🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $3x = 243$. 2. **Understand the equation:** The equation means $3$ multiplied by $x$ equals $243$.

1. **State the problem:** We are given an arithmetic progression (A.P.) with terms $T_7 = 23$, $T_n = 43$, and $T_{2n} = 91$. We need to find the first term $a$, the common differe

1. **State the problem:** Solve the inequality $\frac{4}{x} \geq x$. 2. **Rewrite the inequality:** Multiply both sides by $x$, but remember to consider the sign of $x$ because it

1. **Problem Statement:** Given an arithmetic progression (A.P.) with terms $T_7 = 23$, $T_n = 43$, and $T_{2n} = 91$, find the first term $a$, the common difference $d$, and the t

1. **Problem:** Calculate the value of $20P_3$. 2. **Formula:** The permutation formula is given by

1. **State the problem:** There are 364 first-grade students in total at Park Elementary School. There are 26 more girls than boys. We need to find out how many girls there are. 2.

1. Diberikan fungsi parabola $y = 3x^2 - 30x + 77$. Kita diminta menentukan letak dan jenis titik ekstrimnya. 2. Titik ekstrim parabola terjadi pada titik stasioner, yaitu saat tur

1. **State the problem:** Calculate the value of $-24 + 33$. 2. **Formula and rules:** Addition of integers involves combining their values. When adding a negative and a positive n

1. **State the problem:** We need to find the length and width of a tennis court given that the perimeter is 228 feet and the length is 6 feet longer than twice the width. 2. **Set

1. **State the problem:** We want to analyze the function $$y = \sqrt[3]{x^5}$$. 2. **Rewrite the function using exponents:** The cube root can be expressed as a fractional exponen

1. **State the problem:** Calculate the product of the two binomials $(-1 - 11)$ and $(13 - 5)$. 2. **Simplify each binomial:**

1. **State the problem:** Solve for $w$ in the equation $$-4(w+1) = -24$$. 2. **Use the distributive property:** Multiply $-4$ by each term inside the parentheses:

1. **State the problem:** Solve for $h$ in the equation $$\frac{h}{6} - 1 = -3$$. 2. **Add 1 to both sides** to isolate the term with $h$:

1. **State the problem:** Subtract the rational expressions $$\frac{9x^2 + 3}{14x^2 - 9} - \frac{-3x^2 + 11}{14x^2 - 9}$$. 2. **Identify the common denominator:** Both expressions

1. The problem is to simplify the function $f(x) = x + 2 - 2\sqrt{x - 1}$.\n\n2. We start by recognizing that the function contains a square root term $\sqrt{x - 1}$. The domain of

1. Menyatakan masalah: Selesaikan persamaan kuadrat $2x^2 - 3x - 5 = 0$.

1. **State the problem:** We are given the system of equations: $$x + 13 + y = 0$$

1. **State the problem:** We are given two linear equations and a value for $x$: $$x + 13 + y = 0$$

1. **State the problem:** Solve the equation $X + 13 + y = 0$ for one variable in terms of the other. 2. **Rewrite the equation:** The equation is $X + 13 + y = 0$.

1. The problem is to solve the quadratic equation $2x^2 - 5x + 3 = 0$. 2. We use the quadratic formula to solve equations of the form $ax^2 + bx + c = 0$:

1. مسئله را بیان می‌کنیم: تابع داده شده است $f(x) = a - 2 \sin^2\left(\frac{\pi}{b} x\right)$ و چهارضلعی $OABC$ مربع است. باید مقدار $f\left(\frac{1}{3}\right)$ را پیدا کنیم. 2. چو