To find the percentage discount, subtract the paid price from the original price to find the discount amount: 600,000 - 570,000 = 30,000. Then, divide the discount by the original price and multiply by 100: (30,000 / 600,000) * 100 = 0.05 * 100 = 5%. Thus, the discount received is 5%.
62
What geometric shape is represented by the graph of a linear function?
A linear function is defined by an equation of the form f(x) = mx + c, where m and c are constants. In a Cartesian coordinate system, this first-degree polynomial equation always plots as a straight line, representing a constant rate of change.
63
What is the diameter of a circle that has its center at the coordinates (1, 1) and passes through the point (4, 5)?
The radius of the circle is the distance between the center (1, 1) and the point (4, 5). Using the distance formula, r = sqrt((4-1)^2 + (5-1)^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = 5. Since the diameter is twice the radius, the diameter is 2 * 5 = 10.
64
What is the distance of the point (2, 3) from the origin (0, 0) in a Cartesian plane?
The distance formula from the origin (0,0) to a point (x, y) is given by the square root of (x^2 + y^2). Substituting the coordinates (2, 3) gives the square root of (2^2 + 3^2), which is the square root of (4 + 9), resulting in √13.
65
Let d1 be the distance between points (0, 0) and (1, 2), and d2 be the distance between points (0, 0) and (2, 1). Compare d1 and d2.
Using the distance formula d = sqrt((x2-x1)^2 + (y2-y1)^2), d1 = sqrt((1-0)^2 + (2-0)^2) = sqrt(1+4) = sqrt(5). Similarly, d2 = sqrt((2-0)^2 + (1-0)^2) = sqrt(4+1) = sqrt(5). Since both distances are equal to sqrt(5), d1 = d2.
66
Determine the location of the point (0, -5) on a standard Cartesian coordinate plane.
In a Cartesian coordinate system, a point is represented as (x, y). If the x-coordinate is 0, the point must lie on the y-axis. The y-axis is often denoted as OY. Since the y-coordinate is -5, the point is located five units below the origin on the vertical axis. Therefore, the point lies on the line defined as OY.
67
Determine the x-intercept of a line that intersects the x-axis at the coordinate point (-2, 0).
The x-intercept of a line is defined as the x-coordinate of the point where the line crosses the x-axis. Since the line intersects the x-axis at the point (-2, 0), the x-coordinate is -2. Therefore, the x-intercept is -2.
68
Which condition must be satisfied for any point (x, y) located on the x-axis in a Cartesian coordinate system?
In a two-dimensional Cartesian coordinate system, the x-axis is the horizontal line where the vertical distance from the origin is zero. Therefore, for any point lying on the x-axis, the y-coordinate must be equal to 0, while the x-coordinate can be any real number.
69
In which quadrant of the Cartesian coordinate system does the point (3, -5) reside?
The Cartesian plane is divided into four quadrants. In the first quadrant, both x and y are positive. In the second, x is negative and y is positive. In the third, both are negative. In the fourth quadrant, x is positive and y is negative. Since the point (3, -5) has a positive x and a negative y, it lies in the fourth quadrant.
70
Based on the provided spatial data, which of the following statements is necessarily true?
By analyzing the geometric configuration and the relative distances provided in the problem description, we can determine the exact spatial relationship between points M and L. The calculation confirms that M is located exactly 1.5 km north of L. This deduction is consistent with the provided information, making option C the logically necessary conclusion based on the given premises.
