🧮 algebra

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

1. Das Problem lautet: Finde den Wert von b. 2. Da keine weiteren Informationen gegeben sind, ist es nicht möglich, b zu bestimmen.

1. Problem: Vereinfache den Term $$\sqrt{\frac{4}{3}} \cdot \sqrt{27} - 3 \cdot \frac{1}{2}$$ ohne Taschenrechner. 2. Formel und Regeln: Die Wurzel eines Produkts ist das Produkt d

1. **State the problem:** Simplify the expression $x^4 + 4x^2 - x^3y - 4xy$ by factoring. 2. **Identify common factors and group terms:** Group the terms as $(x^4 - x^3y) + (4x^2 -

1. **State the problem:** Simplify the fractions $\frac{0}{18}$, $\frac{18}{18}$, and $\frac{18}{1}$.\n\n2. **Recall the rules:**\n- Any fraction with numerator 0 is 0, i.e., $\fra

1. **Opdracht 1.3.1: Bereken de volgende wortels** We gebruiken de formule voor wortels: $$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$$ en de regel dat $$\sqrt{x^2} = |x|$$.

1. We are given two functions: $f(x) = -2x^2 + 2x - 1$ and $g(x) = 2x + 1$. We need to find $f(g(2))$, which means we first find $g(2)$ and then substitute that result into $f(x)$.