🧮 algebra

1. The problem asks which equation represents a proportional relationship. 2. A proportional relationship between two variables $x$ and $y$ means $y$ is directly proportional to $x

1. **State the problem:** We have line L with equation $3x + 2y = 17$, point A at $(0,2)$, and line M perpendicular to L passing through A. We need to find the area of triangle ABC

1. The problem is to analyze the behavior of the exponential function shown in the graph. 2. From the description, the function approaches a horizontal asymptote at $y=5$ as $x \to

1. **State the problem:** We analyze the features of the function $$f(x) = -\left(\frac{1}{2}\right)^x + 5$$ including its asymptote, range, domain, monotonicity, and end behavior.

1. We beginnen met het probleem: we zoeken het grootste getal $n$ zodat elk paar opeenvolgende getallen $(n, n+1)$ volkomen kwadraten zijn. 2. Een volkomen kwadraat is een getal da

1. The problem is to simplify the square root of 98, written as $\sqrt{98}$.\n\n2. Recall the rule for simplifying square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. We

1. The problem is to find the square root of 49. 2. The square root of a number $x$ is a value $y$ such that $$y^2 = x$$.

1. **Problem:** Expand and simplify the expression $a (2x + 1)^2$. 2. **Formula and rules:** To expand a binomial squared, use the formula $ (A + B)^2 = A^2 + 2AB + B^2 $.

1. Stating the problem: Find the integer value of $$\frac{\sqrt{90}}{\sqrt{10}}$$. 2. Use the property of square roots that $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$.

1. **State the problem:** We are given a piecewise linear graph of the function $f(x)$ and asked to determine which of the given equations are true by reading values from the graph

1. **State the problem:** A consumer buys orange juice cartons of 3 liters and 1.5 liters.

1. **Problem Statement:** A consumer buys orange juice in 3-Liter cartons and 1.5-Liter cartons.

1. **State the problem:** Solve the equation $$x^2 - 49 = 0$$ by square rooting. 2. **Rewrite the equation:** Add 49 to both sides to isolate the squared term:

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

1. **State the problem:** Find the solutions of the equation $$2 - x^2 = -x$$ by graphing. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero

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