Henry divided his socks into five equal groups. Let s represent the total number of socks. Which expression and solution represe
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Answer:
We conclude that, at 4 minutes, both will have the same height which is 200 feet.
Step-by-step explanation:
Given the system of equations
Important Tip:
- The point of intersection of the two lines would give us the point at which both have the same height.
Graphing the system of equations
<u>The graph of the equation y = 400 + 50x</u>
First, determine the y-intercept of the equation y = 400 + 50x by substituting x = 0
Thus, we determine that the ordered pair (0, 400) represents the y-intercept of the equation y = 400 + 50x.
Next, determine the x-intercept of the graph of the equation y = 400 + 50x by substituting y = 0
switch sides
Subtract 400 from both sides
Simplify
Divide both sides by 50
Simplify
Thus, we determine that the ordered pair (-8, 0) represents the x-intercept of the equation y = 400 + 50x.
Important Tip:
- The point at which the graph crosses the y-axis is called the y-intercept.
- The point at which the graph crosses the x-axis is called the x-intercept.
The red graph on the diagram represents the equation y = 400 + 50x having the y-intercept (0, 400) and x-intercept (-8, 0)
Please check the attached diagram.
<u>The graph of the equation y = 300 + 25x</u>
Now, determine the y-intercept of the equation y = 300 + 25x by substituting x = 0
Thus, we determine that the ordered pair (0, 300) represents the y-intercept of the equation y = 300 + 25x.
Next, determine the x-intercept of the graph of the equation y = 300 + 25x by substituting y = 0
switch sides
Subtract 300 from both sides
Simplify
Divide both sides by 25
Simplify
Thus, we determine that the ordered pair (-12, 0) represents the x-intercept of the equation y = 300 + 25x.
The blue graph on the diagram represents the equation y = 300 + 25x having the y-intercept (0, 300) and x-intercept (-12, 0)
Please check the attached diagram.
Analyze the POINT OF INTERSECTION:
As we already know that the point of intersection of the two lines would give us the point at which both have the same height.
The diagram indicates that:
at x = -4, the value of y = 200.
It is the point where both lines meet.
Thus, the point of intersection of the two lines is:
(x, y) = (-4, 200)
Conclusion:
As x represents the time in minutes and y represents the height in feet.
Thus, we conclude that at x = 4 minutes, both will have the same height i.e. y = 200 feet
Therefore, we conclude that, at 4 minutes, both will have the same height which is 200 feet.
