🧮 algebra

1. **State the problem:** Find the smallest number $n$ such that $$169^{80} \leq n^{120}.$$\n\n2. **Use the inequality and properties of exponents:** We want to solve for $n$ in $$

1. **State the problem:** Find the smallest number $n$ such that $160^n > 80$. 2. **Formula and approach:** To solve inequalities involving exponents, we use logarithms. The inequa

1. Masalah yang diberikan adalah menghitung nilai dari ekspresi $$RM150 \times 30^0 \div 0$$. 2. Kita tahu bahwa aturan pangkat menyatakan bahwa $$a^0 = 1$$ untuk setiap bilangan $

1. The problem is to find the equation of the line passing through the points $(-3, 4)$ and $(2, -1)$. 2. The formula to find the slope $m$ of a line passing through two points $(x

1. Problem: Solve the system of equations: $$\begin{cases} x + y = 10 \\ x - y = 2 \end{cases}$$

1. The problem is to understand the function $f(x) = 2^x$ with domain $\{1, 2, 3, 4\}$ and find its range and graph points. 2. The formula for an exponential function is $f(x) = a^

1. **State the problem:** We are given two equations: $$8p - 9 = 6$$

1. **State the problem:** Expand the expression $$36y - 49(x + 1)(x + 1)$$. 2. **Recall the formula:** The expression involves expanding a binomial squared: $$(x + 1)^2 = x^2 + 2x

1. Nyatakan masalah: Cari titik persilangan bagi garis lurus $y=-3x$ dan $y=3x-6$ menggunakan kaedah graf. 2. Titik persilangan berlaku apabila nilai $y$ bagi kedua-dua garis adala

1. The problem is to understand the meaning or solve for "pqr" as given. 2. Since "pqr" is a sequence of letters without any mathematical operators or context, it is not a standard

1. The problem is unclear as only the letter "i" was provided. 2. "i" typically represents the imaginary unit in algebra, defined as $i^2 = -1$.

1. The problem asks to solve the expression $$P(1 + \frac{R}{100})^T$$ which represents the amount after $T$ years with an initial principal $P$ and an annual growth rate $R$ perce

1. **State the problem:** Find the area of an ellipse with semi-major axis $a$ and semi-minor axis $b$ without using polar coordinates. 2. **Recall the formula for an ellipse:** Th

1. **State the problem:** Simplify the expression $$(4a^3 b^6 c^{-2})^{-3}$$. 2. **Recall the power of a product rule:** $$(xyz)^n = x^n y^n z^n$$ and the power of a power rule: $$

1. The problem is to solve the inequality $$4x^2 - 5x - 6 > 0$$. 2. To solve quadratic inequalities, first find the roots of the corresponding quadratic equation $$4x^2 - 5x - 6 =

1. **Problem:** Solve the equation $|x + 2| = 4$. 2. **Formula and rules:** The absolute value equation $|A| = B$ means $A = B$ or $A = -B$ if $B \geq 0$.

1. **State the problem:** We have the function $$y = \frac{1}{x - 5} + 2$$.

1. **State the problem:** We are given the vector equation $(x - y, 2x - y) = (1, 6)$ and need to find the values of $x$ and $y$. 2. **Set up the system of equations:** Since the v

1. **Problem statement:** Given two equal ordered pairs, find the values of $x$ and $y$. 2. **Understanding ordered pairs:** Two ordered pairs $(a,b)$ and $(c,d)$ are equal if and

1. The problem asks for the line in the form $y = mx + c$ that should be drawn on the graph to solve the quadratic equation $x^2 - 7x + 4 = 0$. 2. To solve $x^2 - 7x + 4 = 0$ graph

1. **بيان المسألة:** لدينا العبارة $$z = x(3x + 20) + 25$$ ونريد إثبات أنها تساوي $$z = (3x + 5)^2 - (6x^2 + 10x)$$ ثم تحليل العبارة إلى جداء عاملين، وحساب القيمة الفعلية للعبارة ع