We invested $7000 invested in two accounts, we don't know how much exactly is in each account, therefore we will assign variables to these amounts. The amount invested in the "8%" account is "x", while the other one is "y". The sum of these two numbers must be equal to $7000, therefore:
The sum of interest of each account should be equal to 580, therefore:
We need to solve the system in order to determine the values.
Now we can replace the value of "x" in the first equation to determine the value of "y".
The values are 6500 in the 8% account and 500 in the 12% account.
Answer: Conjecture: There is no triangle with side lengths N, 2N, and 3N (where N is a positive real number)
Proof:
We prove this by contradiction: Suppose there was an N for which we can construct a triangle with side lengths N, 2N, and 3N. We then apply the triangle inequalities tests. It must hold that:
N + 2N > 3N
3N > 3N
3 > 3
which is False, for any value of N. This means that the original choice of N is not possible. Since the inequality is False for any value of N, there cannot be any triangle with the given side lengths, thus proving our conjecture.
Answer:
If one angle of a triangle is 110 deg and the other two angles are both 35 deg, then the figure is an obtuse isosceles triangle.
First Way:
7: 10am to 8:00am = 50 mins
8:00am to 8:15am = 15 mins
Total = 50 min + 15 min = 65 mins = 1 hour 5 mins
Second Way:
7: 10am to 8:10am = 1 hour
8:10am to 8:15am = 5 mins
Total = 1 hour + 5 mins = 1 hour 5 mins
Answer : 1 hour 5 mins
