In 2012 there were approximately 8,950 public libraries in the United States. A survey found that 76% of those libraries offered
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The equation that has the solution is 3x^2 - 10x + 6 = 0
The solution is given as:
The solution to a quadratic equation is
By comparing both equations, we have:
-b = 5
b^2 - 4ac = 7
2a = 3
Solve for b in -b = 5
b = -5
Solve for a in 2a = 3
a = 1.5
Substitute values for a and b in b^2 - 4ac = 7
(-5)^2 - 4 * 1.5c = 7
Evaluate
25 - 6c = 7
Subtract 25 from both sides
-6c = -18
Divide by - 6
c = 3
So, we have:
a = 1.5
b = -5
c = 3
A quadratic equation is represented as:
ax^2 + bx + c = 0
So, we have:
1.5x^2 - 5x +3 = 0
Multiply through by 2
3x^2 - 10x + 6 = 0
Hence, the equation that has the solution is 3x^2 - 10x + 6 = 0
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Using Pythagorean theorem, the student walked 53.58 meters more compared to the total displacement from the starting point.
If a student walks 100 meters north, then 100 meters west, then the path he travels resembles the sides of a right triangle (see attached photo).
Using Pythagorean theorem, we can solve for the total displacement from the starting point to the end point.
c^2 = a^2 + b^2
where c is the total displacement from the starting point to the end point
a is the distance he walks up north
b is the distance he walks to the west
c^2 = 100^2 + 100^2
c^2 = 10,000 + 10,000
c^2 = 20,000
c = 141.42 meters
Comparing the total distance the student walked and the total displacement from the starting point to the end point by subtraction.
100 meters + 100 meters - 141.42 meters = 53.58 meters
Learn more about Pythagorean Theorem here: brainly.com/question/343682
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