🧮 algebra

1. Let's start by understanding what a graphical inequality means. When you have an inequality involving a function, such as $y > f(x)$ or $y \leq f(x)$, it represents all the poin

1. Problem: Find the inverse of each function. 2. For function a: $f(x) = 3x - 2$

1. **State the problem:** You manage a 90-unit apartment building. Rent starts at 20000 per unit with full occupancy. For every 1000 increase in rent, one more unit becomes vacant.

1. The problem is to graph the function, but no specific function was provided. 2. To graph a function, we need its explicit formula, for example, $y = x^2$ or $y = \sin(x)$.

1. **State the problem:** You are managing a 90-unit apartment building. The base rent is 20000 per unit with full occupancy. For every 1000 increase in rent, one unit becomes vaca

1. Let's analyze the problem: We want to determine the value of $x$ and check if it could be 36 or 24, given the statement that $x$ is clearly larger than 12. 2. Since $x$ is large

1. نبدأ بكتابة المعادلة المعطاة: $$ س^2 + ص^2 = ك $$ 2. نريد التعبير عن $$ ص^2 $$ بدلالة $$ ك $$ و $$ س^2 $$.

1. The problem is to find the equation of the line passing through the points $(1,2)$ and $(3,8)$. 2. First, calculate the slope $m$ using the formula:

1. The user asked if the formula provided is correct, but no specific formula was given in the message. 2. To verify correctness, please provide the exact formula or problem statem

1. The problem asks to draw the graphs of three functions: a. $y=(x-1)^2+2$

1. Let's create a math problem involving quadratic equations. 2. Problem: Solve the quadratic equation $$2x^2 - 4x - 6 = 0$$.

1. Let's consider a simple algebra problem: Solve for $x$ in the equation $2x + 3 = 7$. 2. Start by isolating the variable term. Subtract 3 from both sides:

1. The problem: Understand how to use the completing the square method to solve quadratic expressions or equations. 2. Completing the square is a technique to rewrite a quadratic e

1. The problem is to find the vertex of the quadratic function given by the equation $$y = x^2 - 8x + 14$$. 2. Recall that the vertex form of a quadratic function is $$y = a(x-h)^2

1. **State the problem:** Solve the inequality $$2 - \frac{x}{6} \geq -\frac{2}{5}$$. 2. **Isolate the term with $x$:** Subtract 2 from both sides:

1. **State the problem:** Expand the expression $ (x+3)(x-2) $. 2. **Apply the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term in th

1. समस्या को समझें: एक व्यापारी ने वस्तु को 20% लाभ पर बेचा। यदि उसने वस्तु को 40% अधिक कीमत पर खरीदा होता और 24 रुपये कम पर बेचा होता, तो उसे 20% हानि होती। हमें वस्तु का क्रय मूल

1. The problem is to evaluate the expression $5:2:4 \div 5:4:6$. Here, the colon ":" is interpreted as division, so the expression can be rewritten using division symbols. 2. Rewri

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. Start by isolating the variable term $2x$ on one side. Subtract 3 from both sides:

1. **State the problem:** A man bought a shirt for 50 and sold it for 65. We need to find the percentage profit. 2. **Identify the cost price (CP) and selling price (SP):**

1. The problem asks if $x^{-5}$ can be written as $\frac{1}{x^5}$.\n\n2. Recall the rule of exponents: for any nonzero $x$ and integer $n$, $x^{-n} = \frac{1}{x^n}$.\n\n3. Applying