🧮 algebra

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:**

1. **Problem:** The opposite of a number is tripled and then decreased by 7. The result is 3 greater than twice the number. Find the number. Step 1: Let the number be $x$.

1. **Problem:** The opposite of a number is tripled and then decreased by 7. The result is 3 greater than twice the number. Find the number. Step 1: Let the number be $x$.

1. **State the problem:** Solve the equation $$4^{x+1} + 4^x = 320$$ for $x$. 2. **Recall the properties of exponents:**

1. **State the problem:** Solve the equation $$4^{x^2} = 8^x$$ for $x$. 2. **Rewrite the bases as powers of 2:**

1. (a) Express $16x^2 - 24x + 10$ in the form $(4x + a)^2 + b$. Start with the expression:

1. **State the problem:** We have the graph of $y=f(x)$ formed by lines AB and BC, and the graph of $y=g(x)$ formed by lines A'B' and B'C' which is obtained by applying two transfo

1. **State the problem:** Solve the system of linear equations using the elimination method: $$\begin{cases} 4x - y = 1 \\ 2x + 3y = 11 \end{cases}$$

1. **State the problem:** Mason owns 48 books in total. Hanna owns 6 times as many non-fiction books as Mason. We need to find how many books Hanna owns in total. 2. **Analyze Maso

1. We are given two systems of linear equations to solve for $x$ and $y$. 2. First system: