🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $3.8 = \frac{x}{7}$.\n\n2. **Formula and rule:** To solve for $x$ when it is divided by 7, multiply both sides of the equati

1. **State the problem:** Solve for $x$ in the equation $3.8 = \frac{x}{7}$.\n\n2. **Formula and rule:** To solve for $x$, multiply both sides of the equation by 7 to isolate $x$.\

1. ປະກາດບົດບັນຫາ: ຈົດແຕ່ລິມມີອຸ່ມນີ້ ກ. 3x^2 + 5x - 4 = 0 2. ໃຊ້ສູດສຳລັບສູດຄວາມສົມດຸນຄະນິຍາມສະກັດ (quadratic formula):

1. The problem is to understand what happens when the denominators in fractions are not the same. 2. When adding or subtracting fractions, the denominators must be the same to comb

1. **Problem statement:** Solve the first system of linear equations: $$\begin{cases} x + y = 3 \\ 2x + 3y = 7 \end{cases}$$

1. The problem is to simplify and find the value of the expression $$\frac{\sqrt{a \sqrt{a \sqrt{a}}}}{\sqrt[3]{a^{5/2} a}}$$. 2. First, rewrite the expression inside the radicals

1. The problem asks to compare two variables, $\alpha$ and $\beta$, in different situations. 2. To compare $\alpha$ and $\beta$, we need to understand the context or the mathematic

1. **Problem 1: Addition of Integers** The temperature starts at $-7^\circ C$ and changes by $+5^\circ C$, $-3^\circ C$, and $+8^\circ C$ over three hours.

1. **State the problem:** Simplify the expression $\frac{65}{x}$ or understand its meaning. 2. **Formula and rules:** The expression $\frac{65}{x}$ represents division where 65 is

1. **State the problem:** Solve the two-step equation $$65x + 18 = 31$$. 2. **Understand the goal:** We want to isolate $x$ on one side of the equation to find its value.

1. সমস্যাটি হলো: 44% কর্মী কফি পছন্দ করে, 28% চা পছন্দ করে, এবং 40 জন কর্মী কেউ পছন্দ করে না। মোট কর্মী সংখ্যা কত? 2. আমরা জানি, মোট কর্মী সংখ্যা $N$ হলে, কফি পছন্দকারীর সংখ্যা $0.

1. **State the problem:** Solve the system of linear equations: $$4x + y = -114$$

1. **Problem 12:** Identify the linear system modeled by the balance scales. Given: Each small square represents 2 kg.

1. **State the problem:** Solve the quadratic equation $12x^2 = 25$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero.

1. **State the problem:** Determine if the given pairs of functions are inverses. 2. **Recall the rule:** Two functions $f$ and $g$ are inverses if and only if $f(g(x)) = x$ and $g

1. The problem asks for the sum of the items from 1 to 12. 2. We use the formula for the sum of an arithmetic series: $$S_n = \frac{n}{2}(a_1 + a_n)$$ where $n$ is the number of te

1. We are asked to find the inverse of each given function and then graph both the function and its inverse. 2. To find the inverse of a function $f(x)$, we swap $x$ and $y$ in the

1. The problem is to multiply the expressions $3s^2$ and $8s^5$. 2. The formula for multiplying terms with the same base is $a^m \times a^n = a^{m+n}$.

1. Stating the problem: We need to find the principal amount given the interest earned, rate, and time. 2. Formula for simple interest: $$I = P \times r \times t$$ where $I$ is int

1. Let's state the problem: We want to understand why in the quadratic formula, the product of the denominators of the roots equals $a$ when solving $ax^2 + bx + c = 0$. 2. The qua

1. **Problem:** Given the quadratic equation $ax^2 + \alpha x + c = 0$ with roots in the ratio $p:q$, prove that $$\sqrt{\frac{p}{q}} + \sqrt{\frac{c}{a}} = 0.$$ 2. **Step 1: Expre