🧮 algebra

1. **State the problem:** We are given two functions $f(x) = \frac{x+4}{x}$ and $g(x) = x+3$. We need to find the composition $(f \circ g)(x)$, which means $f(g(x))$, and then dete

1. **State the problem:** A city starts with a population of 62,000 and after 25 years, the population is 78,000. We need to find how much the population increases each year. 2. **

1. **State the problem:** Henny spends 95 buying 2 identical pants, 1 shirt, and 1 hat. The shirt and hat each cost 16. We need to find the price of each pair of pants. 2. **Write

1. **State the problem:** We are given two linear equations: $$y = \frac{7}{2}x - 3$$

1. The problem is to analyze and graph the system of linear equations: $$y=\frac{7}{2}x - 3$$

1. **Problem:** Find how high a ball goes, and do an example with a drawing. 2. **Formula used:** For vertical motion, the height is often modeled by

1. The problem asks to write the number 0.007752 in scientific notation. 2. Scientific notation expresses a number as $a \times 10^n$ where $1 \leq |a| < 10$ and $n$ is an integer.

1. The problem asks to rewrite the expression $3^{-4}$ without using an exponent. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$ and $n$ is a

1. El problema es representar una función lineal que pase por dos puntos o que tenga una pendiente dada. 2. La fórmula general de una función lineal es $$y = mx + b$$ donde $m$ es

1. **State the problem:** Multiply the fractions $\frac{2}{3}$ and $\frac{7}{9}$. 2. **Formula for multiplying fractions:** To multiply two fractions, multiply the numerators toget

1. **State the problem:** Multiply the fractions $\frac{4}{7}$ and $\frac{8}{9}$. 2. **Formula:** To multiply fractions, multiply the numerators together and the denominators toget

1. **State the problem:** Solve the linear equation $$4x + 10 = -26$$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Su

1. **State the problem:** Solve the equation $$27 = x^3$$ for real number $$x$$. 2. **Formula and rules:** To solve for $$x$$ when given $$x^3 = a$$, use the cube root formula:

1. **State the problem:** Calculate the product of $3.2 \times 10^5$ and $2 \times 10^9$ and write the answer in scientific notation. 2. **Recall the rule for multiplying numbers i

1. **State the problem:** We are given the linear function $y = -10x + 2$ and need to fill in the table for the values of $x = -1, 0, 1, 5$. 2. **Formula:** The function is $y = -1

1. **State the problem:** Evaluate the expression $10^{-5}$. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and integer $n$, $a^{-n} = \frac{1}{a^n}$.

1. **State the problem:** Simplify the expression $\sqrt{3} \cdot \sqrt{2}$. 2. **Recall the property of square roots:** The product of square roots can be combined as $\sqrt{a} \c

1. **State the problem:** Find the slope and y-intercept of the line given by the equation $$y = 4x - 1$$. 2. **Recall the slope-intercept form:** The equation of a line in slope-i

1. **Stating the problem:** We have a function $f: \mathbb{R} \to \mathbb{Z}$ defined by $f(x) = \lfloor 2x - 1 \rfloor$, where $\lfloor \cdot \rfloor$ denotes the floor function (

1. **State the problem:** Calculate the sum of $1.13 \times 10^{6}$ and $6.8 \times 10^{3}$ and write the answer in scientific notation. 2. **Recall the rule:** To add numbers in s

1. **State the problem:** Calculate $$(4.15 \times 10^{-3}) - (3.64 \times 10^{-3})$$ and write the answer in scientific notation. 2. **Recall the rule:** When subtracting numbers