🧮 algebra

1. The problem is to express a given set or solution in interval notation. 2. Interval notation is a way of writing subsets of the real number line using intervals.

1. **State the problem:** Solve the quadratic equation $$f(x) = x^2 - 5x + 6 = 0$$ to find its roots. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx +

1. The problem asks us to form a quadratic function $f(x)$ and solve $f(x)=0$, find its minimum or maximum point, and sketch the quadratic. 2. A quadratic function has the form $$f

1. **State the problem:** Solve the equation $$\frac{69}{m} = 3$$ for the variable $m$. 2. **Formula and rules:** To solve for $m$ when it is in the denominator, multiply both side

1. The problem asks to write down the inequality shown on the number line. 2. The number line shows a segment from $-2$ to $3$ with filled circles at both ends, which means the end

1. **State the problem:** Find the number of integer values of $x$ that satisfy the inequality $$3 < 2x + 1 \leq 11.$$\n\n2. **Rewrite the inequality:** We want to find all integer

1. **Stating the problem:** Given the ratio 5:10:20, if the term corresponding to 5 is multiplied by $x$ where $x$ is 7, 8, or 9, find the value of the term corresponding to 20 mul

1. **Problem:** Factorise the expression $3x^2 - 48$. 2. **Formula and rules:**

1. Let's clarify the concept of placing a function, which usually means defining or writing the function explicitly. 2. A function is a rule that assigns each input exactly one out

1. **State the problem:** Simplify the expression $$-2 + \left( \frac{2 - \left(-\frac{1}{2}\right)}{-3 + (-1)^{-5}} \right)^2 \times \left( \frac{\frac{5}{2^2} - \frac{3}{4} + 1}{

1. **State the problem:** Factorize the expression $$d\beta cd^{3} - \lambda \beta cd^{2} e + \lambda d^{3} e^{i t} \beta cd^{2} e^{i} + \lambda bcd e^{i} + \lambda abcd + \lambda

1. Задача: разложить на множители выражение $x^2$. 2. Формула: $x^2 = x \cdot x$.

1. **Stating the problem:** Simplify the expression $$\frac{8z}{xy} : \left(\frac{3x + 15}{2x + 10} \cdot \frac{16xz}{3x^2y}\right)$$. 2. **Rewrite the division as multiplication b

1. Problem: Calculate the value of the expression $\sqrt{32} + \sqrt{21} - \sqrt{23} + \sqrt{4}$.\n\n2. Formula and rules: We simplify square roots by factoring out perfect squares

1. Problem: Simplify the expression $$\left(\frac{8z}{xy}\right) : \left(\frac{3x + 15}{2x + 10} \cdot \frac{16xz}{3x^2y}\right)$$ 2. Recall that division by a fraction is the same

1. Problem: Simplify the expression \( \frac{x - z}{y - z} \cdot \left( \frac{y - z}{x - z} : \frac{y - z}{x - z} \right) \). 2. Recall that division of fractions means multiplying

1. **State the problem:** We are given a profit function $p$ that depends on the number of students $n$ attending a dance. The profit is calculated as 4 times the number of student

1. The problem states that the profit $p$ from the dance depends on the number of students $n$ who attend. 2. The profit is 4 times the number of students minus 200 dollars for the

1. The problem is to simplify the expression $\lceil x \rceil \lceil x \rceil$. 2. The ceiling function $\lceil x \rceil$ returns the smallest integer greater than or equal to $x$.

1. The problem gives three equations: $$u = p \sin\phi \cos\theta$$

1. The problem involves simplifying and understanding expressions with variables and division by zero. 2. Division by zero is undefined in mathematics, so any expression like $\fra