We will use the Unitary method to solve this question
304/4=76
Therefore The train travels 76 miles per hour
76*7.5=570
Therefore the train travels 570 miles in 7.5 hours
Answer:
(2,0)
Step-by-step explanation:
The solution of the inequality
is shown in attached diagram.
The boundary line is dotted line, because the sign of inequality is without notion "or equal to". The dotted line means that points lying on this line are not solutions of the inequality. The solutions are those points lying in the shaded region.
From the points (0,2), (2,0), (1,-2), (-2,1) only point (2,0) lies on the shaded region, so only point (2,0) is a solution to the inequality
Calleigh should put in 30 pennies
Answer:
The coordinate of the rest stop is: ![(5,2.5)](https://tex.z-dn.net/?f=%285%2C2.5%29)
The distance between the hotel and the stadium is 32 miles
Step-by-step explanation:
Given
--- Team hotel
--- Stadium
Solving (a): The coordinates of the rest stop
The rest stop is at half way;
So, the coordinate is:
![(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x_1%2Bx_2%2Cy_1%2By_2%29)
This gives:
![(x,y) = \frac{1}{2}(3+7,4+1)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%283%2B7%2C4%2B1%29)
![(x,y) = \frac{1}{2}(10,5)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2810%2C5%29)
Open bracket
![(x,y) = (5,2.5)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%285%2C2.5%29)
Solving (b): Distance between the hotel and the stadium
We have:
--- Team hotel
--- Stadium
The distance (d) is:
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D)
So, we have:
![d = \sqrt{(3 - 7)^2 + (4 - 1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%283%20-%207%29%5E2%20%2B%20%284%20-%201%29%5E2%7D)
![d = \sqrt{(-4)^2 + 3^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28-4%29%5E2%20%2B%203%5E2%7D)
![d = \sqrt{16 + 9}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B16%20%2B%209%7D)
![d = \sqrt{25}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B25%7D)
![d =5](https://tex.z-dn.net/?f=d%20%3D5)
From the question, we have:
![1\ unit = 6.4\ miles](https://tex.z-dn.net/?f=1%5C%20unit%20%3D%206.4%5C%20miles)
So:
![d =5 * 6.4\ miles](https://tex.z-dn.net/?f=d%20%3D5%20%2A%206.4%5C%20miles)
![d =32\ miles](https://tex.z-dn.net/?f=d%20%3D32%5C%20miles)