🧮 algebra

1. The problem asks to write $9^{-2}$ as a fraction without indices. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$.

1. **State the problem:** We have data points $(20, 57.5)$, $(33, 34.8)$, and $(42, 27.4)$ and want to extrapolate $y$ at $x=49$ assuming the model $y = Ax^p$. 2. **Formula and app

1. **Problem statement:** We are given two functions: $$f_9(w) = w^2 + 2$$

1. **State the problem:** Describe the end behavior of the cubic function whose graph passes through the origin and exhibits typical cubic end behavior. 2. **Recall the general beh

1. **State the problem:** We are given the first 4 terms of an arithmetic sequence: 12, 7, 2, -3. We need to find an expression for the nth term of the sequence.

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{\frac{(x+2)!}{x!}} = \sqrt{3!} \times 7.$$\n\n2. **Recall factorial and square root properties:** The factorial $n!$

1. **State the problem:** We are given two functions:

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{\frac{(x+2)!}{x!}} = \sqrt{3!} \times 7.$$\n\n2. **Recall factorial and square root properties:**\n- Factorial: $n!

1. **State the problem:** We have two functions:

1. **State the problem:** You start with the number 5036. Then you add 60, subtract 462, and divide the result by 1.5. You want to find the 10th number in this sequence. 2. **Under

1. The problem asks to describe the end behavior of a cubic function graph passing through the origin (0,0). 2. For cubic functions of the form $f(x) = ax^3 + bx^2 + cx + d$, the e

1. **Problem statement:** A gardener plants peas in 30 rows, each producing 4000 g. For every additional row, production per row decreases by 100 g. We need to model this with a qu

1. **State the problem:** Solve the inequality $3x + 5 \le 4x + 1$. 2. **Isolate variable terms:** Subtract $3x$ from both sides to get

1. The problem asks us to list at least 5 points on the graph of the cubic function $f(x) = x^3$. 2. The function $f(x) = x^3$ means for any input $x$, the output $y$ is $x$ multip

1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} 6x + 5 & \text{for } x < -1 \\ -2 & \text{for } x = -1 \\ x & \text{for } -1 < x \leq 2 \e

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} 5x - 2 & \text{for } x \leq 1 \\ -(x - 1)^2 + 1 & \text{for } 1 < x < 4 \\ \frac{3}{2}x - 13 & \

1. Planteamos el problema: Resolver la ecuación $$\frac{2(x-3)}{3} - x - \frac{5}{10} = \frac{3(2x-1)}{5} + \frac{4x}{15}$$. 2. Para resolver ecuaciones con fracciones, buscamos un

1. **State the problem:** Find the discriminant of the quadratic equation $$1 - 5x^2 - 2x = 0$$ and determine what the discriminant tells us about the number of real solutions. 2.

1. **Stating the problem:** We are asked to group algebraic expressions with their corresponding model cards representing variables and expressions. 2. **Understanding the models a

1. **State the problem:** We have 50 players who can only play in 6-player games (3 on 3) or 2-player games (1 on 1). Let $x$ be the number of 6-player games and $y$ be the number

1. The problem is to differentiate between the expressions "Multiply n by two, then add three" and "Add three to n, then multiply by two". 2. Let's translate each phrase into algeb