🧮 algebra

1. The problem asks us to find the integer that is 5 more than -4 using a number line. 2. Start at -4 on the number line.

1. The problem is to calculate $\frac{2}{3} \div 2$. 2. Division by a number is the same as multiplication by its reciprocal. So, rewrite the expression as:

1. The problem is to divide the fraction $\frac{3}{2}$ by the number 2. 2. Division by a number is the same as multiplication by its reciprocal. So, we rewrite the division as mult

1. The problem is to simplify the fraction $\frac{6}{9}$. 2. Find the greatest common divisor (GCD) of 6 and 9, which is 3.

1. The problem gives two equations: $y=1-x$ and $y=5-2x-x^2$. We want to analyze or find the points where these two functions intersect. 2. To find the intersection points, set the

1. The problem provides two points: $$\left(\frac{-1 + \sqrt{17}}{2}, \frac{3 - \sqrt{17}}{2}\right)$$ and asks for further analysis or interpretation. 2. First, simplify each coor

1. Problem: Find the value of $\vec{i} \cdot \vec{j}$ where $\vec{i}$ and $\vec{j}$ are standard unit vectors along X and Y axes respectively. Step 1: Recall that $\vec{i} = (1,0)$

1. The problem asks to find the linear equation relating $x$ and $y$ from the table: | $x$ | 1 | 2 | 3 |

1. The problem is to simplify the expression $\sqrt{2} + \sqrt{2 + \sqrt{2\cos 4\theta}}$. 2. First, focus on the inner square root: $\sqrt{2\cos 4\theta}$. Recall the double-angle

1. The problem is to solve the system of equations by graphing: $$y = x - 9$$

1. **State the problem:** Solve the system of equations: $$2x = -9 + 3y$$

1. **State the problem:** Solve the system of equations using determinants: $$3r = -3s + 3$$

1. **State the problem:** Solve the system of equations using determinants (Cramer's Rule): $$2x - 3y - 6 = 0$$

1. **State the problem:** Solve the system of equations using the substitution method: $$x + 8y = 48$$

1. **State the problem:** Solve the system of equations using the addition method: $$6x - 7y = -6$$

1. The problem gives two linear equations: $$6x + 5y = -4$$

1. El problema es simplificar la expresión \( (-2x^{2}y - 3x^{3} - 2y^{3} + 2xy^{2}) - (-3x - 4x^{2}y + yx - 5x^{2}y^{2} - 3y^{2}x) \). 2. Primero, eliminamos los paréntesis y camb

1. The problem is to solve the equation $x = x + 1$ for $x$. 2. Start by subtracting $x$ from both sides to isolate the constant term:

1. The problem asks to simplify the expression $w + w$. 2. Since both terms are the same variable $w$, we can combine them by addition.

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} 3x + 5 & -4 \leq x \leq -1 \\ 2 & -1 \leq x < 3 \\ -x + 2 & 3 \leq x \leq 4 \end{cases}$$

1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} 3x + 5 & -4 \leq x \leq -1 \\ 2 & -1 \leq x < 3 \\ -x + 2 & 3 \leq x \leq 4 \end{cases}$$