🧮 algebra

1. Let's revisit how we found $x = 3$ as a root of the quadratic equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1

1. Let's solve a random algebra problem: Find the roots of the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. The formula to find roots of a quadratic equation $$ax^2 + bx + c = 0$$ i

1. The problem states: Solve the equation $$\log_4 x + \log_2 y = 5$$ given the conditions from the previous system. 2. Recall the change of base formula and properties of logarith

1. The problem is to express the equation $\frac{1}{x-2} - \frac{2}{x+5} = \frac{3}{x+1}$ in the form $ax^2 + bx + c = 0$. 2. To do this, we first find a common denominator for the

1. **State the problem:** We are given the exponential population model $$A=886.3e^{0.019t}$$ where $A$ is the population in millions and $t$ is the number of years after 2003. We

1. **State the problem:** Solve the logarithmic equation $$\log_3 (x + 5) = 4$$ and find the exact solution(s), rejecting any values not in the domain. 2. **Recall the definition a

1. **Problem:** Solve for $x$ in the equation $\log_2(x + 3) = 5$. 2. **Formula and rules:** Recall that $\log_b(a) = c$ means $b^c = a$. Here, $b=2$, $a = x+3$, and $c=5$.

1. The problem asks us to evaluate $\log_6 4^8$ without a calculator. 2. Recall the logarithm power rule: $\log_b (a^n) = n \log_b a$.

1. **State the problem:** Determine if the relation given by the set of ordered pairs \((2, 3), (-18, 9), (2, -9), (0, 15)\) is a function. 2. **Recall the definition of a function

1. **State the problem:** We are given a relation as a set of ordered pairs from the table: $$\{(12, -20), (-12, 4), (0, 20), (0, 4)\}$$

1. **State the problem:** We are given the set of ordered pairs \((16, -18), (1, 18), (16, 10), (1, 10)\) and asked whether this relation is a function. 2. **Recall the definition

1. The problem asks whether the given relation is a function. 2. A relation is a function if every input $x$ has exactly one output $y$.

1. **State the problem:** Determine if the relation consisting of the points (19, 18), (19, -8), and (-12, 18) is a function. 2. **Recall the definition of a function:** A relation

1. **State the problem:** Determine if the given relation is a function. 2. **Recall the definition of a function:** A relation is a function if every input (x-value) corresponds t

1. The problem asks whether the given relation \{(-3, 14), (20, 2), (20, 9)\} is a function. 2. A relation is a function if every input (x-value) corresponds to exactly one output

1. The problem is to use the quadratic formula to factor a quadratic expression. 2. Let's consider the quadratic equation $2x^2 - 4x - 6 = 0$.

1. The problem is to understand if the quadratic formula can be used for factoring quadratic expressions. 2. The quadratic formula is primarily used to find the roots (solutions) o

1. The problem is to find the solutions of a quadratic equation of the form $ax^2 + bx + c = 0$. 2. The quadratic formula used to solve this is:

1. Let's start by stating the problem: You want to know about factoring and the different ways to factor expressions. 2. Factoring is the process of breaking down an expression int

1. **State the problem:** Determine if the given relation \{(-20,0), (19,18), (19,7), (19,8)\} is a function. 2. **Recall the definition of a function:** A relation is a function i

1. The problem asks whether the given relation is a function. 2. A relation is a function if every input $x$ corresponds to exactly one output $y$.