🧮 algebra

1. Given function: $f(x) = x^2 + 6x + 5$ 2. Domain: $(-\infty, \infty)$

1. **State the question:** You asked if the domain represents the $x$ values and the range represents the $y$ values for the function $f(x) = x^2 + 6x + 5$. 2. **Explanation:** Yes

1. **State the problem:** Solve the equation $$2\left(\frac{1}{8}\right) = 32^{n-1}$$ for $n$. 2. **Rewrite the equation:** Simplify the left side:

1. **State the problem:** Find the domain and range of the function $$f(x) = x^2 + 6x + 5$$. 2. **Domain:** The domain of a polynomial function like this is all real numbers becaus

1. **State the problem:** Simplify the expression $$\frac{6ab - 3a^3}{21a^2 - 9ab^2}$$. 2. **Rewrite the expression:** The numerator is $6ab - 3a^3$ and the denominator is $21a^2 -

1. **State the problem:** We are given two quadratic functions: $$y = -2x^2 - 8x - 8$$

1. **State the problem:** Simplify the expression $$\frac{x^2-5x-14}{x^2-9x+14}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor both numerator and

1. **State the problem:** Factor the expression $x^2 - 4$. 2. **Important rule:** When you see something like $a^2 - b^2$, it can be factored as $(a - b)(a + b)$.

1. **State the problem:** We need to find the value(s) of $x$ for which the expression $$\frac{5x+3}{6x(x+1)}$$ is undefined. 2. **Recall the rule:** A rational expression is undef

1. **State the problem:** We want to break down the expression $x^2 - 4$ into simpler parts multiplied together. 2. **What is difference of squares?** When you have something like

1. **State the problem:** Factor the quadratic expression $x^2 - 4$. 2. **Recall the formula:** This is a difference of squares, which follows the rule:

1. **State the problem:** Given the equation $\log y = 3\log 2 + \log 3 - \log 6$, find the value of $y$. 2. **Recall logarithm properties:**

1. **State the problem:** Factor the expression $x^2 - 9$. 2. **Recall the formula:** This is a difference of squares, which follows the rule:

1. **State the problem:** Given the equation $\log y = 3\log + \log 3 - \log 6$, find the value of $y$. 2. **Clarify the expression:** The term $3\log$ is incomplete. Assuming it m

1. **State the problem:** Simplify the expression given by $\log y = 3\log x + \log 3 - \log 6$. 2. **Recall logarithm rules:**

1. The problem is to understand how to express or interpret $n^2$. 2. The notation $n^2$ means $n$ raised to the power of 2, which is also called "n squared".

1. **State the problem:** Simplify the expression $\frac{n \times n + n}{n} = 10$ and solve for $n$. 2. **Write the expression clearly:** The numerator is $n \times n + n$, which i

1. **State the problem:** Simplify the expression $$\sqrt{45} - \frac{1}{\sqrt{5}}$$. 2. **Recall the formulas and rules:**

1. **State the problem:** Factor the quadratic expression $x^2 - 4$. 2. **Recall the formula:** This expression is a difference of squares, which follows the rule:

1. The problem is to analyze the function $f(x) = x^2 - 4$. 2. This is a quadratic function in the form $ax^2 + bx + c$ where $a=1$, $b=0$, and $c=-4$.

1. Let's start by stating the problem: factoring is the process of breaking down an expression into simpler expressions (factors) that, when multiplied together, give the original