🧮 algebra

1. Problema cere să calculăm suma divizorilor naturali ai numărului $a + 22$, unde $$a = \sqrt{2024} + 6\sqrt{2015} - \sqrt{2024} - 6\sqrt{2015}.$$\n\n2. Observăm că termenii $\sqr

1. Problema cere să calculăm suma divizorilor naturali ai numărului $22 + a$, unde $a$ este definit prin ecuația $$2015^6 - 2024^6 + 2015^6 - 2024^6 = a.$$ 2. Mai întâi, calculăm v

1. **State the problem:** Find the equation of the straight line passing through the points $(5, 10)$ and $(9, 24)$ in the form $y = mx + c$. 2. **Formula for slope:** The slope $m

1. Planteamos el problema: Evaluar la expresión del ejercicio 46: $$2\cdot[8 - 3(4 + 2)] - 3$$. 2. Primero, resolvemos dentro del paréntesis interior: $$4 + 2 = 6$$.

1. **Stating the problem:** We start with the exponential growth function $$y=1\cdot 2^x$$ where $x$ is the day number and $y$ is the number of people who know the information. The

1. Problema: Resolver la operación con monomios $(-5x^5 y^2)(-3x^6 y^4)$. 2. Fórmula y reglas: Para multiplicar monomios, multiplicamos los coeficientes y sumamos los exponentes de

1. **State the problem:** We need to find the slope of the line passing through points approximately (-7, -9) and (6, 10) on the Cartesian plane. 2. **Formula for slope:** The slop

1. The problem involves comparing different reading speeds given in pages per hour: 0.08, 0.25, 12.5, and 25 pages per hour. 2. To understand these speeds, we can analyze how long

1. **State the problem:** Solve the equation $$1 + 4x \sin\left(\frac{1}{x}\right) - 2 \cos\left(\frac{1}{x}\right) = 0.$$\n\n2. **Rewrite the equation:** We want to find $x$ such

1. **State the problem:** Solve the equation $$\frac{4x - 2}{6} = \frac{3}{2x + 7}$$ for $x$. 2. **Use the cross-multiplication rule:** When two fractions are equal, their cross pr

1. **Simplify the algebraic expressions:** i. Simplify $9x + 2y - 4z + 8y - 3x + 11z$

1. **State the problem:** Simplify the expression $(8x+7y-5)-(5xy+y-3x)$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to each term

1. The problem asks us to write a function notation statement based on the given temperature graph $h(t)$, where $t$ is the number of hours since midnight. 2. From the graph descri

1. **State the problem:** We need to find the total weight in kilograms if 350 grams is 20% of it. 2. **Formula used:** If $x$ is the total weight in kilograms, then 20% of $x$ equ

1. **State the problem:** Simplify the expression $3 \times (x - 2)$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses. The distributive propert

1. **State the problem:** Calculate $\log_6 \left( \frac{216 \cdot 1296 \cdot \sqrt[3]{6}}{\sqrt{1296}} \right)$. 2. **Recall logarithm properties:**

1. **State the problem:** Solve the system of equations by elimination: $$3x + y = 16$$

1. **State the problem:** We are given the quadratic function $f(x) = -0.1x^2 + 8x + 1$ and want to analyze it. 2. **Formula and rules:** A quadratic function is generally written

1. **State the problem:** Convert each percentage to a fraction in its simplest form. 2. **Formula and rules:** To convert a percentage to a fraction, use the formula:

1. **Problem:** Solve the equation $14 \times (4x + 2) = 140$ algebraically. 2. **Formula and rules:** Use the distributive property to expand and then isolate $x$ by performing in

1. Stating the problem: Simplify the expression $$\sqrt{\frac{18x^2}{z^6}}$$. 2. Recall the rule for square roots: $$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$$ and $$\sqrt{x^