Answer:
168). C
169). C
170). C
Step-by-step explanation:
For the first angle, it is a right angle, so it measures 90 degrees.
x and 50 are complementary angles, meaning they add up to 90 degrees.
So, subtract 50 from 90 to get 40, which is equal to x.
45 and x are supplementary angles, meaning they add up to 180 degrees.
Subtract 45 from 180 to get 35 degrees, which is the measure of angle x.
All angles in a triangle add up to 180 degrees.
So, 70 + 56 = 126, 180 - 126 = 54.
Since the unknown angle is x - 5, 54 + 5 = 59, which the the measure of angle x - 5.
Step-by-step explanation:
A man by the name of Luigi Fonti wrote this. I hope it can guide you, as it did for me! "The set of rational numbers is closed for all the four operations, so x+y, x-y, x*y and x/y are rational too. And it is easy to demonstrate. A rational number can be expressed as a fraction of two integers. So, x can be expressed as a/b and y as c/d. Hence x+y = a/b + c/d = (ad+bc)/bd, which, as fraction of two integers, is rational."
Answer:
Speed of the biker is 13 mph and that of wind is 1 mph.
Step-by-step explanation:
Given:
Time taken by the biker to cover a distance is 7 hrs when he was travelling against the speed of the wind.
Time taken to cover same distance is 6 hours when he was travelling with the speed of the wind.
We have to find the speed of the biker and that of the wind.
Let the speed of the biker is "b" mph
And the speed of the wind is "w" mph
As we know:
Distance = Product of speed and time
Re-arranging the above situation in terms of equation.
⇒
⇒ ![(b+w)\times 6 =84](https://tex.z-dn.net/?f=%28b%2Bw%29%5Ctimes%20%206%20%3D84)
⇒
...(i) ⇒
...(ii)
Multiplying equation (i) with 6 and equation (ii) with 7 so that we can eliminate one variable that is "w" after adding both the equation.
⇒
equation (iii)
⇒
equation (iv)
⇒ Adding both the equations.
⇒ ![84b=1092](https://tex.z-dn.net/?f=84b%3D1092)
⇒ ![b=\frac{1092}{84}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B1092%7D%7B84%7D)
⇒
mph.
Speed of the biker is 13 mph.
⇒ Plugging b=13 in equation (ii),we have:
⇒ ![6b+6w=84](https://tex.z-dn.net/?f=6b%2B6w%3D84)
⇒ ![6w=84-6b](https://tex.z-dn.net/?f=6w%3D84-6b)
⇒ ![6w=84-6(13)](https://tex.z-dn.net/?f=6w%3D84-6%2813%29)
⇒
⇒ ![6w=6](https://tex.z-dn.net/?f=6w%3D6)
⇒ ![w=\frac{6}{6}](https://tex.z-dn.net/?f=w%3D%5Cfrac%7B6%7D%7B6%7D)
⇒
mph.
Speed of the biker is 13 mph and the speed of the wind is 1 mph whenever the biker is with the speed of the wind the biker's speed increases by 1 mph and subsequently decreases when he is against the speed of the wind.
Answer:
Both buses will arrive at the stop at 6:52 AM
Step-by-step explanation:
Wilkenson Bus = Arrives every 21 minutes
Harris Road Bus = Arrives every 15 minutes
Let's find the Least Common Multiple (LCM) of 21 and 15. LCM is found, listing the prime factors of each numbers and then multiplying each factor the greatest number of times it occurs in either numbers:
LCM 21 = 3 × 7
LCM 15 = 3 × 5
LCM (21 , 15) = 3 × 7 × 5 = 105
In 105 minutes both buses will arrive at the same time again
105 minutes = 1 h 45 min
5:07 AM + 1h 45 min = 6:52 AM
Hey there! I'm happy to help!
First, let's turn these into improper fractions. We keep the denominators and to find the new numerator you multiply the denominator by the whole number and add then numerator.
![\frac{18}{5} *\frac{19}{7} =\frac{342}{35} =9\frac{27}{35}](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B5%7D%20%2A%5Cfrac%7B19%7D%7B7%7D%20%3D%5Cfrac%7B342%7D%7B35%7D%20%3D9%5Cfrac%7B27%7D%7B35%7D)
Therefore, the answer is 9 27/35. Now you can multiply mixed numbers!
Have a wonderful day!