🧮 algebra

1. The problem asks about the possible values of the average (mean) height of 5 people with heights $h_1 < h_2 < h_3 < h_4 < h_5$. 2. The average height is calculated by the formul

1. The problem asks about the possible values of the average height of a group of 5 people with heights $h_1 < h_2 < h_3 < h_4 < h_5$. 2. The average height $\bar{h}$ is calculated

1. The problem is to solve a linear equation in two variables using a table. 2. A linear equation in two variables generally has the form $ax + by = c$, where $a$, $b$, and $c$ are

1. **State the problem:** Simplify or analyze the expression $$\frac{1}{s^2(s-a)}$$ where $s$ and $a$ are variables. 2. **Formula and rules:** This is a rational expression with a

1. **Stating the problem:** We want to analyze the inequality $$(a - \frac{1}{2})(b - \frac{1}{2}) \neq 0$$ which means the product of the two terms is not equal to zero. 2. **Form

1. **Énoncé du problème :** Trouver $f \circ g(x)$ avec $f(x) = 2x - 1$ et $g(x) = x^2 + 3x + 1$. 2. **Formule utilisée :** La composition de fonctions est définie par $f \circ g(x

1. The problem asks to determine the domain and range of the inverse function $y = f^{-1}(x)$ given the domain and range of $y = f(x)$. 2. Recall that the domain of $f^{-1}$ is the

1. The problem is to find the square root of 4. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** We are given the total revenue function $R=400+25x-x^2$ and the total cost function $C=50+50x$. We need to find the minimum number of units $x$ to produce

1. **State the problem:** Solve the equation $x^x = 2^{10\sqrt{200}}$ for $x$. 2. **Rewrite the right side:** Simplify the exponent on the right side.

1. ננסח את הבעיה: ראובן משחק בגולות במשך $n$ תורים. 2. בתור הראשון, ראובן הכניס 3 גולות והפסיד, כלומר איבד את כל 3 הגולות.

1. ננסח את הנתונים: ראובן משחק 4 תרורים.

1. נניח שראובן שיחק $n$ תורים. 2. לפי הנתון, בכל תור ראובן הכניס 2 גולות יותר מהמשתתפים האחרים.

1. **State the problem:** Find the values of $k$ for which a certain condition or equation holds. Since the equation or condition is not provided, please provide the full equation

1. **State the problem:** Solve the equation $x - y = 0$ for $y$ in terms of $x$. 2. **Understand the equation:** The equation $x - y = 0$ means that $x$ and $y$ are equal because

1. The problem states: If $x=2$ and $y=3$ is a solution of the equation $$8x - ay + 2a = 0,$$ find the value of $a$. 2. Substitute $x=2$ and $y=3$ into the equation:

1. The problem is to understand the value of $n$ given as $n=9$. 2. Here, $n$ is simply assigned the value 9. There is no equation to solve or further simplification needed.

1. Найдите произведение матриц $AB$. Дано:

1. **State the problem:** Solve the linear equation $x + 2y = 3$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. This

1. **State the problem:** We know 9 men produce 30 pans in 6 days. We want to find how long 12 men will take to produce 42 pans at the same work rate.

1. **State the problem:** Given the function $f(x) = x^2 + 2x + 9$, find $f(x+2)$, $f(x+10)$, and $f(x+h)$ where $h$ is any constant. 2. **Recall the function substitution rule:**