🧮 algebra

1. **Problem Statement:** Suppose a square and an equilateral triangle have the same perimeter. Each side of the equilateral triangle is 6 centimeters longer than each side of the

1. Diberikan persamaan kuadrat $$3x^2 - 2x + 10 = 0$$ dengan akar-akar $$x_1$$ dan $$x_2$$. 2. Kita gunakan rumus jumlah dan hasil kali akar persamaan kuadrat:

1. **State the problem:** We need to find the rate of change in cost per visitor for a tour given two data points: 3 visitors cost 31 and 10 visitors cost 80. 2. **Formula used:**

1. **State the problem:** Solve the equation $$\frac{2x - 4}{3} = \frac{4x - 2}{5}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by th

1. **Problem 1:** Two airplanes leave St. Louis at the same time and fly in opposite directions. One travels at 500 km/h, the other at 600 km/h. Find the time $t$ when they are 192

1. **State the problem:** We need to find which two fractions from the list $\frac{1}{4}$, $\frac{6}{23}$, $\frac{2}{7}$, $\frac{3}{5}$, and $\frac{9}{8}$ multiply together to give

1. نبدأ بحل التعبير $5\sqrt{0.0003}$. 2. نعرف أن الجذر التربيعي لـ $0.0003$ يمكن كتابته كـ $\sqrt{3 \times 10^{-4}}$.

1. **State the problem:** Solve for $x \in \mathbb{R}$ in the equation $$2^{3x+1} - 3 \cdot 2^{2x} + 2^{x+1} = 2^x.$$\n\n2. **Rewrite the equation using properties of exponents:**

1. **State the problem:** Solve the equation $$2^{3x+1} - 3 \cdot 2^{2x} + 2^{x+1} = 2x$$ for $x$. 2. **Rewrite terms using properties of exponents:**

1. **State the problem:** Simplify the expression $$\frac{3q^5rt^2}{24q^7t}$$. 2. **Write the expression:** $$\frac{3q^5rt^2}{24q^7t}$$.

1. **Problem Statement:** We are given three fractions and need to verify or understand the relationships between their terms. 2. **Fraction 1:** $\frac{24 \text{ inches}}{2 \text{

1. The problem asks to write ratios and identify them as part-to-whole or part-to-part. 2. Ratio 1: Number of games won to number of games lost.

1. **State the problem:** Simplify and analyze the polynomial expression $x^3 - 5x^2 + 7x - 2$. 2. **Recall the polynomial form:** A cubic polynomial is generally written as $ax^3

1. **State the problem:** We are given two scenarios with scatter plots: Adriana's distance traveled over time and Angelina's calories burned rowing over time. We want to understan

1. **State the problem:** We need to evaluate the function $$f(x) = \frac{x^3 - 5x^2 + 7x - 2}{x - 2}$$ at the values $x = 1.9, 1.99, 1.999, 2.001, 2.01, 2.1$. 2. **Understand the

1. **Problem Statement:** We are given two tables showing ratios of paint quantities (white paint to red paint, and white paint to purple paint) and need to find the missing values

1. **Problem:** Given 10 yellow marbles correspond to 45 green marbles, find the number of yellow marbles when there are 9 green marbles. **Formula:** Use the ratio and proportion

1. **State the problem:** We want to determine if the expression $$\frac{(x^3 - 5x)^2 + 7x - 2}{x - 2}$$ can be factored and simplified by canceling out common factors. 2. **Rewrit

1. **Problem 1: Write 17/3 as a mixed number in simplest form.** 2. To convert an improper fraction to a mixed number, divide the numerator by the denominator.

1. **State the problem:** Simplify the expression $5 \frac{2}{5} + \frac{1}{10}$ and understand how it relates to $5 -$ (which seems incomplete). 2. **Convert mixed number to impro

1. **Problem 1: Find angle $n$ given that $n$ and $47^\circ$ are adjacent angles on a straight line.** 2. Angles on a straight line add up to $180^\circ$. This is called the supple