🧮 algebra

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

1. **Problem:** Find the equation of the resulting graph $g(x)$ when $f(x) = x^2 + 2$ is vertically stretched with scale factor 2. 2. **Formula and Explanation:**

1. **State the problem:** Prove that $3\sqrt{3}$ (three times the square root of 3) is an irrational number. 2. **Recall definitions and properties:**

1. **State the problem:** We are given the distance between two cities as 17000 km, rounded to the nearest 1000 km. We want to write an inequality to show the possible limits of th

1. The problem states that 1/7 of the animals in a pet shop are gerbils. 2. We need to find the ratio of gerbils to other animals.