🧮 algebra

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

1. **State the problem:** Solve the system of equations for $x$ and $y$: $$\begin{cases} 2x + y = 8 \\ 2x - y = 12 \end{cases}$$

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

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

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

1. **State the problem:** We have a sequence defined by the recurrence relation $$u_{n+1} = k u_n + k$$ where $k$ is a constant. Given: $$u_1 = 9$$ and $$u_2 = 4$$.

1. **State the problem:** Simplify the expression $$\left( \frac{-vu^3}{2u^4v^{-3} \cdot -u^4v^{-4}} \right)^3$$. 2. **Rewrite the denominator:** Multiply the terms inside the deno

1. **Stating the problem:** Calcolare il valore dell'espressione $$\left(\frac{1}{\sqrt[3]{3}} + \frac{1}{\sqrt[3]{9}}\right) \cdot \frac{6}{\sqrt[3]{3} + \sqrt[3]{9}}$$.

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 the reciprocal:**

1. **Problem:** Find a function for the sinusoidal graph with amplitude 3, midline $y=0$, x-intercepts at $-\frac{2\pi}{3}$, $0$, and $\frac{2\pi}{3}$, and a negative slope at $x=0

1. **State the problem:** Simplify the expression $$(2u^{-2}v^{2})^{2} \cdot 2v^{-5}$$. 2. **Apply the power of a product rule:** $$(ab)^n = a^n b^n$$, so

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. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Recall the division rule for fractions:** Dividing by a

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

1. Il problema chiede di risolvere l'espressione $y^3 + \frac{7}{4}y + 1 : \left(y + \frac{1}{2}\right)$ usando il metodo di Ruffini. 2. Il metodo di Ruffini si usa per dividere un

1. **Stating the problem:** Simplify the expression $$\frac{y(alla 3)+\frac{7}{4}y+1}{y+\frac{1}{2}}$$. It seems "alla 3" means $y^3$, so the expression is $$\frac{y^3 + \frac{7}{4

1. **Resuelve el sistema de ecuaciones:** \[\begin{cases} 3 \log x - 2 \log y = 4 \\ \log(xy) = 3 \end{cases}\]

1. **Planteamiento del problema:** Resolver el sistema de ecuaciones: $$\begin{cases} 3 \log x - 2 \log y = 4 \\ \log(x \cdot y) = 3 \end{cases}$$

1. **Problem statement:** Tina drives 150 km from Cork to Kilkenny, leaving at 7:45 a.m. She stops for 15 minutes to charge her car. The average speed for the whole journey is 60 k

1. **State the problem:** We need to calculate the income tax Artem pays on his gross earnings with a tiered tax rate and an annual tax credit.