🧮 algebra

1. The problem is to create a mapping statement, which in mathematics typically means defining a function that maps elements from one set to another. 2. A mapping statement usually

1. The problem states the inequality $t \leq 100$ which means the total weight $t$ of the produce carried by the truck must be less than or equal to 100 kilograms. 2. The truck is

1. **State the problem:** We are given the function $f(x) = \frac{1}{2} \sqrt{-4x}$ and need to understand its domain and simplify it if possible. 2. **Recall the domain rule for s

1. Let's clarify the origin of the term $8x^2$ in the expression. 2. Typically, $8x^2$ comes from multiplying constants and variables, for example, $4 \times 2x^2 = 8x^2$.

1. **State the problem:** Simplify the expression $$5^{2x+3} \cdot 5^{x-5}$$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the sam

1. **State the problem:** Simplify the expression $$\frac{(-2)^4 - 4 + 9x - 2 + 6}{2 - (-3)(2 - 5)}$$

1. **State the problem:** We have an exponential function $f(x) = ab^x$ passing through points $A(\frac{1}{4}, 3)$ and $B(\frac{1}{2}, 4.5)$. We want to find the $y$-coordinate of

1. **State the problem:** Solve the equation $$-\frac{1}{5}p + \frac{3}{4}p = 11$$ for $p$. 2. **Combine like terms:** To combine the terms with $p$, find a common denominator for

1. **State the problem:** Alex has a $\frac{5}{6}$ interest in a partnership. She sold $\frac{5}{8}$ of her interest for 2400. We need to find the total amount of Alex's interest b

1. The problem asks to graph the lines: $y=3x$, $y=4$, and $x=2$. 2. The line $y=3x$ is a linear function with slope 3 and passes through the origin $(0,0)$.

1. The problem involves understanding the relationship between variables $x$ and $y$ given two different values of $k$ and their corresponding data tables. 2. Typically, $k$ repres

1. The problem involves analyzing three tables of values $(x, y)$ and their corresponding constants $k$. 2. Each table suggests a relationship between $x$ and $y$ that can be expre

1. **State the problem:** Solve the system of linear equations: $$-2x + y = 8$$

1. **State the problem:** Solve the equation $$\frac{2}{x+5} + \frac{1}{x-5} = \frac{16}{x^2 - 25}$$ where $x^2 - 25$ can be factored as $(x+5)(x-5)$. 2. **Identify the common deno

1. **State the problem:** Solve the equation $$6 \sqrt{4x} - 3 = 2x - 1$$ for $x$. 2. **Isolate the square root term:** Add 3 to both sides:

1. **State the problem:** Solve the equation $$\sqrt{4x - 3} = 2x - 1$$ for $x$. 2. **Recall the rule:** To solve equations involving square roots, we isolate the square root term

1. **State the problem:** Multiply the rational expressions $$\frac{9y^2-4}{4y-12} \times \frac{18-6y}{9y^2+12y+4}$$. 2. **Factor all polynomials:**

1. **State the problem:** Simplify the expression $$\frac{9y^2-4}{4y-12}x \cdot \frac{18-6y}{9y^2+12y+4}$$. 2. **Factor all polynomials:**

1. **State the problem:** Solve the system of linear equations: $$\frac{3}{5}$$

1. **State the problem:** The ratio of Skittles to Gummy Bears is 3 to 7. There are 51 Skittles. We need to find the total number of pieces of candy. 2. **Understand the ratio:** T

1. **State the problem:** Find the equation of a line parallel to the line given by $$y = -8x + 8$$ that passes through the point $$(4, -7)$$. 2. **Recall the rule for parallel lin