🧮 algebra

1. The problem is to divide fractions and mixed numbers as given: $\frac{3}{10} \div \frac{1}{5}$. 2. The formula for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{

1. **State the problem:** Solve the equation $$0.6 = \frac{(1 + \frac{x}{2})^2}{(1 - x)^2}$$ for $x$. 2. **Rewrite the equation:** We have

1. Énoncé du problème : Factoriser le polynôme $2x^3 - 4x^2 - 6x$. 2. Identifier le facteur commun : Tous les termes contiennent un facteur commun $2x$.

1. **State the problem:** We need to find the relationship between the number of Fuji apple trees (x) and Gala apple trees (y) at Hillsdale Orchard using the given ratio table and

1. **Problem (a):** Jacob buys a kayak priced at 870. It is reduced by 15%, then a further 10% reduction is applied. 2. **Formula:** To find the final price after successive percen

1. **State the problem:** We need to find the number of new Fuji apple trees to plant so that the ratio of Fuji to Gala apple trees remains the same.

1. **State the problem:** We need to solve the system of inequalities graphically: $$y \leq \frac{1}{2}x - 6$$

1. **State the problem:** Given the circle equation $$x^2 + y^2 - ax - by - 12 = 0$$ and the center of the circle is at point $(2,3)$, find the values of $a$ and $b$. 2. **Recall t

1. Stating the problem: We need to find the largest common factor (also called greatest common divisor, GCD) of each pair of numbers. 2. Formula and rules: The largest common facto

1. Het probleem is om de uitdrukking of vergelijking correct in te vullen of te corrigeren. 2. Omdat er geen specifieke vergelijking of uitdrukking is gegeven, kan ik niet direct e

1. We are asked to calculate powers and rewrite powers with negative exponents as positive exponents and simplify without a calculator. 2. For powers, recall the rules:

1. **Problem statement:** Given the function $$f(t) = -\frac{1}{400} t^{2} + \frac{1}{10} t$$ and the parameterized function $$f_a(t) = - \frac{a}{400} t^{2} + \frac{a}{10} t,$$ wh

1. Énoncé du problème : Dériver la fonction $$y = \frac{4x^2 - 7x + 5}{2x^3 + 3x - 1}$$, développer le numérateur en produit, simplifier la dérivée et calculer $y'$ en $x = -2$.

1. The problem asks to write each number as a product of its prime factors. 2. Prime factorization means expressing a number as a product of prime numbers only.

1. Il problema richiede di moltiplicare i due binomi $ (a + 5b)(3a - 1) $. 2. Usiamo la proprietà distributiva (o metodo FOIL) per moltiplicare ogni termine del primo binomio per o

1. **State the problem:** Simplify the expression $$(a-2)^2 \times (a+2)^2$$. 2. **Recall the formula:** The expression is a product of two squares. We can use the property $$(x^2)

1. Tehtävässä pyydetään piirtämään koordinaatistoon kahden funktion kuvaajat ja määrittämään niiden nollakohdat. 2. Funktiot ovat:

1. **State the problem:** Calculate the value of $\frac{1}{5} \div \left(5 \frac{1}{2} - 3 \frac{1}{2}\right)$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Luna wants to buy 2 key lime pies at 8.99 each and some pounds of shrimp at 8.50 per pound. She wants to spend less than 45 total. 2. **Write the inequali

1. Problem: Berechnen Sie die Menge $x$, für die der Erlös $E(x)$ die Kosten $K(x)$ übersteigt. 2. Gegebene Funktionen:

1. **Problemstellung:** Berechnen Sie die Menge $x$, für die der Erlös $E(x)$ die Kosten $K(x)$ übersteigt.