🧮 algebra

1. **State the problem:** We are given six equations representing times $t$ when two vehicles meet. We need to sort these equations based on how often the vehicles meet: always, on

1. **State the problem:** We need to find the time $t$ when the blue car and the purple truck are at the same position on the road. The positions are given by the expressions $18t

1. The problem asks to describe the function representing the number of flyers Joaquin hands out over time based on the graph. 2. From the graph, the function is linear, starting a

1. **State the problem:** Solve the equation $14t = 14t + 18$ for $t$. 2. **Rewrite the equation:**

1. The problem asks what the value of a function at $x=0$ represents in a given situation. 2. Generally, for a function $f(x)$, the value at $x=0$ is $f(0)$.

1. The problem asks to write algebraic expressions for given verbal phrases. 2. For "Sum of q and x": The sum means addition, so the expression is $q + x$.

1. Write the algebraic expression for the messaging problems. 2. For 5x + 9x + x, combine like terms: $$5x + 9x + x = (5 + 9 + 1)x = 15x$$

1. **State the problem:** We need to find the final price of a sno-cone machine originally priced at 139 after applying a 20% discount and then adding a 6.75% sales tax. 2. **Formu

1. **State the problem:** Determine if 1.82 is a rational number. 2. **Recall the definition:** A rational number is any number that can be expressed as a fraction \( \frac{p}{q} \

1. The problem asks to write algebraic expressions for given verbal phrases. 2. For each phrase, we translate the words into algebraic terms:

1. **State the problem:** We need to find all real solutions to the equation $f(x) = 0$ based on the graph of $y = f(x)$. 2. **Understanding the problem:** The solutions to $f(x) =

1. The problem asks to find $f(10)$ for the piecewise function defined as: $$f(x) = \begin{cases} -\frac{x}{2} + 7 & \text{if } x \leq 6 \\ x - 2 & \text{if } x > 6 \end{cases}$$

1. **Problem Statement:** We need to determine which cubic equation matches the graph described. 2. **Given Information:** The graph is a cubic function with roots near $x = -4$, $

1. The problem is to identify the graph of the absolute value function $$y = |x - 1|$$. 2. The general form of an absolute value function is $$y = |x - h|$$, where the vertex is at

1. **Problem Statement:** Find all real solutions of the equation $f(x) = 0$ given the graph of $y = f(x)$. 2. **Understanding the problem:** The solutions to $f(x) = 0$ are the $x

1. The problem is to find the other answers to a given equation or expression. 2. To find other answers, we typically look for all solutions that satisfy the equation.

1. **Problem Statement:** We need to identify which equation matches the given graph of a cubic polynomial with three x-intercepts and two turning points. 2. **Given Options:**

1. **State the problem:** We are given parametric equations $x = 5 \cos t$ and $y = 2 \sin t$ with parameter $t$ ranging from $0$ to $2\pi$. We want to understand the relationship

1. **State the problem:** We are given the system of equations:

1. **State the problem:** We are given temperature changes over time starting at 6 a.m. with 50°F, and we need to understand the temperature at various times and graph the data. 2.

1. **State the problem:** We need to model the temperature changes throughout the day starting at 6 a.m. with 50°F and graph the temperature based on the given rates of change. 2.