🧮 algebra

1. **State the problem:** Given $a=5$ and $b=3$, solve the equation $$ (2a)^2 = 3b $$ for the values of $a$ and $b$. 2. **Write the formula and substitute values:** The equation is

1. The problem is to graph the system of inequalities: $$\begin{cases} 2x - 5y > 3 \\ 3x - 7y \leq 4 \\ 5x + 3y \geq 1 \\ x - 6y \geq 2 \end{cases}$$

1. We are given a system of inequalities: $$\begin{cases} 2x - 5y > 3 \\ 3x - 7y \leq 4 \\ 5x + 3y \geq 1 \\ x - 6y \geq 2 \end{cases}$$

1. The problem is to graph the relationship between variables $x$ and $y$. 2. To graph $y$ as a function of $x$, we need a specific equation or relationship between $x$ and $y$. Si

1. The problem is to graph the inequality $2x - 5y > 3$. 2. Rewrite the inequality in slope-intercept form $y < \frac{2}{5}x - \frac{3}{5}$.

1. **Problem 30:** A traveler goes 8 km upstream and then returns downstream. The stream speed is 4 km/h, and the upstream trip took 20 minutes longer than the downstream trip. Fin

1. **State the problem:** Simplify the expression $1+1-1+4@-1$. 2. **Identify the operations:** The expression contains addition (+), subtraction (-), and an unknown symbol '@'. Si

1. State the problem: Compute the sum $\sum_{i=1}^{n} i^2$ for positive integer $n$.\n2. Goal and formula: We will prove the closed form\n$$\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}

1. The problem is to understand and simplify the expression $\frac{a}{b}$. 2. This is a fraction where $a$ is the numerator and $b$ is the denominator.

1. **State the problem:** Solve the equation $4r + 30 = 2$ for $r$. 2. **Write the formula and rules:** This is a linear equation. To solve for $r$, isolate $r$ by performing inver

1. The problem asks to find the values of variables $a$ and $b$. 2. To solve for $a$ and $b$, we need an equation or system of equations involving these variables.

1. **Stating the problem:** Caitlin has 140 coins initially. She adds 15% more coins during the year. 2. **Formula used:** To find the number of new coins added, use the percentage

1. The problem asks to justify the general rule for solving algebraic expressions or equations. 2. A common general rule in algebra is the distributive property: $$a(b+c) = ab + ac

1. **Stating the problem:** We need to find the amount of tax added to a computer that costs 968 when a tax rate of 16.5% is applied. 2. **Formula used:** The amount of tax can be

1. The problem states: 10% of a number is 60, and we need to find 100% of that number, which is the number itself. 2. Recall that 10% means \( \frac{10}{100} = 0.1 \) of the number

1. **Problem Statement:** Find the nth term of the quadratic sequence defined by the terms 2, 6, 12, 20, 30, ... 2. **Understanding Quadratic Sequences:** A quadratic sequence has

1. Enunciamo il problema: risolvere l'equazione $2x + 3 = 7$. 2. La formula base per risolvere equazioni lineari è isolare la variabile $x$ su un lato dell'equazione.

1. نبدأ بكتابة المعادلتين المعطاة ونهدف إلى حذف أحد المتغيرين للحصول على معادلة واحدة تحتوي على متغير واحد فقط. 2. لنفترض أن المعادلتين هما:

1. **State the problem:** We are given two functions:

1. Risolviamo l'equazione data. 2. Applichiamo le regole algebriche necessarie per isolare la variabile.

1. সমস্যাটি হলো: ক) $R = 1 + x^2 + x^4$ কে উপাদানে ৪ দ্বারা ভাগ করতে হবে।