The easiest way to find the vertex is to convert this standard form equation into vertex form, which is y = a(x - h)^2 + k.
Firstly, put x^2 - 10x into parentheses: y = (x^2 - 10x) + 30
Next, we want to make what's inside the parentheses a perfect square. To do that, we need to divide the x coefficient by 2 and square it. In this case, the result is 25. Add 25 inside the parentheses and subtract 25 outside of the parentheses: y = (x^2 - 10x + 25) + 30 - 25
Next, factor what's inside the parentheses and combine like terms outside of the parentheses, and your vertex form is: y = (x - 5)^2 + 5.
Now going back to the formula of the vertex form, y = a(x - h)^2 + k, the vertex is (h,k). Using our vertex equation, we can see that the vertex is (5,5).
Answer: x=4
Steps: (I am assuming your question has a typo in it and by "c" you meant "x")
The rational expression equals zero
only when the numerator equals 0 (the denominator cannot ever be zero):
and that happens only for x=4
The balance in Yolanda's saving plan after 14 years is; $9,455.36
<h3>How to calculate future value?</h3>
We want to find the balance in Yolanda's saving plan after 14 years.
For Yolanda;
PV = 0
PMT = 250
i% = 4%/12 = 0.33%
N = 14 yrs * 12 = 168
FV = ?
For Zach:
PV = 0
PMT = $3300
i% = 4%
N = 14 yrs
FV = ?
From online future value calculator, we have;
Yolanda FV = $9,455.36
Zach FV = $47,204.19
Read more about Future Value at; brainly.com/question/24703884
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The prime factorization of 36 would be B. 2 x 2 x 3 x 3
