🧮 algebra

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

1. **State the problem:** We need to select the equation that best represents the first model (bottom-left) where the scale has one star on the left and three rectangles on the rig

1. **State the problem:** Simplify the expression $$(9m^{\frac{5}{3}})(4m^{-\frac{7}{2}})$$. 2. **Use the product rule for exponents:** When multiplying terms with the same base, a

1. **State the problem:** Simplify the expression $$\frac{\sqrt{y^7} \times \sqrt[5]{y^2}}{\sqrt[5]{y^4}}$$. 2. **Rewrite roots as exponents:** Recall that $$\sqrt{y^7} = y^{\frac{

1. The problem asks to describe each given roster (list of elements) using set-builder notation. 2. Set-builder notation describes a set by stating the properties that its members

1. The problem is to create a table of values and graph the linear function $y = -x + 4$. 2. The formula for a linear function is $y = mx + b$, where $m$ is the slope and $b$ is th

1. **State the problem:** Simplify the expression $$\left(\frac{100a}{25a^{2}b^{\frac{1}{2}}}\right)^{-\frac{1}{2}}$$. 2. **Recall the rules:**

1. **State the problem:** We are given a graph of a function $f(x)$ which is a straight line descending from top left to bottom right. 2. **Identify key points from the graph:** Th

1. **State the problem:** Solve the equation $$-\frac{1}{2}x - 3 = 4$$ for $x$. 2. **Add 3 to both sides** to isolate the term with $x$:

1. **State the problem:** We are given the equation $c = 3 + n$, which represents the number of coins $c$ a player has after winning $n$ levels in a video game. 2. **Understand the

1. The problem states that the number of coins $c$ a player has after winning $n$ levels is given by the equation $$c = 3 + n.$$ 2. We are asked to find how many coins the player s

1. **State the problem:** Solve the system of equations: $$\frac{x}{10} + \frac{y}{20} = 4$$

1. **Problem:** Find the values of the following logarithms to four decimal places using the property of logarithms and the given table values. 2. **Formula and rules:**

1. **State the problem:** Factor the expression $$242f^2 - 32$$ completely. 2. **Identify the type of expression:** This is a difference of two terms, which can be factored using t

1. **State the problem:** Factor the quadratic expression $$27q^2 + 144q + 192$$ completely. 2. **Identify the greatest common factor (GCF):** Look for the largest number that divi

1. **Problem:** Identify the center and radius of the circle given by the equation $$(x - 4)^2 + (y - 1)^2 = 3$$ 2. **Formula:** The standard form of a circle's equation is $$(x -

1. **State the problem:** We have populations of six towns given by exponential functions of the form $P = P_0 (r)^t$, where $P_0$ is the initial population and $r$ is the growth/d

1. **State the problem:** We need to match each exponential function with its corresponding graph based on the function's behavior. 2. **Recall the general form of an exponential f

1. Simplify $2x^5 y \cdot 3x^2 y$. Use the product rule for exponents: $a^m \cdot a^n = a^{m+n}$.

1. **State the problem:** Find the point that is $\frac{1}{3}$ of the way from point A to point B, where A is at $(-3, -2)$ and B is at $(1, 5)$. 2. **Formula used:** The point $P$

1. **State the problem:** Find the equation of a quadratic function in vertex form given the vertex at $(3,-6)$ and points $(1,0)$ and $(5,0)$ on the parabola. 2. **Recall the vert