🧮 algebra

1. **Énoncé du problème :** Simplifier l'expression $$P = \frac{2(x + 3y)}{5} - \frac{x + 3y}{2} + \frac{1}{5}$$

1. **State the problem:** Solve the system of linear equations: $$2x + 2y + 2z = 15$$

1. The problem is to find the new value after a 30% increase on 4000. 2. The formula to calculate the increased value is:

1. **State the problem:** Theo starts with 18 and saves 4.5 each week.

1. **Stating the problem:** We have rent values for the years 2013 and 2014, and we want to find the rent for 2015. 2. **Given data:**

1. Diberikan fungsi $f(x) = 3x + 1$. Kita diminta mencari nilai $f(1 - 2x)$. 2. Substitusikan $1 - 2x$ ke dalam fungsi $f(x)$, sehingga

1. **State the problem:** We are given two linear equations: $$y = 2kx + 3$$

1. **State the problem:** We need to check if the population in 2021, calculated by adding the same absolute increase from 2001 to 2011, matches the claim that the population incre

1. Vamos trabalhar com a função quadrática, que tem a forma geral $$f(x) = ax^2 + bx + c$$, onde $a$, $b$ e $c$ são números reais e $a \neq 0$. 2. A tarefa é: para a função $$f(x)

1. **State the problem:** We need to divide the polynomial $2x^3 + 3x - 5$ by the binomial $x - 1$. 2. **Formula and method:** Polynomial division can be done using long division o

1. **State the problem:** We need to find the equation of Line B in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 2. **Identify points on the line:** Fr

1. The problem is to simplify the expression $5^{\log_5(2)}$. 2. We use the property of logarithms and exponents: $a^{\log_a(b)} = b$ for any positive $a \neq 1$.

1. **State the problem:** Find the exact value of $\frac{\log_4(6)}{4}$. 2. **Recall logarithm properties:** The expression can be rewritten using the power rule of logarithms:

1. The problem asks for the nth term of the arithmetic sequence with first five terms: 1, 5, 9, 13, 17. 2. Recall the formula for the nth term of an arithmetic sequence: $$a_n = a_

1. **State the problem:** We need to revise the hat size table so that it includes all possible head sizes measured to the nearest 1/8 inch between 21 inches and 24 inches. 2. **Un

1. **State the problem:** Simplify the expression $\frac{5\frac{1}{4}}{1\frac{2}{3} - \frac{1}{2}}$. 2. **Convert mixed numbers to improper fractions:**

1. The problem is to understand the value of the variable $a$ given as $a=2$. 2. This is a simple assignment where the variable $a$ is set to the number 2.

1. **State the problem:** We need to find the constants $a$, $b$, and $c$ in the function $$y = a \tan(x - b) + c$$ given the graph's vertical asymptotes and points.

1. **State the problem:** We want to express $\frac{100^m}{100^n}$ in the form $10^z$ and find $z$ in terms of $m$ and $n$. 2. **Recall the properties of exponents:**

1. **State the problem:** Solve the quadratic equation $$4x^2 - x - 3 = 0$$ using an algebraic method. 2. **Formula and method:** We use the quadratic formula to solve equations of

1. **State the problem:** We are given the equation $$(ar^b)^4 = 81^{24}$$ where $a$ and $b$ are positive integers. We need to find the values of $a$ and $b$. 2. **Rewrite the equa