🧮 algebra

1. **State the problem:** We have a car traveling a distance $d$ as a function of time $t$. The car travels 425 miles at a speed of 50 miles per hour. We need to find the domain an

1. **State the problem:** We have a vehicle traveling 315 miles over 6 hours. The distance traveled as a function of time is $d(t)$, where $t$ is in hours.

1. **State the problem:** Jeremy has an $8 gift card and wants to buy comic books costing $5.25 each. The function $f(x) = 5.25x - 8$ gives the cash needed to buy $x$ comic books.

1. **State the problem:** The band wants to earn 500 by selling posters. The number of posters sold depends on the price per poster $p$ and is given by the expression $-3.5p + 85$.

1. The problem asks to identify the domain of a function from given options. 2. The domain of a function is the set of all possible input values (usually $x$) for which the functio

1. The problem asks for the total cost to join a gym for one year, given a monthly fee of 45 and a one-time starting fee of 75. 2. The total cost for one year includes paying the m

1. **State the problem:** We are given the sequence 3, 7, 11, 15, 19, … and need to determine which given explicit or recursive definitions correctly describe the n-th term of this

1. **State the problem:** We are given the sequence 95, 80, 65, 50, ... and need to find the function $a(n)$ that represents this sequence. 2. **Identify the pattern:** The sequenc

1. The problem asks to graph the equation $$y=\frac{1}{3}x$$ and plot at least 3 points with their coordinates. 2. The formula is a linear function where the slope is $$\frac{1}{3}

1. **State the problem:** Simplify the expression $$\frac{3n^4}{2n^{-3}}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{k^4}{4k^3}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same base, subt

1. **State the problem:** Factor the quadratic trinomial $$x^2 - 4x - 12$$. 2. **Recall the factoring formula:** For a trinomial of the form $$x^2 + bx + c$$, we look for two numbe

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} N_{N} + N_{D} = 50 \\ 5N_{N} + 10 N_{D} = 450 \end{cases}$$

1. **State the problem:** Simplify by adding like terms the expression: $$\frac{xy}{y^{-2}} - \frac{3x^{4}y^{4}}{x^{3}y} + \frac{7xy^{-2}}{xy^{-3}}$$

1. **State the problem:** Simplify the expression $$-( -3 - 2) + 4(-2) + \frac{1}{-2^{-3}} - (-2)^{-3}$$. 2. **Recall important rules:**

1. **State the problem:** Simplify the expression $$\frac{2^{-3} \cdot x^{0} \cdot x^{2}}{x^{-3} \cdot x \cdot y^{-3} \cdot y}$$. 2. **Recall the rules:**

1. **State the problem:** Find the measure of angle A if five times the complement of angle A is 150° greater than the supplement of angle A. 2. **Recall definitions:**

1. The problem is to simplify the expression $2^{-3} x^0 (x^2)$. 2. Recall the rules of exponents:

1. **State the problem:** We are given four relations from a domain set \{k, b, v, d, c\} to a range set \{-2, 3\} and need to determine which relations represent functions. 2. **R

1. The problem is to evaluate the step function $g(x)$ at specific points: $g(0)$, $g(0.0001)$, $g(2.999)$, and $g(3)$, and analyze the behavior of the function. 2. Step functions

1. The problem asks to find the values of $g(0)$, $g(0.0001)$, and $g(2.999)$ from the given piecewise graph of $y = g(x)$. 2. From the graph description: