Answer:
The length of the line segment is of 5.9 units.
Step-by-step explanation:
Distance between two points:
Suppose that we have two points,
and
. The distance between these two points is given by:
![D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
How long is the line segment?
The distance between points P and Q. So
P(1,3), and Q(4,8).
![D = \sqrt{(4-1)^2+(8-3)^2} = \sqrt{3^2 + 5^2} = \sqrt{34} = 5.9](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%284-1%29%5E2%2B%288-3%29%5E2%7D%20%3D%20%5Csqrt%7B3%5E2%20%2B%205%5E2%7D%20%3D%20%5Csqrt%7B34%7D%20%3D%205.9)
The length of the line segment is of 5.9 units.
For this case we have:
Diana:
mile in 5 minutes.
To find the speed we divide the distance by the time:
![v = \frac {\frac {3} {8}} {5} = \frac {3} {40} = 0.075 \frac {mile} {min}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%20%7B%5Cfrac%20%7B3%7D%20%7B8%7D%7D%20%7B5%7D%20%3D%20%5Cfrac%20%7B3%7D%20%7B40%7D%20%3D%200.075%20%5Cfrac%20%7Bmile%7D%20%7Bmin%7D)
Thus, Diana's speed is ![0.075 \frac {mile} {min}](https://tex.z-dn.net/?f=0.075%20%5Cfrac%20%7Bmile%7D%20%7Bmin%7D)
Fernando:
mile in ![\frac {3} {4}](https://tex.z-dn.net/?f=%5Cfrac%20%7B3%7D%20%7B4%7D)
![v = \frac {\frac {5} {2}} {\frac {3} {4}} = \frac {4 * 5} {2 * 3} = \frac {20} {6} = 3.33 \frac {mile} {min}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%20%7B%5Cfrac%20%7B5%7D%20%7B2%7D%7D%20%7B%5Cfrac%20%7B3%7D%20%7B4%7D%7D%20%3D%20%5Cfrac%20%7B4%20%2A%205%7D%20%7B2%20%2A%203%7D%20%3D%20%5Cfrac%20%7B20%7D%20%7B6%7D%20%3D%203.33%20%5Cfrac%20%7Bmile%7D%20%7Bmin%7D)
Thus, Fernando's speed is![3.33 \frac {mile} {min}](https://tex.z-dn.net/?f=3.33%20%5Cfrac%20%7Bmile%7D%20%7Bmin%7D)
We find the speed in miles per hour considering that an hour has 60 minutes.
Diana:
![0.075 \frac {mile} {min} * \frac {60} {1} \frac {min} {h} = 4.5 \frac {mile} {h}](https://tex.z-dn.net/?f=0.075%20%20%5Cfrac%20%7Bmile%7D%20%7Bmin%7D%20%2A%20%5Cfrac%20%7B60%7D%20%7B1%7D%20%5Cfrac%20%7Bmin%7D%20%7Bh%7D%20%3D%204.5%20%5Cfrac%20%7Bmile%7D%20%7Bh%7D)
Fernando:
![3.33 \frac {mile} {min} * \frac {60} {1} \frac {min} {h} = 199.8 \frac {mile} {h}](https://tex.z-dn.net/?f=3.33%20%5Cfrac%20%7Bmile%7D%20%7Bmin%7D%20%2A%20%5Cfrac%20%7B60%7D%20%7B1%7D%20%5Cfrac%20%7Bmin%7D%20%7Bh%7D%20%3D%20199.8%20%5Cfrac%20%7Bmile%7D%20%7Bh%7D)
Answer:
Diana's speed is ![0.075 \frac {mile} {min} = 4.5 \frac {mile} {h}](https://tex.z-dn.net/?f=0.075%20%5Cfrac%20%7Bmile%7D%20%7Bmin%7D%20%3D%204.5%20%5Cfrac%20%7Bmile%7D%20%7Bh%7D)
Fernando's speed is ![3.33 \frac {mile} {min} = 199.8 \frac {mile} {h}](https://tex.z-dn.net/?f=3.33%20%5Cfrac%20%7Bmile%7D%20%7Bmin%7D%20%3D%20199.8%20%5Cfrac%20%7Bmile%7D%20%7Bh%7D)
The answer is (2-3)-(4+1)
They spend $360 on clothing and entertainment.
Answer:
-68 is not a term in the given sequence
Step-by-step explanation:
The given sequence is -12, -17, -22, -27...
There is a common difference of d=-17--12=-5
The explicit rule for this sequence is ![f(n)=-12-5(n-1)](https://tex.z-dn.net/?f=f%28n%29%3D-12-5%28n-1%29)
Or ![f(n)=-5n-7](https://tex.z-dn.net/?f=f%28n%29%3D-5n-7)
To find the term that has a value of -68 we equate the explicit formula and solve for n.
![-68=-5n-7](https://tex.z-dn.net/?f=-68%3D-5n-7)
![\implies -68+7=-5n](https://tex.z-dn.net/?f=%5Cimplies%20-68%2B7%3D-5n)
![\implies -61=-5n](https://tex.z-dn.net/?f=%5Cimplies%20-61%3D-5n)
![n=\frac{61}{5} =12.2](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B61%7D%7B5%7D%20%3D12.2)
The position should be a natural number.
Since n is a decimal, it tells us that -68 is not a term in the given sequence