🧮 algebra

1. **State the problem:** We want to evaluate the infinite series $$\sum_{n=2}^{\infty} \left(\frac{3}{4}\right)^n \cos(180n^\circ).$$ 2. **Recall the cosine values:** Since $$\cos

1. **State the problem:** Solve the linear equation $$16 - 2t = 5t + 9$$ for the variable $t$. 2. **Write down the equation:** $$16 - 2t = 5t + 9$$

1. **Problem:** Solve the equation $16 - 2t = 5t + 9$. 2. **Formula / goal:** Use inverse operations to get all $t$ terms on one side and numbers on the other.

1. **Problem stated:** 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:** $$\frac{x^2-25}{

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

1. Has compartido una fórmula general de conversión entre diferentes unidades o variables representadas como $S$, $C$, y $R$. 2. La fórmula muestra varias igualdades: $$\frac{S}{18

1. **Problem:** Simplify the expression $\frac{x^2-25}{x^2+5x}\div\frac{xy+6x-5y-30}{5x-15}$. 2. **Use the division rule for fractions:**

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. Let's clarify the problem: You asked why we didn't factor for $x^3$ in a previous problem. 2. Factoring depends on the expression given. If the expression contains $x^3$ as a co

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

1. **State the problem:** Solve the equation $x^3 - 8 = 0$ for $x$. 2. **Formula and rules:** This is a cubic equation. We can isolate $x^3$ and then take the cube root of both sid

1. **Problem:** Describe vectors and draw some to understand how they work. 2. A **vector** is a quantity that has **magnitude** and **direction**.

1. Problem: describe vectors and draw some. 2. A vector is a quantity that has both magnitude and direction.

1. **Problem:** Teach the 4 quadrants in a full $360^\circ$ circle and draw them clearly. 2. **Formula / rule:** A full turn is $360^\circ$, and the coordinate plane is split by th

1. **Problem:** Teach the 4 quadrants in the $360^\circ$ coordinate plane and draw a diagram. 2. **Formula / rule:** The coordinate plane is split by the $x$-axis and $y$-axis into

1. **State the problem.** We need to solve the equation $a^3+a^2=36$ and find $a$.

1. **State the problem:** Solve for $a$ in the equation $$a^3 + a^2 = 36.$$\n\n2. **Rewrite the equation:** We want to find $a$ such that $$a^3 + a^2 - 36 = 0.$$\n\n3. **Factor the

1. The problem is to find the cube root of 64, written as $\sqrt[3]{64}$.\n\n2. The cube root of a number $x$ is a value $y$ such that $y^3 = x$.\n\n3. We want to find $y$ such tha

1. El problema no está explícito, pero se solicita solo el desarrollo, por lo que se asume que se requiere el desarrollo de una expresión o ecuación. 2. Para desarrollar una expres

1. **Problem:** Evaluate $$\frac{(a-b)^2+(b-c)^2}{(a-c)^2}$$ given that $a-b=b-c=2$. 2. **Formula and rule:** Use the given values directly, and also note that $a-c=(a-b)+(b-c)$.