🧮 algebra

1. **State the problem:** Factor the expression $$8s^2 + 4s$$. 2. **Identify the common factor:** Look for the greatest common factor (GCF) of the terms $$8s^2$$ and $$4s$$.

1. **State the problem:** Solve the system of linear equations:

1. **Problem:** Find the x- and y-intercepts of the linear equation $3x + 4y = 12$. 2. **Formula and rules:**

1. **Problem:** Simplify the algebraic expression $m + m + r + 7 - 3$. 2. **Formula and rules:** Combine like terms by adding or subtracting coefficients of the same variable and s

1. **State the problem:** Solve the equation for $y$ in the equation $$-3y + 8 = 83$$. 2. **Isolate the term with $y$:** Subtract 8 from both sides to get rid of the constant on th

1. **State the problem:** Solve for $m$ in the equation $$1 = 6\sqrt{-19} + 2m - 5$$. 2. **Rewrite the equation:** Add 5 to both sides to isolate terms with $m$:

1. **State the problem:** Solve for $b$ in the equation $$\sqrt{19b - 13} = \sqrt{19 + 11b}.$$\n\n2. **Formula and rules:** To solve equations involving square roots, we can square

1. **State the problem:** We are given points (1, 12), (3, 36), and (4, 48) and asked to write an equation of the form $y = kx$ that fits these points. 2. **Understand the form:**

1. The problem is to express a solution or set in interval notation. 2. Interval notation is a way to write subsets of the real number line using parentheses \( () \) for open inte

1. **Problem:** Simplify and factor the expression $4(7x + 6) - 3(6x - 7)$. Step 1: Distribute the constants:

1. **State the problem:** Given two functions $f(x) = \frac{3}{1 - 4x}$ and $g(x) = \frac{1}{x}$, find the compositions $(f \circ g)(x)$ and $(g \circ f)(x)$, and determine the dom

1. **State the problem:** Manny can put together 3 airplane models in 4.5 hours and 4 models in 6 hours. We need to find the time it takes to put together 1 model, write an equatio

1. The problem is to understand the vertex form of a quadratic function, which is given by the formula: $$y = a(x - h)^2 + k$$

1. The problem is to factor each polynomial expression by finding the greatest common factor (GCF) and simplifying. 2. The formula for factoring by GCF is: $$a \cdot b + a \cdot c

1. The problem is to simplify the polynomial expression by distributing the factor outside the parentheses to each term inside the parentheses. 2. The general formula for distribut

1. The problem asks which set of ordered pairs $(x, y)$ could represent a linear function. 2. A linear function has a constant slope between any two points. The slope formula betwe

1. **State the problem:** We need to find the area $A$ of a square with side length $s = 4m^2n^4$. 2. **Formula:** The area of a square is given by the formula:

1. **State the problem:** Simplify the expression $$(x^3 y^{-3}) (2 x^5 y^4)^3$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\left(\frac{x^3 y^2}{z^4}\right)^2$$. 2. **Recall the power of a quotient rule:** When raising a fraction to a power, raise both

1. **State the problem:** Simplify the expression $$6 \left( \frac{x^3 y^{12}}{z^4} \right)^2 \cdot \frac{x^5}{1}$$. 2. **Recall the exponent rules:**

1. **State the problem:** Multiply the expressions $(-2x)$ and $(3x^4)$. 2. **Write the multiplication:** $$(-2x)(3x^4)$$