Step-by-step explanation:
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Answer: 2.2 units</h3>
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Explanation:
I'll define these point labels
- B = Blake's starting position
- F = finish line
- C = the third unmarked point of the triangle
The locations of the points are
- B = (-8,1)
- C = (-6,-3)
- F = (4,-2)
Use the distance formula to find the distance from B to C
![B = (x_1,y_1) = (-8,1) \text{ and } C = (x_2,y_2) = (-6,-3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-8-(-6))^2 + (1-(-3))^2}\\\\d = \sqrt{(-8+6)^2 + (1+3)^2}\\\\d = \sqrt{(-2)^2 + (4)^2}\\\\d = \sqrt{4 + 16}\\\\d = \sqrt{20} \ \text{ ... exact distance}\\\\d \approx 4.47214 \ \ \text{... approximate distance}\\\\](https://tex.z-dn.net/?f=B%20%3D%20%28x_1%2Cy_1%29%20%3D%20%28-8%2C1%29%20%5Ctext%7B%20and%20%7D%20C%20%3D%20%28x_2%2Cy_2%29%20%3D%20%28-6%2C-3%29%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-8-%28-6%29%29%5E2%20%2B%20%281-%28-3%29%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-8%2B6%29%5E2%20%2B%20%281%2B3%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-2%29%5E2%20%2B%20%284%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B4%20%2B%2016%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B20%7D%20%5C%20%5Ctext%7B%20...%20exact%20distance%7D%5C%5C%5C%5Cd%20%5Capprox%204.47214%20%5C%20%5C%20%5Ctext%7B...%20approximate%20distance%7D%5C%5C%5C%5C)
Segment BC is roughly 4.47214 units long.
Following similar steps, you should find that segment CF is approximately 10.04988 units long.
If Blake doesn't take the shortcut, then he travels approximately BC+CF = 4.47214+10.04988 = 14.52202 units. This is the path from B to C to F in that order.
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Use the distance formula again to find the distance from B to F. This distance is about 12.36932 units. He travels this amount if he takes the shortcut.
Subtract this and the previous result we got
14.52202 - 12.36932 = 2.1527
That rounds to 2.2
This is the amount of distance he doesn't have to travel when he takes the shortcut.
In other words, the track is roughly 2.2 units shorter when taking the shortcut.
Side note: Replace "units" with whatever units you're working with (eg: feet or meters).
Answer:
Natural numbers
Step-by-step explanation:
Rational numbers are numbers which can be expressed in the form a/b ; such that b ≠ 0 ; hence, rational numbers can be certain non-recurring decimal values.
Integer values are numbers which can be written without any fractional component. While natural numbers are characterized as being whole and non-negative
To represent population values, number of people or species cannot be fractional and cannot be negative, hence natural numbers is the best option.
First thing First. You must find have a common denominator. If you want to find it then you do this
3: 3 6 9 12 15 18 21
7: 7 14 21 28
Once you found a number they have in common (21) You do this next
3/7 * 3/3 = 9/21
2/3 * 7/7 = 14/21
Now the next thing you do is subtract your numerators but not the denominators
14-9=5
5/12
you cant simplified so your done! Hope this helps!!!! <span />