🧮 algebra

1. **State the problem:** Solve the equation $6x + 9 = 2x - 5$ for $x$. 2. **Write down the equation:**

1. **State the problem:** We are given the function $$f(x) = \frac{1}{2} \cdot 4^x + 3$$ and asked to find the value of its inverse function $$f^{-1}$$ at $$x = 5$$. 2. **Recall th

1. **State the problem:** Simplify the expression $2 \log m - \log n - 4 \log p$ into a single logarithm. 2. **Recall logarithm properties:**

1. The problem presents three separate expressions: - $5w + 2y - v - x$

1. **State the problem:** Solve the equation $2v^2 = 18$ given $v = 3$. 2. **Recall the formula:** The equation is $2v^2 = 18$.

1. **State the problem:** We are given three tables of $x$ and $y$ values and asked which tables represent functions and how to tell. 2. **Recall the definition of a function:** A

1. **State the problem:** We need to add the numbers $3.8 \times 10^{22}$ and $3.8 \times 10^{23}$ and express the result in standard form. 2. **Recall the rule for adding numbers

1. Add and Simplify the polynomials: $ (3h^2 - 6h) + (5h + 9h^2 - 7) $ 2. Combine like terms by grouping powers of $h$:

1. The problem is to divide the fractions $\frac{2}{5}$ by $\frac{3}{4}$.\n\n2. The formula for dividing fractions is: \n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d

1. Problem: Calculate $\frac{1}{9} + \frac{4}{9}$. 2. Since the denominators are the same, add the numerators:

1. The problem asks us to evaluate the quadratic function $f(x) = -4x^2 - 11$ at $x = -6$. 2. The formula for evaluating a function at a given value is to substitute the value into

1. **Problem 8: Find the removable point of discontinuity (RPOD) for** $f(x) = \frac{x+1}{x^2 - 1}$. 2. **Recall the formula and rules:**

1. **State the problem:** Find the x-intercept(s) of the function $$f(x) = \frac{x+2}{x^2 - 4}$$. 2. **Recall the rule for x-intercepts:** The x-intercept(s) occur where the functi

1. **State the problem:** Find the x-intercept of the function $$f(x) = \frac{x + 2}{x^2 - 4}$$. 2. **Recall the rule for x-intercepts:** The x-intercept occurs where the function

1. **State the problem:** Multiply and simplify the expression assuming $u \geq 0$: $$\sqrt{6u^5} \cdot \sqrt{3u^3} \div \sqrt{3^2} \cdot 2 \cdot (u^2)^4$$

1. **Problem 8: Find the R P O D (Removable Point of Discontinuity) for $f(x) = \frac{x+1}{x^2 - 1}$.** 2. The function is a rational function where the denominator is $x^2 - 1 = (

1. The problem is to understand why 0.0002 might be considered wrong or to clarify its value. 2. The number 0.0002 in decimal form means $2 \times 10^{-4}$.

1. **Problem 7: Find the horizontal asymptote of** $f(x) = \frac{3x^2 + 2x}{x^2 - x - 6}$. 2. **Recall the rule for horizontal asymptotes:**

1. The problem asks: "What goes in the boxes?" which suggests filling in missing values or expressions in a mathematical context. 2. Without additional context or a specific equati

1. **State the problem:** We have three systems of linear equations A, B, and C. We want to find the transformations between these systems. 2. **Analyze System A to System B:**

1. **Problem:** Find the vertical asymptote(s) for the function $$f(x) = \frac{x+2}{x^2 - x - 6}$$. 2. **Recall:** Vertical asymptotes occur where the denominator is zero and the n