🧮 algebra

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

1. **State the problem:** We need to find the combined budget for Sales, Engineering, and Media departments given the total annual budget is 100000000. 2. **Identify the percentage

1. The problem is to simplify the expressions: 200 - 2a^2 and 3a^5 - 4a^3. 2. For each expression, we look for common factors to factor out.

1. **State the problem:** Simplify the expression $$\frac{-3x^4 - 3x^3 - 9x^2}{3x^2}$$. 2. **Formula and rules:** When simplifying a fraction with polynomials, divide each term in

1. The problem asks for the equation of the trend line passing through two points on a scatter plot. 2. The two yellow points given are approximately $(0,8)$ and $(9,4)$.

1. **State the problem:** Simplify the expression $$\frac{-3x^4 - 3x^3 - 9x^2}{3x^2}$$. 2. **Formula and rules:** When dividing polynomials, divide each term in the numerator by th

1. **State the problem:** Anwar built a square deck with an area of 256 square feet. He wants to build a railing on three sides of the deck. We need to find the total length of the

1. **State the problem:** Paul and Kate bought a total of 6 CDs, paying 78 in total. Each CD Paul bought costs 12, and each CD Kate bought costs 15. We need to find how many CDs Ka

1. **State the problem:** Write the quadratic function $$f(x) = 4 - 9x - 3x^2$$ in vertex form $$f(x) = a(x - h)^2 + k$$ and identify the vertex. 2. **Rewrite the function in stand