🧮 algebra

1. **State the problem:** Solve the system of equations: $$5x - 2y = 23$$

1. **Stating the problem:** Given the ratios $x : y = 4 : 6$ and $2 : x = 1 : 2$, find the value of $y$. 2. **Understanding the ratios:** The ratio $x : y = 4 : 6$ means $\frac{x}{

1. **Stating the problem:** Given the ratios $x : y = 4 : 6$ and $2 : x = 1 : 2$, find the value of $y$. 2. **Understanding the ratios:** The ratio $x : y = 4 : 6$ means $\frac{x}{

1. **State the problem:** Solve the system of equations: $$\frac{x+2}{6} - 3\frac{y+2}{2} = 1$$

1. **Problem Statement:** Use the numbers 1.45 and 1.14 in a mathematical context. Since the user did not specify an operation, let's explore basic operations: addition, subtractio

1. The problem asks to describe the translation of the graph of the parent function for each given function $g(x)$. 2. Recall that for a function $g(x) = f(x - h) + k$, the graph o

1. **State the problem:** Solve for $w$ in the equation $$|2w + 2| - 25 = -5.$$\n\n2. **Isolate the absolute value expression:** Add 25 to both sides to get $$|2w + 2| = 20.$$\n\n3

1. Nyatakan masalah: Ungkapkan $$\frac{5}{x+5} - \frac{5x}{x^2 + 6x + 5}$$ sebagai satu pecahan tunggal dalam bentuk termudah. 2. Faktor penyebut kedua: $$x^2 + 6x + 5 = (x+1)(x+5)

1. **State the problem:** Solve for $x$ in the equation $$3^{x-7} = 17^{-6x}$$ and round the answer to the nearest thousandth. 2. **Recall the formula and rules:** When solving equ

1. Problem: Find the rate of change in the amount of water in the pool from 8:00 A.M. to 11:00 A.M. 2. Given: Initial amount at 8:00 A.M. is 2000 gallons, amount at 11:00 A.M. is 5

1. **State the problem:** We are given two functions: $$f(x) = \frac{x}{x-3}$$

1. **State the problem:** Mr. Hernandez's pool had 2000 gallons of water at 8:00 A.M. and 500 gallons at 11:00 A.M. We need to find the rate of change in the amount of water in gal

1. The problem is to analyze the function $y = e^{2.8x}$. 2. The general form of an exponential function is $y = ae^{bx}$ where $a$ and $b$ are constants.

1. **State the problem:** Solve for $x$ in the equation $$3^{x^2} - 19x + 1 = 27^{5 - 8x}.$$ 2. **Rewrite the equation using the same base:** Note that $27 = 3^3$, so we can write

1. **State the problem:** Solve for $x$ in the equation $$3x^{2} - 19x + 1 = 27^{5 - 8x}.$$\n\n2. **Rewrite the right side:** Note that $27 = 3^{3}$, so $$27^{5 - 8x} = (3^{3})^{5

1. **Problem Statement:** Find the approximate and exact number of days between the given date ranges. 2. **Important Notes:**

1. **State the problem:** We are given the formula for simple interest: $$P = H(1 + r t)$$ where $P$ is the total amount, $H$ is the principal, $r$ is the interest rate per time pe

1. **State the problem:** Find the value of $r$ such that the line passing through the points $(-5, 2)$ and $(3, r)$ has a slope of $0$. 2. **Recall the slope formula:** The slope

1. **Problem Statement:** Determine which polynomial function has the end behavior: as $x \to -\infty$, $y \to \infty$ and as $x \to \infty$, $y \to -\infty$. 2. **Key Concept:** T

1. The problem asks to explain the three different types of solutions obtained from questions 3, 4, and 12 using Desmos 3D. 2. In algebra and equations, solutions can be categorize

1. Let's clarify the problem: We have an expression where $6y$ is also in the denominator. 2. Suppose the expression is $\frac{3x}{6y}$ or similar, where both numerator and denomin