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disa [49]
3 years ago
7

Goran and karen walk around a track . goran walks each lap in 10 minutes. karen walks each lap in 6 minutes. they both start at

the starting line at the same time. they walk until they meet again at the starting line. answer the following questions:
How many laps does Goran complete?

How many laps does Karen complete?

How much time does it take for them to meet again at the starting line?
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
7 0
Goran completes 6. karen completes 10. it takes 60 minutes
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Answer:

\large\boxed{f(x)=(x+1)^2-4}

Step-by-step explanation:

\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================

\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================

\bold{METHOD\ 2:}\\\\\text{Use the formulas:}\ h=\dfrac{-b}{2a},\ k=f(k)\\\\f(x)=x^2+2x-3\to a=1,\ b=2,\ c=-3\\\\h=\dfrac{-2}{2(1)}=\dfrac{-2}{2}=-1\\\\k=f(-1)=(-1)^2+2(-1)-3=1-2-3=-4\\\\f(x)=(x-(-1))^2-4=(x+1)^2-4

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4 years ago
Please answer this question!
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