🧮 algebra

1. **State the problem:** We are given the linear equation $y = 7 - 3x$ and a table of $x$ and $y$ values. We need to verify if the $y$ values correspond correctly to the given $x$

1. **State the problem:** Simplify and analyze the expression $x^3 - x$. 2. **Formula and rules:** To simplify expressions like this, factorization is useful. Recall the difference

1. **State the problem:** Create a 1-page cheat sheet with formulas only, covering starred concepts from the notes and user text. 2. **Identify starred concepts:** Arithmetic seque

1. **State the problem:** Factor the trinomial $9x^2 - 24x + 16$ where the leading coefficient is not 1. 2. **Recall the factoring method:** For a trinomial $ax^2 + bx + c$ where $

1. **State the problem:** Simplify the expression $2\sqrt{7} + 7\sqrt{2}$. 2. **Analyze the terms:** The terms $2\sqrt{7}$ and $7\sqrt{2}$ are unlike radicals because the numbers i

1. **Problem statement:** Determine whether the expression $$\frac{\sqrt{38}}{a}$$ is rational or irrational, given that $$a$$ is a non-zero rational number. 2. **Recall definition

1. The problem involves understanding the relationship between price $x$ and a percentage $y$ that ranges from 0% to 100%, with a specific value $y=110$ given. 2. We interpret the

1. **State the problem:** Simplify the quadratic expression $48x^2 - 200x + 200$ by factoring out the greatest common factor (GCF). 2. **Identify the GCF:** The coefficients are 48

1. **State the problem:** Amari bought sneakers for 110 dollars and sold them after a month for 10% less than the original price. 2. **Formula used:** To find the selling price aft

1. **State the problem:** We are given two expressions representing parallel lines: $15x + 4$ and $20x + 1$. We want to find the value of $x$ for which these two lines are equal, i

1. The problem is to solve number 6, but since no specific problem statement was given, I will assume you want a general example of solving a typical algebraic problem. 2. Let's co

1. **State the problem:** Factor the expression $24n^3 + 68n^2 + 48n$. 2. **Identify the common factors:** Each term contains a factor of $n$, so factor out $n$ first.

1. **State the problem:** Calculate the value of $|7 - 3| - |3 - 7|$. 2. **Recall the absolute value definition:** The absolute value $|a|$ is the distance of $a$ from zero on the

1. المشكلة: شرح مفهوم المصفوفات في الرياضيات. 2. تعريف المصفوفة: المصفوفة هي ترتيب مستطيل من الأعداد أو الرموز، مرتبة في صفوف وأعمدة.

1. **State the problem:** Find the value of the determinant of the matrix \(\begin{bmatrix} x & x & a \\ x & a & x \\ a & 2 & x \end{bmatrix}\). 2. **Recall the formula for a 3x3 d

1. **State the problem:** Multiply the radical expression $\sqrt{3}(\sqrt{12} + 4)$. 2. **Recall the distributive property:** $a(b + c) = ab + ac$. We will apply this to multiply $

1. **State the problem:** Factor the perfect square trinomial $4x^2 - 12x + 9$. 2. **Recall the formula for a perfect square trinomial:**

1. **State the problem:** We need to find the break-even quantity and the number of pens to sell to achieve a monthly profit of 15000.

1. The problem is to identify the graph of the function $$f(x) = \sqrt{x} + 2 - 4$$. 2. First, simplify the function:

1. The problem is to identify the graph of the function $$f(x) = \sqrt{x - 5} - 1$$. 2. The function involves a square root, so the domain is where the expression inside the root i

1. The problem is to identify the graph of the function $$f(x) = \sqrt{x} + 1 + 5$$. 2. First, simplify the function: