🧮 algebra

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

1. The problem is to understand and analyze the linear equation $x + 2y = 4$. 2. This equation represents a straight line in the coordinate plane.

1. Problem: Express 6 : 25 as a percent. To convert a ratio to a percent, divide the first number by the second and multiply by 100.

1. The question asks to find the values of $x$ and $y$ but does not specify an equation or context. 2. To solve for $x$ and $y$, we need an equation or system of equations involvin

1. **State the problem:** Given $a = \frac{2 - \sqrt{3}}{2 + \sqrt{3}}$ and $b = \frac{2 + \sqrt{3}}{2 - \sqrt{3}}$, find the value of $$a^2 - 5ab + b^2$$ and also compute $a+b$ an

1. The user asked to simplify answers for all questions, but no specific questions were provided. 2. To assist effectively, please provide the algebraic expressions or problems you

1. **State the problem:** Arthur worked for 65 minutes writing 16 words per minute, and Bryony worked for 90 minutes writing 14 words per minute. We need to find who wrote more wor

1. The problem states that the roots of the equation $f(x) = 0$ are given by $$x = \frac{-5 \pm \sqrt{3 - 12k^2}}{4}.$$ We need to find the values of $k$ for which the roots are eq

1. The problem is to express the equation $3x - y = 6$ in terms of $y$. 2. Start by isolating $y$ on one side of the equation.