🧮 algebra

1. The problem asks for the answer to $abc$. 2. To solve for $abc$, we need values or expressions for $a$, $b$, and $c$.

1. **State the problem:** We need to find the amount of medicine in a mixture where the ratio of medicine to water is $1:4$ and the total volume is $200$ml. 2. **Understand the rat

1. **State the problem:** Solve the equation $$5 + 3x = x$$ for $$x$$. 2. **Isolate the variable:** To solve for $$x$$, we want to get all terms containing $$x$$ on one side and co

1. **State the problem:** We want to find the remaining storage space on the submersible's computer after recording and compressing sonar data, and deleting corrupted files.

1. **Find the inverse of** $f(x) = \frac{1}{3}x - 4$. Start by replacing $f(x)$ with $y$:

1. **State the problem:** We need to write the ratio of $12$ feet to $3$ yards using fraction notation and reduce it. 2. **Convert units to be the same:** Since the units must be t

1. **State the problem:** We need to write the ratio $5$ to $35$ using fraction notation and then reduce it to simplest form. 2. **Write the ratio as a fraction:** The ratio $5$ to

1. **State the problem:** We need to determine if the given relation defines $y$ as a function of $x$. 2. **Recall the definition of a function:** A relation defines $y$ as a funct

1. **State the problem:** Solve the inequality $$|10 - t| - 3 \geq 11$$ and write the solution set in interval notation if possible. 2. **Isolate the absolute value:** Add 3 to bot

1. **State the problem:** We have a rational function $f(x) = \frac{a}{x+b}$ and a new function $g(x) = f(x+4)$. We want to find the equation for $g(x)$. 2. **Analyze the given fun

1. **State the problem:** Find the equation of the line passing through points $(1,6)$ and $(4,3)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_

1. **State the problem:** Find the equation of the line passing through points $(-2, 3)$ and $(-4, -2)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1, y_1)$ an

1. **State the problem:** Solve the equation for $y$ given the options. 2. **Given equation:** We need to find $y$ in terms of $x$ from the equation implied by the options, which i

1. **State the problem:** Solve the linear equation $$3x - 7y = 17$$ for one variable or express the relationship between $$x$$ and $$y$$. 2. **Formula and rules:** This is a linea

1. **State the problem:** Simplify the expression $$\frac{x-4}{(x-4)(\sqrt{x+2})}$$. 2. **Identify the formula and rules:** When simplifying fractions, if the numerator and denomin

1. The problem is to evaluate the expression $\text{now} - 2$. 2. Since "now" is not a defined mathematical variable or number, we interpret the problem as subtracting $2$ from an

1. **State the problem:** Evaluate the expression $$k^5 + 3k^4 - 5k^3 - 15k^2 + 4k + 12$$ when $$k = -1$$.

1. **State the problem:** We have a quadratic function $f(x)$ with vertex at $(3, 6)$. 2. **Recall vertex form:** A quadratic function can be written as $f(x) = a(x - h)^2 + k$ whe

1. **State the problem:** We have a quadratic function $f(x)$ with vertex at $(4, 5)$.

1. **State the problem:** We have a quadratic function $f(x)$ with vertex at $(-6, 3)$. 2. **Understand the transformation:** The function $g(x) = -f(x - 4)$ involves two transform

1. **State the problem:** We have a quadratic function $y = f(x)$ with vertex at $(-4, -6)$. We define a new function $g(x) = f(x) + 3$ and want to find the vertex of $g(x)$. 2. **