🧮 algebra

1. **State the problem:** Mike biked 5 miles on Tuesday, 3 miles on Wednesday, and twice as many miles on Saturday as Wednesday. He hopes to bike a total of 25 miles for the week.

1. **State the problem:** Solve the quadratic equation $x^2 + 6x - 5 = 0$ for $x$. 2. **Formula used:** The quadratic formula is used to solve equations of the form $ax^2 + bx + c

1. **State the problem:** The price of a train ticket increases from 754 to 799.24. We need to find the percentage increase. 2. **Formula:** The percentage increase is given by

1. **State the problem:** We need to find the percentage increase when the price of a flat rises from 112588 to 150867.92. 2. **Formula for percentage increase:**

1. **Stating the problem:** We have a circle divided into five segments with numbers 5, 10, ?, 50, and 122. We need to find the missing number represented by "?". 2. **Analyzing th

1. The problem is to find the value of 8 squared. 2. The formula for squaring a number is $a^2 = a \times a$.

1. **State the problem:** Rationalize the denominator of the fraction $$\frac{1}{\sqrt[3]{5} + \sqrt[3]{7} + 2}$$ where the denominator has two cube roots and one rational part. 2.

1. The problem is to graph the piecewise function: $$y=\begin{cases}2x & 0 \leq x \leq 4 \\ 10 & 4 < x \leq 8\end{cases}$$

1. The problem is to simplify the fraction $\frac{4}{9}$ and express it as a decimal. 2. To convert a fraction to a decimal, divide the numerator by the denominator.

1. **State the problem:** We want to understand why the linear system $$\begin{cases} 3x + y = 10 \\ 2x - 2y = 8 \end{cases}$$

1. Let's understand why we multiply by $-2$ in certain problems. 2. Often, multiplying by $-2$ is used to eliminate a variable or to simplify an equation.

1. **State the problem:** We need to solve the system of linear equations graphically: $$y = x + 1$$

1. **State the problem:** We need to find the ratio of gold to silver to bronze medals won by Switzerland in the 2010 Winter Olympic Games. 2. **Identify the values:** From the tab

1. **State the problem:** Solve the inequality $$\frac{8}{3} u < -12$$ for $u$. 2. **Formula and rules:** To solve inequalities involving multiplication or division by a negative n

1. The problem is to solve the inequality $$-5 > \frac{y}{3}$$ for $y$. 2. To isolate $y$, we multiply both sides of the inequality by 3. Since 3 is positive, the inequality direct

1. **State the problem:** We are given two functions $f(x) = 2x + 4$ and $g(x) = 3x^2$. We need to find the function operation $(f + g)(x)$ and then determine the domain of the res

1. **State the problem:** We are given two functions $f(x) = 2x + 4$ and $g(x) = 3x^2$. We need to find the function operation $(f+g)(x)$ and then determine the domain of the resul

1. **State the problem:** We are given the function $f(x,y) = x^2 y + \cos(x)$ and need to understand or analyze it. 2. **Identify the components:** The function has two variables

1. **State the problem:** Solve the quadratic equation $$x^2 + 18x + 62 = 0$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an equation o

1. **State the problem:** Solve the quadratic equation $$x^2 - 14x + 38 = 0$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an equation o

1. **State the problem:** There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them. We need to find how many kids own their own instruments.