🧮 algebra

1. **Problem statement:** We are given the number of cupcakes sold from Monday to Friday and some information about Saturday and Sunday sales. We need to find: (a) The total cupcak

1. **Problem Statement:** We need to graph the function $f(x) = \sqrt{x}$ and discuss its continuity and domain. 2. **Function Definition:** The square root function is defined as

1. **State the problem:** We are given the profit function for a skateboard manufacturer as $$P(x) = 30x - 0.3x^2 - 250$$ where $x$ is the number of skateboards sold. We need to es

1. **Stating the problems:** We have multiple problems:

1. **Problem statement:** A furniture store sells 40 chairs per week at a price of 80 each. For every 5 price reduction, they sell 5 more chairs. The cost per chair is 30. We want

1. **State the problem:** We need to find the value of $x$ from the equation $$\left(\frac{\frac{x}{0.888}}{12}\right) \times 110\% = 20.$$\n\n2. **Rewrite the equation:** Recall t

1. The problem is to simplify the fraction $\frac{40}{11}$. 2. The formula for simplifying fractions is to divide the numerator and denominator by their greatest common divisor (GC

1. **State the problem:** We are given two functions: $$r(x) = 2x + 1$$

1. **State the problem:** We are given two functions: $$q(x) = -3x + 2$$

1. **Problem Statement:** Determine the end behavior of the graphs of the given polynomial functions. 2. **Key Concept:** The end behavior of a polynomial function depends on the d

1. **State the problem:** We are given the rational function $$r(x) = \frac{2x^2 + 10x - 12}{x^2 + x - 6}$$ and we want to analyze it. 2. **Factor numerator and denominator:** To s

1. **Stating the problem:** We have "Y" shaped figures with numbers at each branch end and a number at the base or origin. The top-left examples show how to relate the numbers on t

1. **State the problem:** Simplify and factor the expression $x^2 - x - (a^2 + 5a + 6)$. 2. **Rewrite the expression:** Distribute the negative sign inside the parentheses:

1. The problem involves interpreting Y-shaped branching diagrams with labeled branches. 2. Each branch label represents a value or fraction associated with that branch.

1. The problem states the equation $65 = 98$. 2. This is a simple equality statement.

1. **State the problem:** We are given the rational function $$r(x) = \frac{4x^2}{x^2 - 2x - 3}$$ and we want to analyze its properties such as domain, intercepts, and asymptotes.

1. **Problem Statement:** Simplify the given expressions using index laws. 2. **Index Laws Used:**

1. Problem: Calculate the value of $\frac{8!}{2! \times 6!}$. Formula: $\binom{n}{r} = \frac{n!}{r!(n-r)!}$, here $\frac{8!}{2!6!}$ is a combination $\binom{8}{2}$.

1. **State the problem:** Simplify the expression $$\frac{2xz^2 + 7x^2z}{12xz^2 + 36x^2z - 120x^3} \div \frac{12z^2 + 42xz}{x^3z + 5x^4}$$. 2. **Rewrite division as multiplication

1. **State the problem:** Simplify the expression $$\frac{3n^{4} - 12n^{2}x^{2}}{8nx^{2} - 4n^{2}x} \cdot \frac{-8x}{n^{2} - 2nx - 8x^{2}}$$

1. **State the problem:** Evaluate the expression $3a + 2b - 6c$ when $a = 10$, $b = 9$, and $c = 4$. 2. **Write the expression:**