🧮 algebra

1. **State the problem:** Solve the system of equations:

1. **Solve the quadratic equation** $m^2 - 5m - 14 = 0$. 2. The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$.

1. **Problem:** Determine if the set defined by $\{(x,y): x = y^2\}$ is a function or just a relation. 2. **Recall:** A relation is a function if for every $x$ there is exactly one

1. **State the problem:** We are given a piecewise function defined as $g(x) = 4$ for $x \geq 3$. We need to evaluate $g(x)$ at $x = -3, 3, -2, 0, 4$.\n\n2. **Understand the functi

1. **State the problem:** We have a bar of total length $50$ units split into two parts: a darker left part labeled $C$ and a lighter right part labeled $D$. The right lighter port

1. **State the problem:** We need to find the unknown numbers A, B, C, and D based on the given unit relationships and equations. 2. **Given information:**

1. **State the problem:** Factor the expression $$16x^2 - 121$$ if possible. 2. **Recognize the formula:** This expression is a difference of squares, which follows the formula $$a

1. **State the problem:** Factor the expression $$49n^2 - 81$$. 2. **Recognize the formula:** This is a difference of squares since $$49n^2 = (7n)^2$$ and $$81 = 9^2$$.

1. The problem asks whether a shortcut for factoring trinomials applies when the coefficient of the variable squared term is one. 2. The standard form of a trinomial is $$ax^2 + bx

1. **State the problem:** Factor the quadratic expression $$x^2 - x - 56$$. 2. **Recall the factoring formula:** For a quadratic trinomial $$ax^2 + bx + c$$, we look for two number

1. **State the problem:** Factor the trinomial $$x^2 + 25x + 144$$ if possible. 2. **Recall the factoring formula:** For a trinomial of the form $$x^2 + bx + c$$, we look for two n

1. **State the problem:** We have a substance undergoing continuous exponential decay. The initial amount is $5800$ kg, and after $18$ hours, $1856$ kg remains. We want to find the

1. **State the problem:** We are given three averages: - $x$ is the average of $m$ and 9.

1. **State the problem:** We need to find the fourth term in the expansion of the binomial expression $$ (3a + b)^7 $$. 2. **Recall the binomial theorem formula:** The expansion of

1. **State the problem:** Simplify the expression $$\sqrt{49a^4b^{40}}$$ assuming all variables are positive real numbers. 2. **Recall the formula:** For any positive real number $

1. **State the problem:** Simplify the cube root $$\sqrt[3]{-8x^{12}y^{9}}$$ assuming all variables represent positive real numbers. 2. **Recall the cube root properties:**

1. **State the problem:** We need to find the slope of a line passing through the points approximately $(-2, 10)$ and $(5, -10)$. 2. **Recall the slope formula:** The slope $m$ of

1. **State the problem:** We need to find the walking rates of Jasmine and Mason in miles per hour and determine whose rate is greater and by how much.

1. **State the problem:** We know the store sells 8 stickers for 3 dollars. We want to analyze the statements about the rate of change, slope, unit rate, and constant of proportion

1. **State the problem:** We need to find the solution set for the system of inequalities: $$2h + 5 > 31$$

1. **State the problem:** We need to find the solution set for the inequality $$-3q + 11 \geq 38$$ or $$-2q + 39 < 45$$ and determine which graph represents this solution. 2. **Sol