What are the solutions of x^2-2x+5=0

8 Line in the xy-plane contains points from each of Quadrants II, III, and IV, but no points from Quadrant I. Which of the follo

iren2701 [21]

Answer:

The correct option is D.

Step-by-step explanation:

The slope of a line is the change in y with respect to x.

$m=\frac{y_2-y_1}{x_2-x_1}$

If the slope of a line is undefined it means it is a vertical line and a vertical line can not passes through three quadrants. So, option A is incorrect.

If the slope of a line is 0 it means it is a horizontal line and a horizontal line can not passes through three quadrants. So, option B is incorrect.

If the slope of a line is positive it means the value of y increases as x increases.

Since it is an increasing line, therefore after a certain period both x and y will positive. It means the line will passes through first quadrant. So, option C is incorrect.

If the slope of a line is negative it means the value of y decreases as x increases. It can passes through each of Quadrants II, III, and IV.

Therefore the correct option is D.

6 0

3 years ago

Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) an

ss7ja [257]

The given information are the coordinates of points H, Z and B. So, the first step to do is to plot these points on a Cartesian plane as shown in the attached picture. We can deduce visually that horse Z is closer to the barns than horse H. But, to further justify the answer, we have to provide the magnitude of the distance of horses H and Z to barn B. In this approach, we use the distance formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.

Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165

Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters

Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012

Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters

Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.