🧮 algebra

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:

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

1. **State the problem:** Solve the equation $$\frac{x + 6}{x - 5} = \frac{5}{4}$$ for $x$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross pr

1. **State the problem:** Solve the equation $$\frac{4}{x+6} = \frac{5}{4x-8}$$ for $x$ and simplify the answer fully. 2. **Use the cross-multiplication formula:** For equations of

1. **State the problem:** Simplify the expression $5x(x-1)-4(x+1)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Convert the equation $2x - 3y = 5$ to slope-intercept form $y = mx + b$. 2. **Recall slope-intercept form:** The slope-intercept form is $y = mx + b$, whe

1. Stating the problem: Calculate the value of the expression $$\frac{\left(\frac{3}{7} + \frac{1}{2}\right)^2 \cdot \left(2 - \frac{1}{3}\right)^2 - 1}{\left(\frac{1}{6} - 1\right

1. Planteamos el problema: Tenemos la función $f(x) = \frac{2x}{2-x}$ y queremos encontrar la función compuesta $f(f(x))$. 2. Recordemos que la función compuesta $f(f(x))$ signific