Answer:
24 in
Step-by-step explanation
Using pythagorean theorem, since OP is 20 inches and has a midpoint. RP= 10 and OR=10. The hypotenuse is given as 26 so do 26^2=10^2+a. 676= 100+a^2, subtract 100 from both sides. square root of 576 is 24
732.4 because just put in a decimal before a # and then do place value to a whole #.
Answer:
Step-by-step explanation:
abc = 1
We have to prove that,
![\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2Ba%2Bb%5E%7B-1%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2Bc%5E%7B-1%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bc%2Ba%5E%7B-1%7D%7D%3D1)
We take left hand side of the given equation and solve it,
![\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2Ba%2B%5Cfrac%7B1%7D%7Bb%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2B%5Cfrac%7B1%7D%7Bc%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bc%2B%5Cfrac%7B1%7D%7Ba%7D%7D)
Since, abc = 1,
and c = ![\frac{1}{ab}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bab%7D)
By substituting these values in the expression,
![\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2Ba%2B%5Cfrac%7B1%7D%7Bb%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2B%5Cfrac%7B1%7D%7Bc%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bc%2B%5Cfrac%7B1%7D%7Ba%7D%7D%3D%5Cfrac%7B1%7D%7B1%2Ba%2B%5Cfrac%7B1%7D%7Bb%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2Bab%7D%2B%5Cfrac%7B1%7D%7B1%2B%5Cfrac%7B1%7D%7Bab%7D%2B%5Cfrac%7B1%7D%7Ba%7D%7D)
![=\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{ab}{ab+1+b}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bb%7D%7Bb%2Bab%2B1%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2Bab%7D%2B%5Cfrac%7Bab%7D%7Bab%2B1%2Bb%7D)
![=\frac{1+b+ab}{1+b+ab}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%2Bb%2Bab%7D%7B1%2Bb%2Bab%7D)
![=1](https://tex.z-dn.net/?f=%3D1)
Which equal to the right hand side of the equation.
Hence, ![\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2Ba%2Bb%5E%7B-1%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bb%2Bc%5E%7B-1%7D%7D%2B%5Cfrac%7B1%7D%7B1%2Bc%2Ba%5E%7B-1%7D%7D%3D1)
Answer:
30 minutes
Step-by-step explanation:
Walk rate = 88 paces/ minute
Average length of pace = 0.875 m
Time taken to walk 2.31 km ;
The distance in metres :
1000 m = 1 km
2.31 km = (1000 * 2.31) = 2310 m
Recall :
Time taken = distance / speed
Distance walked in a minute = 88 * 0.875 = 77 m
Time taken = 2310 / 77
Time taken = 30 minutes
Answer:
x = 4
y = 11
Step-by-step explanation:
You can make the equations 3x - 1 = 2x + 3
x = 4
y = 11