All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
3651
What is the area of the triangle formed by the line x/3 + y/4 = 1 and the coordinate axes?
Answer:
6
Step 1: The equation x/3 + y/4 = 1 shows the x-intercept is 3 and the y-intercept is 4. Step 2: This forms a right-angled triangle with the axes, with base = 3 and height = 4. Step 3: Area = (1/2) * base * height = (1/2) * 3 * 4 = 6.
3652
What is the x-intercept of the line y = 2x - 4?
Answer:
2
Step 1: To find the x-intercept, set the y-value to 0 in the given equation. Step 2: 0 = 2x - 4. Step 3: Solve for x: 2x = 4, which gives x = 2.
3653
What is the y-intercept of the line y = 3x - 7?
Answer:
-7
Step 1: The equation is in the slope-intercept form y = mx + c. Step 2: In this format, 'c' directly represents the y-intercept. Step 3: Comparing y = 3x - 7 to the standard form, we see that c = -7.
3654
What is the sum of the x-intercept and the y-intercept of the line x + y = 5?
Answer:
10
Step 1: Find the x-intercept by setting y = 0: x + 0 = 5, so x-intercept = 5. Step 2: Find the y-intercept by setting x = 0: 0 + y = 5, so y-intercept = 5. Step 3: Add the two intercepts together: 5 + 5 = 10.
3655
In the intercept form of a linear equation x/a + y/b = 1, what do 'a' and 'b' represent respectively?
Answer:
X-intercept and y-intercept
Step 1: If we set y=0, we get x/a = 1, which means x=a. Thus, 'a' is the x-intercept. Step 2: If we set x=0, we get y/b = 1, which means y=b. Thus, 'b' is the y-intercept. Step 3: Therefore, 'a' and 'b' are the x-intercept and y-intercept.
3656
What is the y-intercept of the line given by 4x - 5y = 20?
Answer:
-4
Step 1: The y-intercept occurs where the line crosses the y-axis, meaning the x-coordinate is 0. Step 2: Substitute x = 0 into the equation: 4(0) - 5y = 20. Step 3: Solve for y: -5y = 20, yielding y = -4.
3657
What is the x-intercept of the line given by 2x + 3y = 12?
Answer:
6
Step 1: The x-intercept occurs where the line crosses the x-axis, which means the y-coordinate is 0. Step 2: Substitute y = 0 into the equation: 2x + 3(0) = 12. Step 3: Solve for x: 2x = 12, yielding x = 6.
3658
What is the slope of a line parallel to the line 5x + 5y = 1?
Answer:
-1
Step 1: Convert to slope-intercept form to find the slope. Step 2: 5y = -5x + 1, which implies y = -1x + 1/5. Step 3: The slope of this line is -1. Parallel lines have equal slopes, so the required slope is also -1.
3659
The lines represented by y = x and y = -x are:
Answer:
Perpendicular
Step 1: Find the slope of the first line (y = x). The slope m1 is 1. Step 2: Find the slope of the second line (y = -x). The slope m2 is -1. Step 3: Multiply the slopes: 1 * (-1) = -1. Since the product is -1, the lines are perpendicular.
3660
The equations 3x + 4y = 5 and 6x + 8y = 10 represent lines that are:
Answer:
Coincident
Step 1: Check the ratio of coefficients. a1/a2 = 3/6 = 1/2. b1/b2 = 4/8 = 1/2. c1/c2 = 5/10 = 1/2. Step 2: Since a1/a2 = b1/b2 = c1/c2, the equations represent the exact same line. Step 3: Lines that are exactly the same are called coincident.