🧮 algebra

1. **State the problem:** Simplify the expression $$x^2\sqrt{x^2}$$ assuming $$x > 0$$. 2. **Recall the properties:** The square root of $$x^2$$ is $$|x|$$, but since $$x > 0$$, $$

1. The problem asks to compare the y-intercepts and rates of change of two functions. 2. The first function is given as $y = 6x - 1$.

1. **State the problem:** Compare the y-intercepts and rates of change (slopes) of the line given by the equation $y = 1.2x + 0.4$ and the line passing through the points $(3,4)$ a

1. **State the problem:** Find the slope of the line passing through the points $(3, 8)$ and $(6, 7)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $

1. **State the problem:** Find the slope of the line passing through the points $(1, 9)$ and $(8, 8)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $

1. **Problem stated:** Make a one-page cheat sheet from the pages about **slope, slope-intercept form, graphing linear equations, functions, and relations**. 2. **Key formulas to k

1. **State the problem:** Simplify the expression $(x+9)(x-8)$. 2. **Use the distributive property (FOIL method) for binomials:**

1. **State the problem:** Simplify the expression $$\frac{32x}{x^2 + x - 72} \div \frac{16x - 8}{2x^2 - 17x + 8}$$

1. **State the problem:** Solve the equation $x^2 - 32 = -4x$ for all values of $x$ by completing the square. 2. **Rewrite the equation:** Move all terms to one side to set the equ

1. **State the problem:** Solve the quadratic equation $$x^2 - 12x + 35 = 0$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an equation o

1. **State the problem:** Solve the quadratic equation $$x^2 + 2x = 35$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an equation of the

1. **State the problem:** We want to rewrite the quadratic equation $$-6x^2 - 582 = -60x$$ in the form $$(x + a)^2 = b$$ by completing the square. 2. **Rewrite the equation:** Move

1. **State the problem:** Complete the square for the quadratic equation $$-6x^2 - 582 = -60x$$ and write it in the form $$(x + a)^2 = b$$. 2. **Rewrite the equation:** Move all te

1. **State the problem:** We want to rewrite the equation $$-3x^2 + 49x = -5x + 183$$ in the form $$(x + a)^2 = b$$ by completing the square. 2. **Rearrange the equation:** Move al

1. **State the problem:** We want to rewrite the quadratic equation $$-3x^2 + 6x = -321$$ in the form $$(x + a)^2 = b$$ by completing the square. 2. **Rewrite the equation:** First

1. **State the problem:** Find the greatest common factor (GCF) of the monomials $35x^3y^2$, $10x^4y$, and $5x^5y^3$. 2. **Recall the formula and rules:**

1. **State the problem:** Find the greatest common factor (GCF) of the monomials $10a^3$, $12a^2$, and $14a$. 2. **Recall the formula and rules:** The GCF of monomials is found by

1. **State the problem:** Solve the system of equations: $$\begin{cases}-9a + b + 8c = -18 \\ -5a + 5b + 8c = -10 \\ -2a + 8b + 9c = 1 \end{cases}$$

1. **State the problem:** We need to find which system of equations has the solution $(1, 3, -1)$ for variables $(x, y, z)$. 2. **Recall the method:** To check if $(1, 3, -1)$ is a

1. **State the problem:** Solve the equation $X + (X + 170) = 200$ for $X$. 2. **Write the equation:**

1. **State the problem:** Solve the system of equations given: Top-right: $$n^2 + 4n\left(-\frac{4}{2}\right)^2 = +21\left(\frac{4}{2}\right)^2$$