🧮 algebra

1. **State the problem:** We need to find which expressions are equivalent to $$-6z^3 (2z + 10z^2)$$. 2. **Use the distributive property:** Multiply $$-6z^3$$ by each term inside t

1. **State the problem:** Simplify the expression $$\frac{x^2 - 15x + 54}{x^2 - 14x + 48} \div \frac{1}{x - 8}$$. 2. **Rewrite the division as multiplication:** Dividing by a fract

1. **State the problem:** Simplify the expression \( \frac{6x + 27}{18x^2 + 36x} \div \frac{16x + 72}{2x + 4} \). 2. **Rewrite the division as multiplication by the reciprocal:**

1. **Problem statement:** Simplify each algebraic expression by applying the Distributive Property and combining like terms. 2. **Formula and rules:**

1. **Problem Statement:** Simplify each algebraic expression by combining like terms. 2. **Important Rules:**

1. **State the problem:** We need to subtract the fractions $\frac{7}{8}$ and $\frac{3}{4}$.\n\n2. **Formula and rules:** To subtract fractions, they must have a common denominator

1. The problem is to add the fractions $\frac{11}{12}$ and $\frac{1}{3}$.\n\n2. To add fractions, they must have a common denominator. The denominators here are 12 and 3.\n\n3. Fin

1. **State the problem:** We have a software priced at $20 each with 300 students willing to buy it. If the price increases by $5, 30 fewer students will buy it. We want to find th

1. **State the problem:** Solve the compound inequality $$-71 \leq 7x - 1 \leq 69$$. 2. **Add 1 to all parts of the inequality** to isolate the term with $x$:

1. **Stating the problem:** Solve the compound inequality \(2 - 2m > 16\) or \(9 + 8m \geq 73\). 2. **Solve the first inequality:**

1. **Problem:** Calculate the value of $8.75 \times 10^3$. 2. **Formula:** Multiplying a decimal by a power of ten shifts the decimal point to the right by the exponent number.

1. **State the problem:** A rubber ball is dropped from a height of 12 meters. Each bounce reaches \( \frac{2}{3} \) of the previous height. We want to find how many times the ball

1. **State the problem:** Simplify the expression $$(-6)^5 \times (-6)^4 \div (-6)^7$$ and express the answer as an integer. 2. **Recall the exponent rules:** When multiplying powe

1. **State the problem:** Evaluate $(-2)^3 \times (-2)^2$ and express the answer as an integer. 2. **Recall the property of exponents with the same base:** When multiplying powers

1. **State the problem:** We are given the power function $$P(I) = -5I^2 + 100I$$ where $I$ is the current in amperes. We need to find the current $I$ that maximizes the power and

1. **State the problem:** We want to simplify the expression $5\left(\frac{2}{3}\right) \div 4$. 2. **Recall the division rule:** Dividing by a number is the same as multiplying by

1. **State the problem:** Solve the system of equations using the substitution method: $$\begin{cases}-5x - 8y = 17 \\ 2x - 7y = -17\end{cases}$$

1. **State the problem:** Ms. Tanaka saved 72 on a table that was marked 16% off. We need to find the original price $t$ of the table. 2. **Write the equation:** The savings is 16%

1. **State the problem:** We have a Fibonacci-type sequence where the second term is 5 and the fifth term is 23. We need to find the first term. 2. **Recall the Fibonacci-type sequ

1. **State the problem:** Simplify the expression $$\frac{-128n^{11} + 36n^{21} - 20n^{16}}{8n^{15}}$$ and express it in the form $$16n^x + Bn^y + Cn$$ where $B$ and $C$ are ration

1. **State the problem:** We are given a sequence with terms $a_1=7$, $a_2=35$, $a_3=175$, and $a_4=875$. We need to find a function $a_n$ that represents this sequence. 2. **Ident