🧮 algebra

1. **State the problem:** We are given that $\frac{2}{5}$ of Mabel's stamps equals $\frac{4}{9}$ of Nancy's stamps. We need to find the ratio of the number of Mabel's stamps to Nan

1. **Problem:** Find the values of $x$ and $y$ given the equations: $$x^2 = 7t$$

1. **Stating the problem:** We want to simplify or understand the expression $$|x_{i-1} + 4|4|x_{i-1}|$$.

1. **State the problem:** Find the domain and range of the function $$y = \sqrt[3]{x} + \frac{1}{\sqrt{x-1}}.$$\n\n2. **Understand the function components:**\n- The cube root funct

1. **State the problem:** Solve the equation $$\sqrt{y} + 5 \times \sqrt{x} - 3 = 4$$ for $y$ in terms of $x$. 2. **Rewrite the equation:** Add 3 to both sides to isolate the squar

1. **State the problem:** Find the values of $x$ and $y$ such that $$x^2 - 7x + 9iy = iy + 20i - 12.$$ 2. **Rewrite the equation:** Group real and imaginary parts separately:

1. **Problem:** Find the product of matrices $A$ and $B$ where $$A=\begin{pmatrix}2 & -3 & 4 \\ 1 & -6 & 3 \\ 0 & 5 & -9\end{pmatrix},\quad B=\begin{pmatrix}1 & 3 & -5 \\ 7 & -3 &

1. **Problem Statement:** Find the product of matrices $A$ and $B$ where $$A=\begin{pmatrix}2 & -3 & 4 \\ 1 & -6 & 3 \\ 0 & 5 & -9\end{pmatrix},\quad B=\begin{pmatrix}1 & 3 & -5 \\

1. The problem asks to find $f(-x)$ and $-f(-x)$ for each function $f(x)$, then compare with $f(x)$ to determine if the function is even, odd, or neither. 2. Recall the definitions

1. The problem is to factor the expression <span style='color:#8b4dff; font-weight:600; text-shadow:0 0 4px rgba(139,77,255,0.5)'>$x^2 - 4$</span>. 2. This is a difference of squar

1. **State the problem:** We are given the function $f(x) = x^2 - 4$ and need to analyze it. 2. **Formula and rules:** This is a quadratic function of the form $f(x) = ax^2 + bx +

1. The problem is to factor the expression <span style='color:blue'>$x^2 - 4$</span>. 2. Recognize that this is a difference of squares, which follows the formula <span style='colo

1. **State the problem:** We are given the equations of the sides of a triangle: <span style='color:blue'>$x+2y=4$</span>, <span style='color:blue'>$2x-y=3$</span>, and <span style

1. Let's start by stating the problem: Determine if the function <span style='color:blue'>$K(x) = \frac{5^x}{\sqrt{3} \cdot 6^x}$</span> is exponential. 2. Recall that an exponenti

1. The problem is to factor the quadratic expression <span style='color:blue'>$x^2 + 6x + 5$</span>. 2. We use the factoring formula for quadratics: <span style='color:blue'>$ax^2

1. Masalah yang diberikan adalah menentukan bentuk pecahan biasa paling sederhana dari bilangan desimal periodik 0,2045454… 2. Bilangan ini memiliki bagian non-periodik 0,20 dan ba

1. <span style='color:purple'>We are asked to factor the quadratic expression</span> <span style='color:blue'>x^2 + 6x + 5</span>. 2. <span style='color:purple'>The general form of

1. **Problem Statement:** We have a polynomial $g(x)$ such that when divided by $(x+1)$, $(x-1)$, and $(x-2)$, the remainders are 1, $\frac{1}{2}$, and $\frac{2}{3}$ respectively.

1. **Stating the problem:** Factor the quadratic expression $x^2 + 6x + 5$. 2. **Formula and rules:** To factor a quadratic expression of the form $ax^2 + bx + c$, we look for two

1. The problem states that $x=3$ is a solution to the quadratic equation $$x^2 + kx + 15 = 0.$$ We need to find the value of $k$. 2. Since $x=3$ is a root, it must satisfy the equa

1. **State the problem:** Solve or analyze the equation $$x^2 - y^2 = \tan(xy)$$ where $x$ and $y$ are variables. 2. **Understand the equation:** This is a transcendental equation