🧮 algebra

1. Simplify: $ (2x + 3)(3x^2 - x - 2) $. Step 1: Use distributive property (FOIL method):

1. The problem is to evaluate the expression $5 - [-6] + [8]$. 2. First, recognize that subtracting a negative number is the same as adding its positive counterpart. So, $5 - [-6]$

1. The problem is to understand the effect of adding a positive number on a number line. 2. When you add a positive number to a value, you move that value to the right on the numbe

1. The problem appears to involve comparing or simplifying expressions involving square roots and constants. 2. Let's analyze each option:

1. The problem appears to list several lengths with square root expressions: A is $9\sqrt{2}$ m, B is $\sqrt{2}$ m, C is $\sqrt{47}$ m, D is $\frac{5}{2}$ m, and E is 3 m. 2. To un

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: $$6x + 5y = -4$$