A number between 10 and 20 is both a foctor of 60 anda multiple of 6.What is the number?
1 answer:
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Given:
I have walked 20% of the way to school.
I have 1200 metres more to walk than when I have 20% of the walk remaining.
To find:
The distance from home to school.
Solution:
Let x be the distance from home to school.
I have already walked 20% of the way to school and i have 1200 metres more to walk than when I have 20% of the walk remaining.
It means 1200 is of the total distance from home to school.
Therefore, the distance from home to school is 2000 metres.
9514 1404 393
Answer:
obtuse
Step-by-step explanation:
The law of cosines tells you ...
b² = a² +c² -2ac·cos(B)
Substituting for a²+c² using the given equation, we have ...
b² = b²·cos(B)² -2ac·cos(B)
We can subtract b² to get a quadratic in standard form for cos(B).
b²·cos(B)² -2ac·cos(B) -b² = 0
Solving this using the quadratic formula gives ...
The fraction ac/b² is always positive, so the term on the right (the square root) is always greater than 1. The value of cos(B) cannot be greater than 1, so the only viable value for cos(B) is ...
The value of the radical is necessarily greater than ac/b², so cos(B) is necessarily negative. When cos(B) < 0, B > 90°. The triangle is obtuse.