🧮 algebra

1. **State the problem:** We want to rewrite the equation $$-3x^2 + 49x = -5x + 183$$ in the form $$(x + a)^2 = b$$ by completing the square. 2. **Rearrange the equation:** Move al

1. **State the problem:** We want to rewrite the quadratic equation $$-3x^2 + 6x = -321$$ in the form $$(x + a)^2 = b$$ by completing the square. 2. **Rewrite the equation:** First

1. **State the problem:** Find the greatest common factor (GCF) of the monomials $35x^3y^2$, $10x^4y$, and $5x^5y^3$. 2. **Recall the formula and rules:**

1. **State the problem:** Find the greatest common factor (GCF) of the monomials $10a^3$, $12a^2$, and $14a$. 2. **Recall the formula and rules:** The GCF of monomials is found by

1. **State the problem:** Solve the system of equations: $$\begin{cases}-9a + b + 8c = -18 \\ -5a + 5b + 8c = -10 \\ -2a + 8b + 9c = 1 \end{cases}$$

1. **State the problem:** We need to find which system of equations has the solution $(1, 3, -1)$ for variables $(x, y, z)$. 2. **Recall the method:** To check if $(1, 3, -1)$ is a

1. **State the problem:** Solve the equation $X + (X + 170) = 200$ for $X$. 2. **Write the equation:**

1. **State the problem:** Solve the system of equations given: Top-right: $$n^2 + 4n\left(-\frac{4}{2}\right)^2 = +21\left(\frac{4}{2}\right)^2$$

1. **State the problem:** Solve the quadratic equation $$z^2 - 6z - 63 = 0$$. 2. **Formula used:** For a quadratic equation $$az^2 + bz + c = 0$$, the solutions are given by the qu

1. **State the problem:** We are given the system of linear equations: $$6x - 2y = 10$$

1. The problem asks about the number of solutions to a system of linear equations where the first equation is $f(x) = -4x + 8$ and the second equation has a different slope. 2. Rec

1. **State the problem:** Determine the domain, range, and whether the set of ordered pairs is a function for the first set: $\{ (0, 8), (7, -4), (5, -7), (-2, 3), (7, 0) \}$. 2. *

1. The problem states: "The graph of $y=f(x)$ is shown below." However, no graph or further details are provided to analyze or solve any specific question related to $f(x)$. 2. To

1. The problem is to graph the exponential function $g(x) = 2^x - 2$ and find its domain and range. 2. The general form of an exponential function is $f(x) = a^x + c$, where $a > 0

1. **State the problem:** We are given the function $F(x,y) = x + y + 1$ and want to understand or analyze it. 2. **Formula and explanation:** This is a simple linear function of t

1. The problem states that the function $F(x,y)$ is equal to 10 for all values of $x$ and $y$. 2. This means $F(x,y) = 10$ is a constant function.

1. **State the problem:** Simplify the expression $$\frac{-3x^{\frac{1}{2}}}{2x^{-\frac{3}{4}}}$$. 2. **Recall the rule for dividing powers with the same base:** $$\frac{a^m}{a^n}

1. **State the problem:** A 1150-gallon tank is full initially and water drains at 26 gallons per minute. 2. **Write the linear equation:** The amount of water decreases over time,

1. **Problem:** Solve the equation $$-3y + 17 = 56$$. 2. **Step 1:** Subtract 17 from both sides to isolate the term with $y$.

1. **State the problem:** You have a $13500 scholarship and spend $500 each month. We want to model the remaining scholarship amount after $x$ months. 2. **Write the function:** Th

1. **Problem:** Li rode her bike 25% of the way to school, which equals 5 blocks. We need to find the total number of blocks from Li's home to school. 2. **Formula:** Use the propo