Solve 2x ≤ 30. Round to the nearest ten-thousandth.
1 answer:
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2 Answers:
- B) The lines are parallel
- C) The lines have the same slope.
Parallel lines always have equal slope, but different y intercepts.
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Explanation:
Let's solve the second equation for y
3y - x = -7
3y = -7+x
3y = x-7
y = (x-7)/3
y = x/3 - 7/3
y = (1/3)x - 7/3
The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.
However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.
Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.
Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.
I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.
Answer:
2 minutes.
Step-by-step explanation:
Let t be the time taken in competition and the distance covered by Achilles be x miles.
We have been given that when Achilles reaches the finish line, the Turtle is 2/5 of a mile behind him. This means that distance covered by turtle will be: .
Achilles runs at a speed of 13 mph while the Turtle moves at a speed of 1 mph.
Since we know that , so we can set two equations for time taken by Achilles and turtle as:
From equation (1) we will get,
Upon substituting this value in equation (2) we will get,
Let us have a common denominator.
Upon multiplying both sides of our equation by 5 we will get,
So, the competition took 1/30 hour, let us convert our given time in minutes.
Therefore, the competition took 2 minutes.