🧮 algebra

1. **State the problem:** Simplify and verify the equation: $$\left(2x^{2}y^{-1} / 3z^{2}\right)^{-2} \times \left(3xz^{2} / y\right)^{3} = \frac{3^{7} z^{10}}{2^{2} x y}$$

1. The problem is to identify which graph correctly represents the piecewise function: $$f(x) = \begin{cases} \frac{1}{2}x + 2 & \text{for } x \leq 1 \\ -\frac{5}{4}x + 1 & \text{f

1. The problem is to identify the graph that represents the piecewise function: $$f(x) = \begin{cases} \frac{1}{2}x + 2 & \text{for } x \leq 1 \\ -\frac{5}{4}x + 1 & \text{for } x

1. **مسئله:** دامنه تابع $$\frac{x^2 - x}{x - 1}$$ را بیابید. 2. **فرمول و نکات مهم:** دامنه تابع کسری شامل تمام مقادیر $$x$$ است که مخرج صفر نشود.

1. **State the problem:** Solve the one-step linear equation $b - 2.06 = 3.94$. 2. **Formula and rule:** To isolate $b$, add $2.06$ to both sides of the equation. This uses the add

1. **State the problem:** Solve the equation $$\frac{1}{4}(8x + 56) = 20$$. 2. **Use the distributive property:** Multiply both sides by 4 to eliminate the fraction.

1. The problem is to solve an algebraic expression or equation without using vectors or coordinates. 2. Since the user did not specify a particular problem, let's consider a simple

1. **State the problem:** Solve the equation $$6.4 = \frac{w}{1.5}$$ for $$w$$. 2. **Formula and rule:** To solve for $$w$$ when it is divided by a number, multiply both sides of t

1. **State the problem:** Solve the equation and inequality graphically:

1. **State the problem:** We are given a system of three linear equations with three variables $r$, $s$, and $t$:

1. **State the problem:** Simplify or analyze the expression $2x + 1$. 2. **Understand the expression:** This is a linear expression in terms of $x$.

1. Problem: Simplify the expression $11(3g + 7 - 2g) - 4$. 2. Use the distributive property: $a(b + c) = ab + ac$.

1. **State the problem:** Solve the system of equations: $$2x + 3y = 54$$

1. **State the problem:** Calculate the value of the expression $\frac{1}{2} + \frac{3}{5} - \frac{2}{3}$.\n\n2. **Find a common denominator:** The denominators are 2, 5, and 3. Th

1. **Problem:** Simplify the polynomial expression $6x^3 - 9x + 12$. 2. **Formula and rules:** This is a polynomial expression. Simplification involves combining like terms if any,

1. **State the problem:** We need to write a function that models the height of Emily's rosemary bush over time. 2. **Identify the variables:** Let $x$ represent the number of year

1. The problem states that Nick's camera has a total memory storage of 128 GB and he uses 20 GB each month. 2. We want to write a function $y$ that describes the remaining memory a

1. The problem is to simplify each given expression. 2. Simplification involves reducing expressions to their simplest form by combining like terms, factoring, canceling common fac

1. **State the problem:** Simplify the expression $11(3g+7-2g)-4$. 2. **Apply the distributive property:** Multiply $11$ by each term inside the parentheses.

1. **State the problem:** Factor the polynomial equation $$x^4 - 26x + 144 = 0$$. 2. **Understand the problem:** We want to express the quartic polynomial as a product of polynomia

1. **State the problem:** Distribute and simplify the expression $$(x - 7)(x - 3)$$. 2. **Recall the distributive property (FOIL method):**