🧮 algebra

1. **State the problem:** We have an element with an initial mass of 420 grams that decays by 11.8% per minute. We want to find how much of the element remains after 16 minutes, ro

1. **Problem Statement:** Set a sample algebra question: Solve for $x$ in the equation $$2x + 3 = 11$$.

1. **State the problem:** We are given the equation $$\sqrt{\frac{2x + 3}{2}} = y + 1$$ and need to express $x$ in terms of $y$. 2. **Isolate and square both sides:** To eliminate

1. Problema: Resolver a equação $2x + 3 = 7$. 2. Isolar o termo com $x$: $2x = 7 - 3$

1. **State the problem:** Given the equation $$\frac{3x + 3x + 3x}{4} = 7$$, find the value of $$18x - 6$$.

1. **State the problem:** Simplify the expression $$(2x + 1)(x - 2) - 3(x - 2)$$ and find which option it is equivalent to. 2. **Use the distributive property:** Expand each term.

1. Diberikan ekspresi: $$\frac{30x^3 y^{-2}}{\sqrt{25x^{-2} y^8}} \times (y^{24})^{\frac{1}{2}}$$ 2. Kita mulai dengan menyederhanakan bagian penyebut: $$\sqrt{25x^{-2} y^8} = \sqr

1. We are asked to solve the quadratic equation $x^2 + 6x + 20 = 0$. 2. The general form of a quadratic equation is $ax^2 + bx + c = 0$. Here, $a=1$, $b=6$, and $c=20$.

1. The problem is to factorize the expression $$y^2 - \frac{1}{9}$$. 2. This is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b)(a + b)$$.

1. **State the problem:** Factorize completely the expression $$x^4 - x^2$$. 2. **Identify the common factor:** Notice that both terms have a common factor of $$x^2$$. So, we can f

1. The problem is to factorize the expression $$25x^2 - 36y^2$$. 2. This is a difference of squares, which follows the formula $$a^2 - b^2 = (a + b)(a - b)$$.

1. **Problem Statement:** Factorize the expression $x^2 y^2 - 4$. 2. **Formula Used:** Recognize this as a difference of squares, which follows the rule:

1. **Problem:** Factorize completely the expression $x^4 - 81$. 2. **Formula and rules:** Recognize that $x^4 - 81$ is a difference of squares because $x^4 = (x^2)^2$ and $81 = 9^2

1. **Problem Statement:** Factorize the expression $b^2 - 4$. 2. **Formula Used:** This is a difference of squares, which follows the rule:

1. **State the problem:** Factorize the expression $x^2 - 1$. 2. **Recall the formula:** The expression $x^2 - 1$ is a difference of squares, which follows the rule:

1. **State the problem:** Solve the equation $x = 3x - 7$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the linear equation $4x + 6 = 6x$ for $x$. 2. **Recall the formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the equation

1. **State the problem:** Factorize completely the expression $$x^2 (b - c) + 2x (b - c) + (b - c)$$. 2. **Identify common factors:** Notice that each term contains the factor $b -

1. **State the problem:** We have a function $f$ defined for all real numbers such that $$f(x + y) = f\left(\frac{x}{2}\right) + f\left(\frac{y}{2}\right)$$ for all real $x, y$. We

1. **State the problem:** Sketch the graph of the polynomial function $$y = 3x^4 + 4x^3 + 1$$ and analyze its critical points. 2. **Find the value at $$x=0$$:**

1. Problema ne cere să găsim cifra de pe poziția 40 în șirul format astfel: 1, 22, 333, 4444, 55555, 666666, 7777777, 88888888, 999999999. 2. Observăm că șirul este format din grup