🧮 algebra

1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$

1. **Énoncé du problème :** Calculer l'aire $A$ sous la courbe $C_f$ de la fonction $f(x) = 18\left(-\frac{1}{x} + 1 + a \ln(x)\right)$ entre $x=1$ et $x=3$, avec $a$ une constante

1. The problem is to simplify the fraction $\frac{2}{6}$. 2. The formula to simplify a fraction is to divide the numerator and denominator by their greatest common divisor (GCD).

1. You asked if the graph is correct, but you did not provide the graph or the function it represents. 2. To verify if a graph is correct, we need the function or equation it is su

1. The problem asks to find the graph of the inverse function $y = f^{-1}(x)$ given the graph of $y = f(x)$. 2. The inverse function $f^{-1}$ swaps the roles of $x$ and $y$, so the

1. **Stating the problem:** We have a square sheet of cardboard with side length 10 units. Squares of side length $x$ units are cut from each corner, and the sheet is folded to for

1. **State the problem:** We have a function $f(x) = x + 2$ and its inverse $f^{-1}$. We are given that $f^{-1}(n) = 4$ and need to find the value of $n$. 2. **Recall the definitio

1. **State the problem:** We are given the function $f(x) = 1000^x$ and asked to find $x$ such that $f(x) = 10$. 2. **Write the equation:**

1. **State the problem:** We have a geometric sequence with first term $g_1 = 5$ and for $n \geq 2$, $g_n = 3 \cdot g_{n-1}$. We want to find the function $f(n)$ that matches $g_n$

1. **State the problem:** We have an arithmetic sequence with values given for $n=3,5,7$ as $a_3=85$, $a_5=95$, and $a_7=105$. We want to find the linear function $f(x) = a_0 + d x

1. **State the problem:** Matteo has $1500 to invest and wants it to grow to $2500 in 5 years using simple interest. We need to find the interest rate $r$ that will achieve this. 2

1. The problem states that the terms of the sequence are given by the formula $s_n = 4n + 7$ for $n = 0,1,2,3,\ldots$. 2. We need to determine whether the sequence is arithmetic or

1. **State the problem:** We have a geometric sequence with first term $a_1 = \frac{2}{3}$ and next three terms $\frac{1}{2}$, $\frac{3}{8}$, and $\frac{9}{32}$. We need to find th

1. Énoncé du problème : Résoudre l'équation $$-\frac{1}{2}x + 3 = x - 7$$ dans $\mathbb{R}$ en supprimant d'abord les fractions. 2. Formule et règle importante : Pour éliminer les

1. **Problem:** Determine if the ordered pair $(1,5)$ is a solution to the system: $$-5m + 6n = 25$$

1. **Stel het probleem vast:** We hebben een hoeveelheid $H$ die exponentieel afneemt over tijd $t$ in dagen. 2. **Algemene formule voor exponentiële afname:** $$H(t) = H_0 \cdot e

1. **State the problem:** Determine whether the ordered pair $(1,5)$ is a solution to the system of equations: $$-5m + 6n = 25$$

1. **State the problem:** We need to graph the function $f(x) = 2^x + 4$, and determine its domain, range, horizontal asymptote, and y-intercept. 2. **Formula and transformations:*

1. **State the problem:** Solve the equation $x + \frac{x}{4} = 2$ for $x$. 2. **Formula and rules:** To solve linear equations, combine like terms and isolate the variable.

1. **State the problem:** Simplify the expression $\frac{5!}{(5-3)!}$. 2. **Recall the factorial definition:** For any positive integer $n$, $n! = n \times (n-1) \times (n-2) \time

1. Problema 243: \(\frac{2}{9} - \frac{4}{45}\) \(\cdot\) \(\frac{1}{2} + 1\) : \(\frac{5}{12} - \frac{1}{6} + \frac{1}{20} \cdot \frac{5}{3}\) = \(\left(\frac{7}{100} + \frac{1}{2