c = 0$, we can use facto

1. **Problem Statement:** Find the asymptotes, intercepts, and graph of the function

1. Let's solve the first problem: Calculate $9^{-3/2}$. 2. Recall the exponent rule: $a^{m/n} = \sqrt[n]{a^m}$ and $a^{-b} = \frac{1}{a^b}$.

1. **Stating the problem:** Simplify the expression $$\frac{25^n - 1 \cdot 6^n}{10^{n-1} \cdot 5^n}$$. 2. **Recall the rules:**

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. The problem asks to find $x$ given the equation $\sqrt{5} + \sqrt{4} = \frac{1}{x}$. 2. First, simplify the square roots: $\sqrt{5}$ remains as is since 5 is not a perfect squar

1. Stating the problem: Evaluate the expressions \(\sqrt{\frac{3}{4}}\), \sqrt{2}\), and \(\sqrt{25}\). 2. Formula and rules: The square root of a fraction \(\sqrt{\frac{a}{b}}\) e

1. **State the problem:** Simplify the expression $ (1-2x)^3 $. 2. **Formula used:** The cube of a binomial $ (a-b)^3 $ is expanded using the formula:

1. **State the problem:** Simplify or understand the expression $x^2$. 2. **Formula and rules:** The expression $x^2$ means $x$ multiplied by itself: $$x^2 = x \times x$$

1. The problem is to find the sum of an arithmetic progression (AP) using the arithmetic progression method. 2. The formula for the sum of the first $n$ terms of an AP is $$S_n = \

1. **State the problem:** We have an initial bacteria population of 50, which increases by 80% every 20 minutes. We want to find the time it takes for the population to reach 1,200

1. **State the problem:** Calculate the value of the expression $$(-2 + 3\sqrt{6})^2$$. 2. **Recall the formula:** The square of a binomial $(a + b)^2$ is given by $$a^2 + 2ab + b^

1. The problem is to expand the expression $$(1+2y)^{-3}$$ up to the term containing $y^4$. 2. We use the Binomial series expansion for negative exponents: $$ (1+x)^n = \sum_{k=0}^

1. Zadatak: Rešiti jednačinu $2x + 3 = 7$. 2. Formula i pravila: Da bismo rešili linearnu jednačinu, cilj je izolovati promenljivu $x$ na jednoj strani jednačine.

1. **State the problem:** Simplify the expression $$- \frac{3}{4}(10m + 8) - \frac{1}{2}(21m - 16)$$. 2. **Apply distributive property:** Multiply each term inside the parentheses

1. **State the problem:** Simplify the expression $(-4a^{-5}) \cdot (2a^{-6}b^{0})$ and identify the correct multiple-choice answer. 2. **Recall the rules:**

1. Problem statement: The exponent on 3 is $x+4$, not $x$. 2. Formula and rule: For any base $a$ and exponents $m,n$ we have $a^{m+n}=a^m a^n$.

1. **State the problem:** Solve the equation $$7^x = 3^x + 4$$ for $x$. 2. **Understand the equation:** We want to find the value of $x$ such that the exponential expression on the

1. Problemstellung: Wir haben einen Planeten mit einer Anfangsbevölkerung von 50.000 im Jahr 2016, die jährlich um 2% abnimmt. 2. Formel: Die Bevölkerungszahl $P(t)$ nach $t$ Jahre

1. Problemstellung: Wir haben einen Planeten mit einer Anfangsbevölkerung von 50.000 im Jahr 2016, die jährlich um 2 % abnimmt. 2. Formel: Die Bevölkerungszahl nach $t$ Jahren ist

1. **Développer** **A = (x^2 - \sqrt{7})^2**