🧮 algebra

1. **State the problem:** Two cyclists start simultaneously from two cities 120 km apart and ride towards each other. They meet after 2 hours and 40 minutes. One cyclist covers 1 k

1. **State the problem:** We have an initial value $C_0 = 12000$ and a compound growth formula $C_{n+1} = 1.0062 \times C_n$ with rate $R = 1.0062$.

1. **Problem statement:** A man spends 12.5% of his money. After spending 75% of the remainder, he has 175 left. We need to find the original amount of money he had. 2. **Define va

1. **State the problem:** We have a sequence defined by the recurrence relation $$C_{n+1} = 1.0062 \times C_n$$ with initial value $$C_0 = 12000$$. 2. **Formula used:** This is a g

1. **Stating the problem:** We are given a tree diagram representing the distribution of money in percentages: 12.5% and 87.5%, where 87.5% further splits into 75% and 25%. We also

1. **Stating the problem:** We are given a number pattern: 73085, ( ), ( ), 73100, ( ). We need to find the missing numbers in the sequence. 2. **Understanding the pattern:** The k

1. The problem is to find the missing numbers in the sequence: 73085, ( ), ( ), 73100, ( ). 2. We observe the known numbers 73085 and 73100 with missing numbers in between.

1. Stating the problem: Simplify the fraction $\frac{2}{2}$. 2. Formula and rules: When simplifying fractions, divide numerator and denominator by their greatest common divisor (GC

1. The problem is to express $\sqrt{16}$ as an exponent. 2. Recall that the square root of a number can be written as an exponent with a fractional power: $\sqrt{a} = a^{\frac{1}{2

1. **State the problem:** Simplify the expression $\frac{x}{x}$. 2. **Recall the rule:** For any nonzero value of $x$, $\frac{x}{x} = 1$ because any number divided by itself equals

1. **State the problem:** We start with 15 wind turbines and add 1 turbine each month. We need to complete the table for 12, 24, and 48 months and write an expression for the numbe

1. **State the problem:** We have an arithmetic sequence with terms $u_3 = 12$ and $u_{10} = 40$. The common difference is $d$. We need to write two equations involving $u_1$ (the

1. **State the problem:** We are given three equations:

1. **Problem Statement:** We are given that each Division I school offers 12 softball scholarships per year. We need to complete the table for the number of scholarships given the

1. **State the problem:** Simplify the expression $\frac{x}{x}$. 2. **Recall the rule:** For any nonzero value of $x$, $\frac{x}{x} = 1$ because any number divided by itself equals

1. The problem is to solve the equation Q = 17. 2. Since Q is given as 17, the solution is straightforward: Q equals 17.

1. **State the problem:** We are given a system of three equations with three variables $z$, $y$, and $xe$: $$\begin{cases} Z + y + xe = 1 \\ -1 = z + ye + xe \\ 8 = z + 6y + xe \e

1. **State the problem:** We are given the equation $$\frac{P_1 V_1 T_2}{T_1} = \frac{P_2 V_2}{T_2}$$ and asked to solve for $T_2$. 2. **Write down the equation:**

1. **State the problem:** Simplify the expression $\frac{2x^2 - 8}{4x}$. 2. **Formula and rules:** To simplify a rational expression, factor numerator and denominator and cancel co

1. **State the problem:** Simplify the expression $\frac{2x^2 - 8}{4x}$. 2. **Formula and rules:** When simplifying rational expressions, factor numerator and denominator and cance

1. **State the problem:** We are given the sequence formula $u_n = 5 + 4(n-1)$ and need to determine if 116 is a term in this sequence. 2. **Write the formula:** The general term o