Which ordered pairs are in the solution set of the system of linear inequalities?
1 answer:
The ordered pairs (5 , -2) , (3 , 1) , (4 , 2) are in the set of the solution (Option C)
<h3>What is an ordered pair?</h3>An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order.
It aids visual comprehension by locating a point on the Cartesian plane.
<h3>How do we arrive at the solution?</h3>The first line has negative slope and passing through points (0 , 0) and (4 , -2)
That is y > (-1/2)x
The second line has positive slope and passing through points (-2 , 0) and (2 , 2)
That is: y < (1/2)x + 1.
- Refer to the accompanying diagram to discover the common component of the solutions.
- The inequity is shown by the red shading.
- The inequity is shown by the blue shading.
- The two-colored shaded area reflects the common solutions to the two inequalities.
- Let's discover the ordered pairs in the system of linear inequalities' solution set.
- Points (-4, 2), (-3, 1), (4, -3) define the common shaded area.
- Points (5, -2), (3, 1), (3, -1) (4 , 2)
As a result, Point (5, -2) is in the darkened region.
As a result, Point (3, 1) is in the darkened area.
As a result, Point (4, 2) is in the darkened area.
As a result, the ordered pairings (5, -2), (3, 1), (4, 2) are in the solution set.
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The answer is the second option:
you ride your bike X miles per hour up a mountain for 45 minutes on the way
We convert minutes into hour because speed is in miles per hour
To convert minutes into hour we divide by 60
45 minutes =
it takes 20 minutes to ride your bike down the mountain
20 minutes =
you ride your bike X miles per hour up a mountain
Distance = speed * time taken
distance covered while riding bike up a mountain is
D = x *0.75
on the way down the mountain you ride your bike for 4 miles per hour faster
So time taken is x + 4
distance covered while riding bike up a mountain is
D = (x+4) * 0.33
Distance covered by climbing up and down the mountain are same
so we make the distance equation equal
x *0.75= (x+4) * 0.33
0.75x = 0.33x + 1.32
Subtract 0.33 from both sides
0.42x = 1.32
Divide both sides by 0.42
x = 3.1429 miles per hour
Distance covered up D = 0.75* x = 0.75 * 3.1429 = 2.357175
Distance covered down D = (3.1429 +4) * 0.33 = 2.357157
Total distance covered = 2.357175 + 2.357175 = 4.71435
you ride your bike in total of 4.71 miles approximately .