D =√(x2-x1)^2 + (y2-y1)^2
......._____________
5 =√(3-0)^2 + (k-1)^2
.......__________
5 =√3^2 + (k-1)^2
25 = 9 + (k-1)^2
16 = k^2 - 2k + 1
k^2 -2k - 15 = 0
(k - 5)(k + 3) = 0
k - 5 = 0.....or.......(k + 3) = 0
k = 5.........or.......k = -3
A there are no real zeros
using the discriminant b² - 4ac to determine the nature of the zeros
for y = x² + 4x + 5 ( with a = 1, b = 4 and c = 5 )
• If b² - 4ac > 0 there are 2 real and distinct zeros
• If b² - 4ac = 0 there is a real and equal zero
• If b² - 4ac < 0 there are no real zeros
b² - 4ac = 16 - 20 = - 4
Since discriminant < 0 there are no real zeros
After putting the value of y from the second equation to the first equation, the resultant equation is
.
GIven:
The equations are:

It is required to put the value of y from second equation to the first equation.
<h3>How to solve equations?</h3>
The value of y from the second equation is,

Now, put this value of y in the first equation as,

Therefore, after putting the value of y from the second equation to the first equation, the resultant equation is
.
For more details about equations, refer to the link:
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Calculating the z-score provides additional information regarding how each subject did overall as the z-score takes dispersion into account.
<h3>What is a z score?</h3>
Z-score indicates how much a given value differs from the standard deviation. For example, the mean of a test could be a 73 and if a student scored an 85, that's great.
However, if the data is not spread out, that 85 could be the highest in the class by 10 points. That's much more information than just 15 points above the mean. This way you can tell when someone not only did well but did exceptionally well in comparison to his or her peers.
Learn more about z score on:
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