🧮 algebra

1. The problem asks us to determine which statement about the number of pages read by Jay and Lisa over time is true based on the graph. 2. From the graph description, Jay's line s

1. **State the problem:** Classify the function $h(x) = x^3 + 1$ and find its domain. 2. **Identify the type of function:** The function $h(x) = x^3 + 1$ is a sum of a cubic term $

1. **State the problem:** Find the remainder when the polynomial $f(x) = 7x^{16} - 8x^{11} + x - 3$ is divided by $x - 1$. 2. **Recall the Remainder Theorem:** When a polynomial $f

1. **State the problem:** We are given two functions as sets of ordered pairs: $f = \{(-3,0),(1,-1)\}$ and $g = \{(-3,-5),(4,1),(5,6)\}$. We need to find the composition $f \circ g

1. **State the problem:** We have two functions defined as sets of ordered pairs: $$f = \{(-3,0), (0,-2)\}$$

1. **State the problem:** Multiply and simplify the expression $$56 \left( \frac{x}{7} + \frac{7}{8} \right)$$. 2. **Use the distributive property:** Multiply 56 by each term insid

1. **State the problem:** The theater has a fixed cost of 750 per performance and sells tickets at 8 each. We want to find the minimum number of tickets sold to make a profit of at

1. **State the problem:** Evaluate the expression $$\frac{2^3 + 5(5 - 4)}{17 - 2 \cdot 2}$$. 2. **Recall the order of operations:** We first evaluate exponents, then parentheses, m

1. **State the problem:** We are given the function $f(x) = 3x^2 - 8x$ and want to analyze it. 2. **Identify the function type:** This is a quadratic function of the form $ax^2 + b

1. **State the problem:** Find the natural domain of the function $f(x) = -\frac{16}{x}$. 2. **Recall the domain rules:** The domain of a function is the set of all real numbers $x

1. **State the problem:** Solve the equation $$8x + 4 = 6x + 14$$. 2. **Isolate variable terms:** Subtract $$6x$$ from both sides to get $$8x - 6x + 4 = 14$$.

1. The problem is to analyze the equation without solving for $x$. 2. Typically, to solve for $x$, we isolate $x$ on one side using algebraic operations.

1. **State the problem:** Solve the equation $$27x^3 = (x + 5)^3$$ for $x$. 2. **Recall the formula:** The equation is of the form $a^3 = b^3$, which implies $a = b$ or the cube ro

1. **State the problem:** Alonzo paid a $2 start fee plus $0.12 per minute for a scooter ride, and the total cost was $25.52. We need to find the number of minutes, $x$, he rode. 2

1. **State the problem:** Ivanna has a prepaid card with 20 on it. She buys ribbon at 0.11 per yard and has 16.04 left. We need to find how many yards she bought. 2. **Set up the l

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + 2y = -3 \\ 5x + y = 12 \end{cases}$$

1. **State the problem:** Solve the equation $1 - w = 195$ for $w$. 2. **Recall the additive property of equality:** You can add or subtract the same number from both sides of an e

1. Problem: Vereinfachen und Wurzel ziehen verschiedener Ausdrücke. 1. a) Berechne $\sqrt{32} \cdot \sqrt{8}$.

1. **State the problem:** Solve the equation $$24 = -x + 160$$ for $$x$$. 2. **Use the additive property of equality:** To isolate $$x$$, add $$x$$ to both sides and subtract 24 fr

1. **State the problem:** We need to complete the table for the function $$y = x^2 - 2x - 3$$ by calculating the value of $$y$$ for each given $$x$$ value: $$-4, -3, -2, -1, 0, 1,

1. **State the problem:** Simplify the expression $2\sqrt{3}(2\sqrt{6} + 5)$.\n\n2. **Recall the distributive property:** $a(b + c) = ab + ac$. We will distribute $2\sqrt{3}$ to bo