🧮 algebra

1. **State the problem:** We know that 40% of a Fermium-256 sample has decayed, and 53 grams remain. We need to find the original mass of the sample. 2. **Understand the problem:**

1. **State the problem:** Solve the system of linear equations: $$-\frac{1}{3}x + \frac{1}{2}y = 14$$

1. The problem is to show that two expressions are equal by solving one and demonstrating it results in the other, and vice versa. 2. To prove two expressions are equal, we can sol

1. **State the problem:** Simplify the expression $$x^{\frac{2}{5}} \left(x^{\frac{6}{5}} - x^{\frac{7}{2}}\right)$$ and express the answer with positive exponents. 2. **Recall the

1. **State the problem:** Solve for $x$ in the equation $$\frac{6.11 + x}{5} = 152.4.$$\n\n2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by 5 to e

1. **State the problem:** We have two systems of linear equations and need to determine the nature of their solutions (no solution, unique solution, or infinitely many solutions).

1. **State the problem:** We are given two purchases with amounts of trail mix and jelly beans and their total costs. We want to find the cost per pound of trail mix ($x$) and jell

1. **State the problem:** We need to find the cost of coating a rectangular driveway that measures 15 feet by 20 feet, with a coating cost of 3.00 per square foot. 2. **Formula use

1. **State the problem:** We have two cars, Ahmad's and Greg's, with gas tanks decreasing as miles are driven. Ahmad's starts with about 26 gallons and runs out at 360 miles. Greg'

1. **State the problem:** We need to find the length in hours of two workout plans, Plan A and Plan B, given the number of clients and total training hours on Monday and Tuesday. 2

1. **State the problem:** Two mechanics worked on a car. The first mechanic charges 115 per hour, the second charges 80 per hour. Together, they worked 20 hours and charged a total

1. The problem is to solve the given algebraic expression or equation (not specified by the user). 2. Since the user requests to keep the work simple and provide the answer, we wil

1. **Problem statement:** A local business's sales increased from 120 units at Week 0 to 195 units at Week 3. We need to find the sales growth rate (slope), predict sales at Week 7

1. Soal: Diketahui $P(x) = 3x^3 - 4x^2 + 2x - 1$. Hitung nilai $P(2)$. 2. Gunakan substitusi nilai $x=2$ ke dalam fungsi $P(x)$.

1. Soal: Diketahui P(x) = 3x^3 - 4x^2 + 2x - 1. Hitung nilai P(2). 2. Rumus yang digunakan adalah substitusi nilai x ke dalam fungsi polinomial:

1. **Problem statement:** A rectangular garden is to be built using 100 meters of fencing. One side is along a wall, so fencing is needed only for the other three sides. We want to

1. **State the problem:** We are given the function $f(x) = 2x^3 - 3x^2 - 12x + 4$ and we want to analyze it. 2. **Formula and rules:** For a cubic function $f(x) = ax^3 + bx^2 + c

1. **State the problem:** Simplify the expression $$\left(2x - 4x^2 - 12x + 1\right) \cdot 2x + 4x^2 - 12x + 1 \cdot 2x + 4x^2 - 12x + 1.$$\n\n2. **Rewrite the expression clearly:*

1. The problem asks for the formula of $x$. 2. To find the formula for $x$, we need an equation or context relating $x$ to other variables or constants.

1. **Énoncé du problème :** Simplifier l'expression $$\frac{\sqrt[3]{2} \times \sqrt{6} \times \sqrt[5]{8}}{\sqrt[3]{4}}$$. 2. **Formules et règles importantes :**

1. Énoncé du problème : Simplifier le nombre $$\frac{\sqrt[3]{2} \times \sqrt{6} \times \sqrt[5]{\sqrt[3]{8}}}{\sqrt[3]{4}}$$. 2. Rappel des règles :