After spending some time looking for his pump, Marlon pumps up an uninflated balloon, pumping air into it at a constant rate. He
ties the balloon with a string to prevent the air from escaping.
Which graph could represent this scenario?
Which graph could represent this scenario?
1 answer:
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The two intersection points are (-2.79, -0.58) and (0.79, 6.58).
<h3>How to find the points of intersection?</h3>
Here we want to solve the system of equations:
y = 2x + 5
x² + y² = 36
To solve this, we need to replace the first equation into the second one:
x² + (2x + 5)² = 36
Now we can solve this for x:
x² + 4x² + 10x + 25 = 36
5x² + 10x - 11 = 0
This is a quadratic equation, to solve it we use the general formula:
So we have two solutions for x:
x = (-10 - 17.9)/10 = -2.79
x = (-10 + 17.9)/10 = 0.79
To get the y-values of the solutions, we evaluate the linear equation in these values of x:
y = 2*(-2.79) + 5 = -0.58
y = 2*( 0.79) + 5 = 6.58
Then the two intersection points are (-2.79, -0.58) and (0.79, 6.58).
If you want to learn more about intersection points:
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we are given
62% of the students take math
so,
49% take science
38% take both science and math
n(M∩S)=38
now, we can use union formula
n(M∪S)=n(M)+n(S) -n(M∩S)
now, we can plug values
and we get
n(M∪S)=62+49 -38
n(M∪S)=73
so,
the percentage takes at least one science or math course is 73%..........Answer