🧮 algebra

1. **Problem 2:** Find the equation in slope-intercept form of a line with slope $m=2$ passing through point $(3,4)$. 2. The slope-intercept form is given by the formula:

1. **Problem 1:** Find the equation representing the table and graph with points $(5,-2)$, $(6,-4)$, $(9,-10)$, $(11,-14)$, and $(12,-16)$. The graph shows a line with y-intercept

1. **Problem 1: Find the positive value of $x$ such that matrices $M$ and $N$ commute under multiplication.** Given matrices:

1. **State the problem:** We need to find the equation of the line that matches both the given table of values and the graph description. 2. **Analyze the table:** The table gives

1. **State the problem:** Convert the improper fraction $\frac{45}{8}$ into a mixed number. 2. **Formula and rules:** A mixed number consists of a whole number and a proper fractio

1. **Problem:** Given matrices \(M = \begin{bmatrix}4 & 8 \\ 2 & x\end{bmatrix}\) and \(N = \begin{bmatrix}x^2 & 4 \\ 1 & 4x\end{bmatrix}\), find the positive value of \(x\) such t

1. The problem asks to evaluate the expression $12.41E+\pi$. 2. Here, $E$ represents the scientific notation symbol for "times ten to the power of". So $12.41E+\pi$ means $12.41 \t

1. **State the problem:** Reduce each fraction to its lowest terms. 2. **Formula and rule:** To reduce a fraction $\frac{a}{b}$, find the greatest common divisor (GCD) of $a$ and $

1. **State the problem:** We are given a rectangle with perimeter 105 feet. The sides are labeled as $2f - 2$ and $\frac{3}{2}f + 9$. We need to write an equation for the perimeter

1. **State the problem:** Reduce each fraction to its lowest terms. 2. **Formula and rules:** To reduce a fraction $\frac{a}{b}$, find the greatest common divisor (GCD) of $a$ and

1. **State the problem:** Solve the system of linear equations: $$-x - y = -9$$

1. **State the problem:** We need to find how many miles are in 48 kilometers using the formula: $$\text{distance in miles} = \frac{5}{8} \times \text{distance in km}$$

1. **State the problem:** We need to find the output when the input fraction $\frac{6}{7}$ is multiplied by 35. 2. **Formula used:** The operation is multiplication of a fraction b

1. The problem is to calculate $3 \div \frac{17}{5}$ and express the answer in simplest form. 2. Recall the rule for dividing by a fraction: dividing by $\frac{a}{b}$ is the same a

1. **State the problem:** Simplify the expression $$(5x + \sqrt{5})^2 (5x - \sqrt{5})^2$$. 2. **Recall the formula:** The expression is a product of two squares. We can rewrite it

1. **Problem Statement:** We are given the export function of Avocados from Indonesia as $$E(P) = P - 10000$$ where $$P \geq 10000$$ and $$P$$ represents production in thousands. 2

1. **Problem Statement:** We want to find the volume $V(x)$ of an open-top box formed by cutting out squares of side length $x$ from each corner of a $12 \times 12$ inch square she

1. **State the problem:** Simplify the expression $$(5x + \sqrt{5})^2 (5x - \sqrt{5})^2$$. 2. **Recall the formula:** The expression is a product of squares of binomials. We can us

1. The problem is to simplify the expression or equation given by the user. 2. Simplification involves combining like terms, reducing fractions, and applying algebraic rules.

1. **State the problem:** Simplify the expression $$(5x + \sqrt{5})^2 (5x - \sqrt{5})^2$$. 2. **Recall the formula:** The expression is a product of two squares. We can use the ide

1. **State the problem:** Simplify the expression $$(4x^4y^8 + 49)(2x^2y^4 + 7)(2x^2y^4 - 7).$$ 2. **Identify the formula and rules:** Notice that the last two factors are of the f