Final answer:
The questions provided involve algebraic concepts such as solving for an unknown, finding the slope of a line, and determining the area of a triangle. we get a)x = 7, b) y = 3x + 9, the slope (m) is 3, c)20 square units, d)y = 4.
Step-by-step explanation:
The student's questions cover several areas of algebra which includes finding unknowns, determining the slope of a line, and calculating the area of a triangle.
- Solve for x: To solve the equation 2x - 4 = 10, we first add 4 to both sides to get 2x = 14. Then, we divide both sides by 2 to find x = 7.
- Find the slope of the line: The equation of a line in the slope-intercept form is y = mx + b, where m represents the slope. For example, if the equation is y = 3x + 9, the slope (m) is 3.
- Calculate the area of a triangle: The area (A) can be calculated using the formula A = ½bh, where b is the base and h is the height of the triangle. For example, if the base (b) is 10 and the height (h) is 4, the area is A = ½ × 10 × 4 = 20 square units.
- Solve for y: To solve the equation 3y + 6 = 18, we first subtract 6 from both sides, getting 3y = 12. Next, we divide both sides by 3 to find y = 4.
Each of these problems requires the application of basic algebraic principles and the use of the GCF (Greatest Common Factor) is not directly applicable to these problems.