Pythagoras theorem: leg 1 squared + leg 2 squared = hypotenuse squared
In the diagram, the triangle has angles 90 and 45. So the other angle in the triangle must be 45 degrees as well. (180 - 90 -45 = 45)
This means it is an isosceles triangle (since two angles are the same), so the two legs have the same length.
So we can say that length of leg1 = x, and the length of leg2 also equals x
Now let's use pythagoras' theorem:
leg1 = x
leg2 = x
hypotenuse = 16
x^2 + x^2 = 16^2
2x^2 = 16^2
2x^2 = 256
x^2 = 128
x = √(128)
x = 8√2
Check the picture below, so let's check the equations below hmmm
![\boxed{A}\\\\ y=\cfrac{16-3x}{4}\implies y=\cfrac{-3x+16}{4}\implies y = \cfrac{-3x}{4}+\cfrac{16}{4}\implies y=-\cfrac{3}{4}x\stackrel{\stackrel{b}{\downarrow }}{+4}~\hfill \bigotimes \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cboxed%7BA%7D%5C%5C%5C%5C%20y%3D%5Ccfrac%7B16-3x%7D%7B4%7D%5Cimplies%20y%3D%5Ccfrac%7B-3x%2B16%7D%7B4%7D%5Cimplies%20y%20%3D%20%5Ccfrac%7B-3x%7D%7B4%7D%2B%5Ccfrac%7B16%7D%7B4%7D%5Cimplies%20y%3D-%5Ccfrac%7B3%7D%7B4%7Dx%5Cstackrel%7B%5Cstackrel%7Bb%7D%7B%5Cdownarrow%20%7D%7D%7B%2B4%7D~%5Chfill%20%5Cbigotimes%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
I am presuming that the question is who won or by how much did the winner win.
distance equals rate times time, or d = r*t
For the Hare d = 1600 and r = 10
1600 = 10 t
Divide both sides by 10
t = 160
The hare finished in 160 seconds
For the tortoise d = 1600 - 780 = 820 (due to the head start) and r = 5.3
820= 5.3 t
Divide both sides by 5.3
t = 154.72 (rounded to the hundredths place)
The tortoise won by 5. 28 seconds (160-154.72)
Answer:
0.375 cups or 3/8
Step-by-step explanation:
divide 3/4, or 0.75 by 2!
