🧮 algebra

1. **State the problem:** Find two positive numbers $x$ and $y$ such that $x + 2y = 100$ and the product $P = xy$ is maximized. 2. **Express one variable in terms of the other:** F

1. **State the problem:** Solve the equation $$\frac{-11 + x}{-7} = -15$$ for $x$. 2. **Understand the formula and rules:** To solve for $x$, we need to isolate $x$ on one side of

1. **State the problem:** Solve the equation $-24 = -2(x + 19)$ for $x$. 2. **Use the distributive property:** Multiply $-2$ by each term inside the parentheses.

1. **State the problem:** Solve the inequality $$-x^2 + 8x + 7 < 0$$ and determine which interval from the options A) to D) satisfies it. 2. **Rewrite the inequality:** Multiply bo

1. The problem is to express the product $(-4) \times (-4) \times (-4) \times (-4) \times (-4) \times (-4)$ as a power. 2. When the same number is multiplied by itself multiple tim

1. **State the problem:** Solve the equation $7.23$. 2. **Interpretation:** Since $7.23$ is a number and not an equation, we assume the problem is to understand or simplify the num

1. The problem is to understand and graph the piecewise function given by $y=3x+3$ with the domain restriction $2 \le x \le 1$. 2. First, note that the domain $2 \le x \le 1$ is no

1. **State the problem:** Match each sentence to its corresponding equation. 2. **Analyze each sentence and equation:**

1. The problem asks to match each fraction with its corresponding repeating decimal. 2. To solve this, convert each fraction to a decimal by dividing numerator by denominator and o

1. The problem is to understand and solve proportions in a simple way suitable for sixth grade. 2. A proportion is an equation that states two ratios are equal. It looks like this:

1. The problem asks for the left and right end behavior and the positive and negative behavior of a function, but the function is not specified. 2. To analyze end behavior, we look

1. Énoncé du problème : Trouver la règle de la fonction valeur absolue $f$ connaissant que l'équation d'une des demi-droites est $y=3x+5$ et que le maximum de $f$ est 8. 2. Rappel

1. **State the problem:** Given the quadratic function $y = 4x^2 - 10x + 8$, analyze its key features including intercepts, vertex, domain, range, and behavior. 2. **Formula and ru

1. **State the problem:** Find the intercepts of the function $$y=\frac{8x}{x^2+36}$$. 2. **Recall intercept definitions:**

1. **Problem:** Find the inverse of the relation \(\{(1, -3), (-2, 3), (5, 1), (6, 4)\}\). 2. **Understanding Inverse Relations:** The inverse of a relation swaps each ordered pair

1. **State the problem:** We are given the linear equation $y = 7 - 3x$ and a table of $x$ and $y$ values. We need to verify if the $y$ values correspond correctly to the given $x$

1. **State the problem:** Simplify and analyze the expression $x^3 - x$. 2. **Formula and rules:** To simplify expressions like this, factorization is useful. Recall the difference

1. **State the problem:** Create a 1-page cheat sheet with formulas only, covering starred concepts from the notes and user text. 2. **Identify starred concepts:** Arithmetic seque

1. **State the problem:** Factor the trinomial $9x^2 - 24x + 16$ where the leading coefficient is not 1. 2. **Recall the factoring method:** For a trinomial $ax^2 + bx + c$ where $

1. **State the problem:** Simplify the expression $2\sqrt{7} + 7\sqrt{2}$. 2. **Analyze the terms:** The terms $2\sqrt{7}$ and $7\sqrt{2}$ are unlike radicals because the numbers i

1. **Problem statement:** Determine whether the expression $$\frac{\sqrt{38}}{a}$$ is rational or irrational, given that $$a$$ is a non-zero rational number. 2. **Recall definition