🧮 algebra

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

1. **State the problem:** We need to find a function $f(n)$ that models the geometric sequence given by the terms $9, 3, 1, \frac{1}{3}, \frac{1}{9}$ for $n=1,2,3,4,5$ respectively

1. **State the problem:** Determine if the sequence $2, 12, 72, 432, \ldots$ is geometric and if so, find the common ratio. 2. **Recall the definition:** A sequence is geometric if

1. **State the problem:** We have a 3x3 magic square where every row, column, and diagonal sums to the same total. We need to find the values of $A$ and $B$ using the numbers provi

1. **State the problem:** Find the difference between the highest and lowest values in the list: $-4.3, -1.54, -6.819, -9.04, -12.3, -11$. 2. **Identify the highest and lowest valu

1. The problem is to expand the expression $ (a+b)^2 $. 2. The formula for the square of a binomial is:

1. **State the problem:** A painter uses 1.2 liters of paint to cover 1 square meter of wall. We need to find how many square meters he can cover with 12 liters of paint. 2. **Form