🧮 algebra

1. **State the problem:** We need to express $y$ as the subject of the formula given the equation $$4x = 5 \sqrt[3]{6y - 2p}$$. 2. **Isolate the cube root term:** Divide both sides

1. **State the problem:** We need to express $y$ as the subject of the formula from the equation $$2E = m(v^2 - y^2)$$. 2. **Write down the formula and rules:** The goal is to isol

1. Planteamos el problema: Un comerciante compra mercaderías con un 25% de descuento sobre el precio fijado por la fábrica, luego quiere fijar un nuevo precio de compra con dos des

1. **State the problem:** We need to find the sum of the integers from $1$ to $10$. 2. **Formula used:** The sum of the first $n$ natural numbers is given by the formula $$S = \fra

1. **Problem:** Find the center, vertices, and foci of the conic given by $$16x^2 + 25y^2 + 16x + 4 = 100y$$.\n\n2. **Rewrite the equation:** Move all terms to one side:\n$$16x^2 +

1. **State the problem:** Solve and graph the equation $-x + 4y = 8$. 2. **Rewrite the equation in slope-intercept form:**

1. **Bài toán:** Cho $$a=\sqrt{2}+\sqrt{7-\sqrt[3]{61+46\sqrt{5}}}+1$$. a) Chứng minh $$a^4 - 14a^2 + 9 = 0$$.

1. ปัญหาคือกำหนดค่าของตัวแปร $z_1$, $z_2$, $z_3$, และ $z_4$ ซึ่งมีค่าเป็น $7$, $2$, $5$, และ $8$ ตามลำดับ 2. เนื่องจากเป็นการกำหนดค่าโดยตรง จึงไม่มีการคำนวณเพิ่มเติม

1. Let's start by stating the problem clearly: We need to solve or explain problem 9 step by step in an easy-to-understand way. 2. Since the exact problem 9 is not provided, I will

1. **Problem statement:** Find the sum of the series $$1 + \frac{3}{1!} + \frac{5}{2!} + \frac{7}{3!} + \cdots$$ 2. **General term:** Let the $r^{th}$ term be $$U_r = \frac{2r-1}{(

1. **Problem:** Find the quotient of $$\frac{81x^{3}z}{36y} \div \frac{27x^{2}z^{2}}{12xy}$$. 2. **Formula:** Dividing rational expressions means multiplying by the reciprocal:

1. **State the problem:** Find the quotient of the given rational algebraic expressions. 2. **Recall the division rule for rational expressions:**

1. **State the problem:** Factorize the expression $$\frac{x+2}{3x-12} + \frac{2x+1}{4-x}$$. 2. **Factor denominators:**

1. **State the problem:** Factorize and simplify the expression $$\frac{5x^2 + 15x}{2x+6} : \left(1 + \frac{5}{2x}\right)$$.

1. Let's start with a simple algebra exercise: Solve for $x$ in the equation $$2x + 3 = 7$$. 2. Next, try solving a quadratic equation: Find $x$ such that $$x^2 - 5x + 6 = 0$$.

1. The user asked for "gmdas pls," which likely refers to the order of operations acronym GMDAS (Grouping, Multiplication, Division, Addition, Subtraction). 2. The order of operati

1. **State the problem:** Simplify the expression $$\frac{26x^5y^{10}z^3}{2xy^3z^2}$$. 2. **Write the formula and rules:** When dividing terms with the same base, subtract the expo

1. **Simplify** $3m + 4m - (-6m) + (-8m)$ Step 1: Remove parentheses and change signs where needed:

1. **Problem:** Simplify the function $$h(x) = \frac{3x^4 - 2\sqrt{x} + 5}{x^2}$$. 2. **Formula and rules:** When dividing a polynomial or expression by $$x^2$$, divide each term s

1. **State the problem:** Simplify the expression $$\left(\frac{a}{1-a}\right)^{1-a} + \left(\frac{1-a}{a}\right)^a.$$ 2. **Recall the formula and rules:** We want to simplify sums

1. Problemi anlama: $A$, $B$ ve $C$ tam sayıları için iki eşitlik verilmiştir: $$A^B = 81$$