🧮 algebra

1. **State the problems:** - Problem 28: Simplify $$\frac{(2x^{9})^{3}(x^{2}y)^{-2}}{x^{3}y^{0}}$$

1. **State the problem:** Solve the quadratic equation $$x^2 - 8x = -15$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the equation $$\frac{1}{1 - x} + \frac{1}{1 + \sqrt{x}} = \frac{1}{1 - \sqrt{x}}$$ for $x$. 2. **Identify the domain:** Since $\sqrt{x}$ appears, $x

1. **Stating the problem:** We are given a piecewise linear graph with two line segments. The first segment has an open circle at $(-7,5)$ and passes through $(-10,-9)$. The second

1. Let's start by stating the problem: we want to find the value of $X$ such that $X=3$. 2. The equation is already given as $X=3$, which means $X$ is equal to 3.

1. **State the problem:** Solve the quadratic equation $$5x^2 - 13x - 6 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $

1. **State the problem:** Solve the equation $$\sqrt{2x + 5} + 2\sqrt{x + 6} = 5$$ for $x$. 2. **Isolate one of the square root terms:** Let's isolate $$\sqrt{2x + 5}$$:

1. **State the problem:** We need to find which quadratic function has solutions $x=8$ and $x=-5$. 2. **Recall the factored form of a quadratic:** If the roots are $r_1$ and $r_2$,

1. The problem is to simplify the expression $$(\sqrt{12} + \sqrt{z})(\sqrt{12} - \sqrt{z})$$ assuming all variables are positive. 2. This expression is a product of conjugates, wh

1. **State the problem:** Simplify the expression $$4 \sqrt[3]{81x} - 3 \sqrt[3]{192x}$$ assuming all variables are positive. 2. **Recall the cube root properties:**

1. **State the problem:** Find the greatest common factor (GCF) of 40 and 32 and express the difference $40 - 32$ as a product involving the GCF. 2. **Find the GCF:**

1. The problem asks to find the discriminant of the quadratic equation selected in question #1, which is \(y = x^2 - 13x + 40\). 2. The quadratic formula is \(ax^2 + bx + c = 0\),

1. **State the problem:** Find the greatest common factor (GCF) of 12 and 30, then use it to factor the sum $12 + 30$.

1. The problem is to fill in the blanks and simplify the given expression or equation. Since no specific expression is provided, let's consider a general approach to simplifying al

1. Convert the percent 16 17/27 to decimal and fraction. 2. Convert the percent 53 13/21% to decimal and fraction.

1. **State the problem:** Simplify the expression $$\frac{18 \sqrt[3]{135 a^{8}}}{6 \sqrt[3]{5 a^{2}}}$$. 2. **Write the expression clearly:** $$\frac{18 \sqrt[3]{135 a^{8}}}{6 \sq

1. **Problem Statement:** John is selling ski packages at a price of 1400 with 16 expected buyers. For every 50 decrease in price, 2 more students buy the package. We need to find:

1. **State the problem:** Solve the equation $$4 = 3 + |3 - \frac{1}{3} \times 2|$$. 2. **Understand the absolute value:** The absolute value $|x|$ represents the distance of $x$ f

1. **State the problem:** Solve the equation $$|-2.3q + 2.3| = -3.3$$. 2. **Recall the property of absolute values:** The absolute value of any real number is always non-negative,

1. **State the problem:** Find the equation of the line passing through points $(-2, -3)$ and $(0, 1)$ in the form $y = mx + c$. 2. **Formula used:** The slope $m$ of a line throug

1. **State the problem:** Simplify the expression $$(4^2 \times 4^3)^2 - (5^4 \div 5^2)^2$$ 2. **Use exponent rules:**