🧮 algebra

1. **State the problem:** Find the solutions of the equation $$2 - x^2 = -x$$ by graphing. 2. **Rewrite the equation:** To find the solutions, we want to find the values of $x$ whe

1. **State the problem:** Solve the quadratic equation $$2r^2 + r - 3 = 0$$ by factoring. 2. **Recall the factoring method:** For a quadratic equation $$ax^2 + bx + c = 0$$, we loo

1. **Problem statement:** We are given exponential growth and decay rates for human and black bear populations in Florida from 1953 to 1993.

1. **State the problem:** Solve the linear equation $$17.95x + 24 = 18.95x + 18$$ to find the value of $x$ where the two expressions are equal. 2. **Write the equation:**

1. **State the problem:** We are given the population size formula $$P = 1200 \cdot (0.85)^{12t}$$ where $t$ is in years. We need to find the monthly percent decay rate of the popu

1. The problem asks to classify the equation $$24x + 1 = 24x + 68$$ as having one solution, no solution, or infinitely many solutions. 2. Start by subtracting $$24x$$ from both sid

1. **State the problem:** We are given two lines, $L_1$ and $L_2$, where $L_1$ has equation $y=3x-2$ and $L_2$ passes through the point $(0,7)$. The lines are perpendicular. We nee

1. The problem is to find the value of $8^{\frac{1}{3}}$. 2. The expression $a^{\frac{1}{n}}$ means the $n$th root of $a$. So, $8^{\frac{1}{3}}$ means the cube root of 8.

1. Let's start by stating the problem: Understanding the discriminant in quadratic equations and how it helps determine the nature of the roots. 2. A quadratic equation is generall

1. The problem asks to find equations of lines that intersect the parabola $y = x^2 + 3x + 2$ a specific number of times: 0, 1, and 2 times. 2. To find the number of intersections

1. The user asks to show an equation to represent "it", but no specific context or problem is given. 2. Since no details are provided, I will present a general example of a linear

1. **State the problem:** Julia has run $\frac{5}{6}$ of her weekly goal by Friday and runs 6.5 miles on Saturday. The total distance run this week is 51.5 miles. We need to find h

1. **State the problem:** Solve the quadratic equation $x^2 - 4x + 1 = 0$. 2. **Formula used:** The quadratic formula is given by

1. The problem is to solve the number 51, which is interpreted as finding the prime factorization of 51. 2. The formula or method used is to find the prime factors by dividing the

1. **State the problem:** Express $\sqrt{7} + 2\sqrt{6}$ in the form $\sqrt{x} \pm \sqrt{y}$. 2. **Recall the technique:** We want to find $x$ and $y$ such that

1. The problem asks how much money Lin has saved if she has saved a certain percentage of her goal of 20. 2. The formula to find the amount saved is:

1. Evaluate the expression $(-7)^2 \cdot (-7)^2$. Step 1: Recall the rule for powers: $a^m \cdot a^n = a^{m+n}$.

1. **State the problem:** The area of a rectangle is 14 square units, with side lengths $x$ and $y$. Given values for $x$, find $y$. 2. **Formula:** Area $A$ of a rectangle is give

1. **State the problem:** Simplify the expression $\left(\frac{5}{9}x + \frac{1}{8}\right) + \left(\frac{4}{7}x - \frac{1}{8}\right)$. 2. **Write the expression:**

1. **State the problem:** Simplify the expression $$\left(\frac{5}{9}x + \frac{1}{8}\right) + \left(\frac{7}{12}x - \frac{1}{8}\right)$$. 2. **Write the expression without parenthe

1. **State the problem:** Simplify the expression $$\frac{f^5 g^2 h}{f^0 g^4 h^{-1}}$$. 2. **Recall the rules:**