🧮 algebra

1. **State the problem:** Find the equation of the line passing through the points $(-1, -3)$ and $(1, 11)$. 2. **Formula used:** The slope $m$ of a line through two points $(x_1,

1. **State the problem:** Find the equation of a line with slope $m=\frac{5}{4}$ that passes through the point $(-8,3)$.\n\n2. **Formula used:** The point-slope form of a line is g

1. **State the problem:** Simplify the expression $$\frac{a^{-1} b^{-2} c^{-6}}{4}$$ and express it as a single fraction with positive exponents. 2. **Recall the rule for negative

1. The problem asks whether the decimal representations of the fractions $\frac{2}{5}$, $\frac{15}{20}$, and $\frac{6}{16}$ will repeat or terminate. 2. A fraction in simplest form

1. **State the problem:** Solve the system of equations using diagonal methods (diagonalization or matrix methods): $$\begin{cases} x + y + z = 0 \\ x - 2y + 2z = 4 \\ x + 2y - z =

1. **State the problem:** We want to verify or solve the equation:

1. **State the problem:** We know that three-fifths of the Grade 8 class are in the band.

1. **State the problem:** We know that three-fifths of the Grade 8 class are in the band.

1. **Problem:** Determine if the function $f(x) = 3$ is even, odd, or neither. 2. **Recall definitions:**

1. **State the problem:** We need to solve the simultaneous equations: $$y = -2x + 11$$

1. **State the problem:** Solve the system of linear equations: $$2x + y = 17$$

1. Let's evaluate each expression step-by-step. 2. For $x = 57$, this is just a value assignment.

1. **State the problem:** Simplify the expression $\frac{x-2}{4} - 2 - \frac{x-6}{2}$.\n\n2. **Identify the formula and rules:** To simplify, combine like terms and fractions by fi

1. The problem appears to involve calculating percentages or proportional values based on given numbers and amounts. 2. To find a percentage, the formula is: $$\text{Percentage} =

1. The problem is to simplify the expression $$4d^7 - (5q)^{\frac{3}{5}}$$ without further simplification or evaluation. 2. The expression consists of two terms: the first term is

1. The problem states that Millie truncates the number $N$ to 1 digit and the result is 8. 2. Truncating to 1 digit means keeping only the integer part of $N$ and discarding all di

1. **State the problem:** Rewrite the expression $$4(d)^{2/7} - (5q)^{3/5}$$ using radicals instead of fractional exponents.

1. **State the problem:** Solve the equation $\frac{x-5}{3} - 5 = \frac{x-9}{5}$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $$\frac{x-2}{4} - 3 = \frac{x-4}{5}$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fractions, first eliminat

1. **State the problem:** Solve the equation $\frac{x-2}{4} - 3 = \frac{x-4}{5}$ for $x$. 2. **Formula and rules:** To solve equations with fractions, first eliminate the denominat

1. The problem involves solving for $x$ given the equation $x = 23$ and other expressions involving $x$. 2. The first expression is $x = \frac{45}{23}$, which is a fraction represe