🧮 algebra

1. **State the problem:** Solve the quadratic equation by factoring: $$x^2 - 38 = -3x - 10$$ 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to ze

1. **State the problem:** Solve the quadratic equation $$x^2 + 2x - 80 = 0$$ by factoring. 2. **Recall the factoring method:** To factor a quadratic equation of the form $$ax^2 + b

1. Staðfesta vandamálið: Arna og Örvar eiga að skipta 1800 kr. þannig að Örvar borgi \(\frac{4}{5}\) af því sem Arna borgar. 2. Setja upp breytur: Látum \(x\) vera það sem Arna bor

1. The method to solve quadratic equations is to use the quadratic formula, factoring, or completing the square. 2. The quadratic formula is given by:

1. **Problemstellung:** Gegeben ist eine ganzrationale Funktion dritten Grades $g(x) = ax^3 - cx$ mit $a \neq 0$ und $c > 1$. Es soll gezeigt werden, dass $g$ drei Nullstellen hat

1. **State the problem:** Simplify the expression $$\frac{10x}{x^2+3x} \div \frac{15x}{x^2 - x - 12}$$ as a single fraction in simplest form. 2. **Rewrite division as multiplicatio

1. **Problem statement:** Lise has 24 carrots and eats 2 carrots each day. We want to find the relationship between the number of days $x$ and the number of carrots $f(x)$ left in

1. Il problema non è specificato, quindi non posso risolverlo senza ulteriori dettagli. 2. Per favore, fornisci l'espressione o l'equazione da risolvere.

1. **Stating the problem:** Simplify the expression $$(2a+b)\cdot(2a+b)+4$$ 2. **Formula and rules:** Use the distributive property (FOIL) to expand the product of binomials: $$(x+

1. The problem is to simplify the expression $$\sqrt[3]{\frac{80}{000}} \div \left(7.1 + \sqrt[3]{12,180} + 12,209\right).$$ 2. First, note that the expression $$\frac{80}{000}$$ i

1. **State the problem:** Convert the rectangular equation $$14y = x^2 + y^2$$ to polar form and solve for $$r$$ in terms of $$\theta$$. 2. **Recall the polar-rectangular relations

1. **State the problem:** Convert the rectangular equation $$21x = y^2$$ to polar form and solve for $$r$$ in terms of $$\theta$$. 2. **Recall the polar-rectangular relationships:*

1. Problema: Studiare le funzioni razionali date, trovando il dominio e l'eventuale simmetria. 2. Formula e regole importanti:

1. Problema: Studiare il dominio e la simmetria della funzione $$y=\frac{x-1}{x+3}$$. 2. Dominio: Il denominatore non può essere zero, quindi risolviamo $$x+3=0$$ che dà $$x=-3$$.

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

1. **Problem stated:** Find $30\%$ of $20$ and represent the result for a $20$ meter land length. 2. **Formula used:** To find a percent of a number, use $\text{part} = \frac{\text

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$

1. The problem is to solve a Grade 7 algebra question. Since no specific problem was given, let's consider a common algebra problem: Solve for $x$ in the equation $2x + 3 = 11$. 2.

1. **State the problem:** Subtract 20 from the expression $\frac{15b}{23}$. 2. **Write the expression:** $\frac{15b}{23} - 20$.

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. **State the problem:** A duck flies 9 kilometers in 6 minutes. We want to find how far it can fly in 42 minutes. 2. **Set up the proportion:** Let $d$ be the distance the duck c