🧮 algebra

1. The problem asks for the equation of the vertical asymptote of the given graph. 2. A vertical asymptote occurs where the function approaches infinity or negative infinity as $x$

1. **State the problem:** Solve for $x$ in the equation $x = x$. 2. **Analyze the equation:** The equation $x = x$ is an identity, meaning it is true for all values of $x$.

1. **State the problem:** Solve the equation $h(b+11) = (b+11) + 14$ for $h(b+11)$. 2. **Understand the equation:** The equation states that the function $h$ evaluated at $b+11$ eq

1. **Problem:** Determine if the conjecture "All perfect squares are divisible by 2" is true or false. 2. **Explanation:** A perfect square is a number that can be expressed as $n^

1. The problem is to express the functions and their compositions in Maple syntax. 2. Maple uses := for function definitions and standard mathematical notation.

1. **Problem:** Determine if the conjecture "All perfect squares are divisible by 2" is true or false. 2. **Explanation:** A perfect square is a number that can be expressed as $n^

1. **State the problem:** We need to find the slope of the line on the graph that shows the cost of transporting sugar versus the weight of sugar in tons. 2. **Recall the formula f

1. **Stating the problem:** Factor the given algebraic expression(s). 2. **General formula and rules:** Factoring involves rewriting an expression as a product of simpler expressio

1. **Stating the problem:** We have a function machine that takes inputs $15y$, $15w$, and $15p$ and outputs $y$, $w$, and $p$ respectively. 2. **Understanding the function:** The

1. We are asked to factor the quadratic expression $$15n^2 - 27n - 6$$. 2. The general form of a quadratic is $$ax^2 + bx + c$$. To factor, we look for two numbers that multiply to

1. The problem shows a function machine with inputs $15y$, $15w$, and $15p$ on the left and outputs $y$, $w$, and $p$ on the right. 2. We want to find the function that completes t

1. Stating the problem: Solve the quadratic equation $$0 = x^2 - 6x + 9$$. 2. Formula and rules: The quadratic equation is in standard form $$ax^2 + bx + c = 0$$ where $$a=1$$, $$b

1. Vamos resolver um problema de álgebra envolvendo uma equação do primeiro grau. 2. Suponha que o problema seja: "Resolva a equação $2x + 3 = 11$."

1. **State the problem:** Solve the equation $2x + 10 = 4x - 10$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $2x + 20 = 4x - 10$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Factor the trinomial $$15n^2 - 27n - 6$$ completely. 2. **Recall the factoring formula:** For a quadratic trinomial $$ax^2 + bx + c$$, we look for two num

1. **State the problem:** Solve the system of linear equations: $$x = 16 - 4y$$

1. **State the problem:** Simplify the expression $\frac{x+2}{x^2-4}$. 2. **Recall the formula and rules:** The denominator is a difference of squares, which factors as $a^2 - b^2

1. The problem states that $y$ varies directly as $x$, which means the relationship can be written as $y = kx$ where $k$ is a constant. 2. We are given that $y = 21$ when $x = 6$.

1. **State the problem:** Solve the equation $ (x-2)^2 - 9 = 0 $ for $ x $. 2. **Use the formula:** Recognize this as a quadratic equation in the form $ (a)^2 - b^2 = 0 $, which ca

1. The problem asks to find the function rule for $g(x)$, which is a transformation of $f(x) = |x|$. 2. The general form for transformations of the absolute value function is: