🧮 algebra

1. **Stating the problem:** Determine the lines parallel to the x-axis that cut a segment on the ellipse $$\frac{x^2}{4} + \frac{y^2}{16} = 1$$ whose length equals the semi-focal d

1. **State the problem:** Simplify the expression $2 - 3(3 - x)$. 2. **Apply the distributive property:** Multiply $-3$ by each term inside the parentheses:

1. The original expression to simplify is $48 - x + 26 - x + x + 5$. 2. Combine the constant terms: $48 + 26 + 5 = 79$.

1. **State the problem:** Simplify the expression $\frac{2}{2x^2}$.\n\n2. **Write the expression:** $\frac{2}{2x^2}$.\n\n3. **Simplify the fraction by canceling common factors:** B

1. **State the problem:** Simplify the expression $\frac{3}{5x^2}$. 2. **Understand the expression:** This is a fraction where the numerator is 3 and the denominator is $5x^2$.

1. **Problem statement:** Find an expression in $x$ for $T$, the total time in hours, that it will take Jacob to kayak from $S$ to $B$ and then run from $B$ to $F$.

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