Use the distance formula.
The distance, d, between points
and
![(x_2, y_2)](https://tex.z-dn.net/?f=%20%28x_2%2C%20y_2%29%20)
is given by the distance formula below.
![d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%20)
Now we can apply the formula to your points.
Let Point 1 be (2, 3) and Point 2 be (5, -4).
Then you have
![x_1 = 2~~~~y_1 = 3~~~~x_2 = 5~~~~y_2 = -4](https://tex.z-dn.net/?f=%20x_1%20%3D%202~~~~y_1%20%3D%203~~~~x_2%20%3D%205~~~~y_2%20%3D%20-4%20)
![d = \sqrt{(5 - 2)^2 + (-4 - 3)^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%285%20-%202%29%5E2%20%2B%20%28-4%20-%203%29%5E2%7D%20)
![d = \sqrt{(3)^2 + (-7)^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%283%29%5E2%20%2B%20%28-7%29%5E2%7D%20)
![d = \sqrt{9 + 49}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B9%20%2B%2049%7D%20)
![d = \sqrt{58}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B58%7D%20)
Answer: the distance is sqrt(58)
Answer:
A and D
Step-by-step explanation:
![{4}^{3} = 64 \\ ( {2}^{2} )^{3} = {2}^{6} \\ \\ \sqrt[5]{ {4}^{3} } = \sqrt[5]{64} \\](https://tex.z-dn.net/?f=%7B4%7D%5E%7B3%7D%20%20%3D%2064%20%20%5C%5C%20%28%20%7B2%7D%5E%7B2%7D%20%29%5E%7B3%7D%20%20%3D%20%20%7B2%7D%5E%7B6%7D%20%5C%5C%20%20%5C%5C%20%20%5Csqrt%5B5%5D%7B%20%7B4%7D%5E%7B3%7D%20%7D%20%20%3D%20%20%5Csqrt%5B5%5D%7B64%7D%20%20%5C%5C%20)
Answer:
The explicit formula that can be used is
The account's balance at the beginning of year 3 is
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above