🧮 algebra

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

1. **State the problem:** Solve the proportion $$\frac{11}{5} = \frac{10}{x}$$ for $x$ and round the answer to the nearest tenth. 2. **Use the cross-multiplication formula:** For p

1. **State the problem:** Solve the equation $$x - 5 = 2\sqrt{x} - 5$$ for $x$. 2. **Isolate the square root term:** Add 5 to both sides to simplify:

1. **State the problem:** Solve the linear equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on one side of the

1. **State the problem:** Simplify the factorial expression $$\frac{9! \times 8!}{11!}$$. 2. **Recall the factorial definition:** For any positive integer $n$, $n! = n \times (n-1)

1. **State the problem.** We are given the system of equations:

1. **State the problem:** Solve the linear equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the formula and rules:** To solve for $t$, we want to isolate $t$ on one side of the

1. **State the problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation.

1. **State the problem:** Solve the equation $$\frac{1}{5}(x - 5) = 7$$ for $x$. 2. **Formula and rules:** To solve for $x$, first eliminate the fraction by multiplying both sides

1. **Simplify** $16^{-\frac{3}{4}}$. Recall the rule: $a^{-m} = \frac{1}{a^m}$.