🧮 algebra

1. **State the problem:** Solve the quadratic equation $$x^2 - 11x + 28 = 0$$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solutions

1. **Problem statement:** The roots of the equation $ax^2 + cx + c = 0$ are in the ratio $p : q$. Prove that $$\sqrt{\frac{p}{q}} + \sqrt{\frac{q}{p}} + \sqrt{\frac{c}{a}} = 0.$$\n

1. **State the problem:** Solve the system of linear equations by graphing: $$\begin{cases} x + y = 6 \\ x - y = 2 \end{cases}$$

1. The problem is to understand and explain the concept of an asymptote in mathematics. 2. An asymptote is a line that a graph of a function approaches but never touches or crosses

1. **Énoncé du problème :** Simplifier l'expression $A = \ln(e^3) + 2 \ln(3e) + \ln\left(\frac{1}{9}\right)$. 2. **Formules et règles importantes :**

1. **State the problem:** Determine if the given pairs of functions are inverses of each other. 2. **Recall the definition:** Two functions $f$ and $g$ are inverses if and only if

1. **Problem statement:** Given that $a^p = b^q = c^r$ and $a, b, c$ are in geometric progression (G.P.), prove that $p, q, r$ are in harmonic progression (H.P.). 2. **Recall defin

1. **State the problem:** Simplify the expression $3 \cdot \sqrt{\frac{1}{9}} \cdot \sqrt{3}$.\n\n2. **Recall the properties of square roots:** For any positive numbers $a$ and $b$

1. **State the problem:** Simplify the expression $x^2 - 2x + 1$. 2. **Recall the formula:** This is a quadratic expression that can be factored using the perfect square trinomial

1. Simplify the expression $(8 - 4) \times 5 \div 2$ using the order of operations (GEMDAS). 2. Simplify the expression $(10 - 5)^2 \div 5 + 2$ using GEMDAS.

1. Bài toán: Giải phương trình bậc hai $ax^2 + bx + c = 0$. 2. Công thức nghiệm: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

1. **Problem statement:** b) Find the expression for $M$ such that $$M + (5x^2 - 2xy) = 6x^2 + 9xy - y^2.$$

1. The problem is to verify that the solution you provided matches the expected solution. 2. To do this, we need to compare your solution step-by-step with the standard method or f

1. The problem is to evaluate the expression: $-7 - (11)$ using the KFC (Keep, Flip, Change) method. 2. KFC stands for:

1. The problem is to understand the phrase "Like this" in a math context and provide a relevant example or explanation. 2. Since the user did not specify a particular math problem,

1. **Problem 1: Ages of Bianca and Bryan** The age of Bianca is 4 more than 3 times the age of Bryan. The sum of their ages is 32. Find their ages.

1. **Problem Statement:** Let's understand what "Systems of Linear Equations" and "Gaussian Elimination" mean in simple language.

1. **State the problem:** Solve a linear equation in one variable, for example, $3x + 5 = 11$. 2. **Formula and rules:** A linear equation in one variable has the form $ax + b = c$

1. **State the problem:** Ely's mother is currently 35 years old. Three years ago, she was 4 times as old as Ely was at that time. We need to find Ely's current age. 2. **Define va

1. The problem is to find the result of each subtraction expression involving fractions and mixed numbers. 2. We subtract fractions by finding a common denominator and then subtrac

1. The problem is to convert the equation $y - x + 2 = 0$ into slope-intercept form. 2. The slope-intercept form of a line is given by the formula: