🧮 algebra

1. **Problema 1:** Calcolare il valore di $5a + 3b - 4$ per $a = -3$ e $b = -2$. 2. **Formula:** Sostituiamo i valori dati nell'espressione algebrica.

1. **State the problem:** We are given the function $f(x) = -2x^3$ and want to understand its behavior. 2. **Formula and rules:** The function is a cubic polynomial with a negative

1. **Problem statement:** Simplify the expression $$\sqrt[10]{a^7} : \sqrt[5]{a^3}$$. 2. **Recall the rule for radicals and exponents:**

1. **State the problem:** Find the equation of the linear function passing through points (0, 3) and (1, 0). 2. **Recall the formula:** The equation of a line is $y = mx + b$, wher

1. Het probleem is om het getal 6367 om te zetten naar het priemontbinding in het 10-tallig stelsel. 2. De priemontbinding betekent dat we het getal ontbinden in een product van pr

1. **State the problem:** We need to find the equation of $h(x) = (f - g)(x)$ where $f(x) = \sqrt{x+1}$ and $g(x) = -x + 4$. 2. **Formula used:** The difference of two functions is

1. **State the problem:** We are given two functions: $$f(x) = \sqrt{x} + 1$$ and $$g(x) = -x + 4$$. We want to understand these functions and possibly find their composition or in

1. **State the problem:** Simplify the expression $$-\left[a^2 \cdot (a^2 - 2a^2) + a - 3\right] + \left[(-2a^2)^2 + (a + 1)^2 - \frac{6a^3b}{6ab}\right] - (4 + a)$$. 2. **Simplify

1. **Stel het probleem vast:** We hebben de formule $$r = \frac{\frac{1}{4}b^2 + h^2}{2h}$$ en willen deze herleiden tot de vorm $$b = p \cdot \sqrt{q h - h^2}$$ voor $$r = 1{,}63$

1. **Stel het probleem vast:** We moeten bewijzen dat de functie $$f(x) = \frac{1}{9} \left(3^{-\frac{1}{2}x} + 27\right)$$

1. The problem asks to find the value of the function $f$ at $x=0$, i.e., $f(0)$, by analyzing the given graph. 2. From the description, the graph has a line/ray crossing the y-axi

1. **Stel het probleem vast:** We hebben formule 1:

1. **Problema:** Completiamo ponendo il simbolo opportuno tra <, =, > per le seguenti espressioni esponenziali. 2. **Regola importante:** Se la base $a > 1$, allora $a^{x_1} < a^{x

1. **Problema 94**: Completa ponendo il simbolo opportuno tra le potenze date. Ricordiamo la regola fondamentale per le funzioni esponenziali: se la base $a > 1$, allora $a^{x_1} <

1. **State the problem:** We need to add the numbers $5.3 \times 10^4$ and $4.7 \times 10^4$ and express the result in scientific notation.

1. Staðfesta fyrsta verkefnið: Notaðu ferilinn til að finna f(1). 2. Skilgreina ferilinn: Ferillinn er parabolískur, og gefur gildi f(x) fyrir gefið x.

1. **Problema:** Risolvi l'equazione esponenziale $$2^x + 9 \cdot 2^x = 40$$. 2. **Formula e regole:** Quando abbiamo termini con la stessa base e potenza variabile, possiamo racco

1. **State the problem:** Simplify the expression $$\ln\left(\frac{\sqrt[3]{x^2}}{w+z}\right)$$. 2. **Recall the logarithm property:** For any positive values, $$\ln\left(\frac{a}{

1. **State the problem:** Write the logarithmic expressions as exponential expressions. 2. **Recall the logarithm to exponential conversion formula:**

1. Beseitige die Klammern und fasse so weit wie möglich zusammen: 1.a) \((a-b) - (a+b) - (b-a)\)

1. **State the problem:** Simplify the expression $$\frac{5}{2 - \sqrt{2}}$$. 2. **Formula and rule:** To simplify expressions with radicals in the denominator, multiply numerator