🧮 algebra

1. **State the problem:** Find the points of intersection between the functions $f(x) = \frac{1}{3}x^2$ and $g(x) = -x$, and analyze the right triangle $ABC$ formed by points $A$,

1. **State the problem:** We are given three functions: $$f(x) = x^4 + 8$$

1. The problem asks us to find the composition of functions $f$ and $g$, denoted as $(f \circ g)(x)$, which means $f(g(x))$. 2. Given $f(x) = 2x + 3$ and $g(x) = 4x^{2} + 3x$, the

1. Planteamos el problema: Se cobra 9 soles por enviar 10 kg a 60 km. Queremos saber cuánto costará enviar 8 kg a 200 km. 2. Suponemos que el costo depende directamente del peso y

1. **Planteamiento del problema:** Se atienden inicialmente 10 pacientes diarios, con un tiempo de atención de 30 minutos por paciente.

1. O problema pede para determinar as coordenadas do ponto A, que é um ponto de intersecção entre as funções $f(x) = x^2$ e $g(x) = -x$. 2. Para encontrar os pontos de intersecção,

1. **State the problem:** Solve the inequality $q^2 - q > 1$. 2. **Rewrite the inequality:** Move all terms to one side to set the inequality to zero:

1. **State the problem:** Jack receives 6.20 pounds pocket money weekly. We need to calculate various percentages of this amount and determine how much he spends and saves. 2. **Fo

1. The problem asks to find the percentage of given amounts. 2. The formula to find a percentage of an amount is:

1. **State the problem:** Multiply and simplify the complex numbers $(-2 - 3i)$ and $(-5 - 2i)$. 2. **Recall the formula:** To multiply two complex numbers $(a + bi)(c + di)$, use

1. **State the problem:** Multiply and simplify the complex numbers $(-2 + 2i)$ and $(5 + 5i)$. 2. **Recall the formula:** To multiply two complex numbers $(a + bi)(c + di)$, use t

1. El problema es encontrar la ecuación de la recta que pasa por el punto $C:(2,-1)$ y tiene pendiente $m = -13$. 2. La fórmula para la ecuación de la recta con pendiente $m$ que p

1. Problem statement: We have three scales with markings 0 to 100 and points a, b, c which are natural numbers representing divisions on the scales. - In Şekil I, two identical obj

1. **State the problem:** Simplify the function $$k(x) = \frac{(x-0.9)(x-1.6)(x-2.9)(x-3.55)}{(0-0.9)(0-1.6)(0-2.9)(0-3.55)} \times 0.7 + \frac{(x-0)(x-1.6)(x-2.9)(x-3.55)}{(0.9-0)

1. **State the problem:** Solve the equation $n^2 = 4(4n + 9)$. 2. **Write the equation and expand:** Start with the given equation:

1. **State the problem:** Solve the equation $$y^2 + 2y - x^2 + 6y = -10x$$ for $y$ in terms of $x$. 2. **Combine like terms:** Group the $y$ terms together:

1. **State the problem:** We need to understand and graph the function $f(x) = -4^x$. 2. **Recall the function form:** The function is an exponential function with base 4 and a neg

1. The problem is to draw the graph of the function $f(x) = -4x$. 2. This is a linear function of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. **Énoncé du problème :** Résoudre l'inéquation $$\frac{2x^{2} - 5x + 3}{3x - 1} \geq 0.$$ 2. **Formule et règles importantes :**

1. El problema es demostrar que $\sqrt[n]{a^m} = a^{\frac{m}{n}}$. 2. La fórmula para convertir una raíz en una potencia es:

1. The problem involves two expressions: $x - 8$ and $y - 6$. 2. These expressions represent values shifted from $x$ and $y$ by 8 and 6 units respectively.