🧮 algebra

1. The problem is to find the formula for a given mathematical relationship or function. 2. A formula is an equation that expresses a relationship between variables.

1. **State the problem:** Factor the expression $$2x^2 - 72y^2$$. 2. **Identify the common factor:** Both terms have a common factor of 2.

1. **State the problem:** We are given the function $c(t) = 28 + 4 \sin\left(\frac{\pi}{2} t\right)$ and we want to understand its behavior. 2. **Formula and explanation:** This is

1. The problem asks to find $f(-4)$ for the function $f(x) = -2x + 5$ and then to find the value of $p$ given $f(x) = px - 8$ and $f(4) = 20$. 2. For the first part, substitute $x

1. Masalah ini meminta kita menentukan banyak batang korek api yang diperlukan untuk membuat pola segitiga ke-7. 2. Dari pola yang diberikan, kita lihat jumlah batang korek api unt

1. **Problem Statement:** Convert the polar coordinate point (3, 45°) to rectangular coordinates and plot it. 2. **Formula:** To convert from polar to rectangular coordinates, use:

1. Arithmetic Sequence (AS): An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.

1. Let's start by stating the problem: We need to find the domain, range, and zeros of a function. However, the specific function is not provided, so I'll explain the general appro

1. **State the problem:** We are given the quadratic function $y = x^2 - 6x + 10$ and the equation $1 = x - 3$. We want to analyze the function and solve for $x$ in the equation. 2

1. Let's start with Arithmetic Sequences (AS). An arithmetic sequence is a list of numbers with a constant difference between consecutive terms. 2. The formula for the $n$th term o

1. Let's start with Arithmetic Sequence (AS). An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference, called the commo

1. The problem is to graph the function $y = a^x$ where $a > 0$ and $a \neq 1$. 2. The general form of an exponential function is $y = a^x$, where $a$ is the base and $x$ is the ex

1. **State the problem:** Solve the inequality $$-38d - 57 \geq -19d + 76$$ for $d$. 2. **Isolate the variable terms:** Add $38d$ to both sides to move all $d$ terms to the right s

1. **Stating the problem:** Simplify the expression $$\left( \frac{a^2 b^{-3}}{a^{-1} b^{\frac{3}{2}}} \right)^{\frac{3}{2}}$$. 2. **Recall the rules:**

1. **Problem statement:** The first, seventh, and twenty-fifth terms of an arithmetic progression (A.P.) form the first three consecutive terms of a geometric progression (G.P.). T

1. **State the problem:** We are given a rectangle ABCD with sides DC and AD defined as functions of $x$: $$DC = \frac{5}{x^2 - 25}$$

1. Diberikan fungsi linear $f(x) = 6 - 10x$ dan translasi $T = \left(\frac{10}{3}\right)$. 2. Translasi fungsi linear biasanya berarti menggeser grafik fungsi secara horizontal ata

1. The problem is to understand and apply the Factor and Remainder Theorem. 2. The Factor Theorem states that if a polynomial $f(x)$ is divided by $(x - a)$, then the remainder is

1. The problem is to understand algebraic systems focusing on semigroups, monoids, and groups, including their properties, examples, and homomorphisms. 2. **Semigroups:** A semigro

1. **Problem Statement:** Understand algebraic systems focusing on semigroups, monoids, and groups, including their properties, examples, and homomorphisms. 2. **Algebraic Systems:

1. The problem is to simplify the expressions $\frac{\sqrt{2907}}{51}$ and $\frac{\sqrt{1728}}{18}$.\n\n2. Recall the property of square roots and division: $$\frac{\sqrt{a}}{b} =