Answer:
4 hours
Step-by-step explanation:
Given
Car 1:
![Speed = 26mph](https://tex.z-dn.net/?f=Speed%20%3D%2026mph)
![Time = h](https://tex.z-dn.net/?f=Time%20%3D%20h)
Car 2:
![Speed = 52mph](https://tex.z-dn.net/?f=Speed%20%3D%2052mph)
--- i.e. 2 hours after car 1
Required
Determine the time car 1 will meet car 2
To do this, we calculate the distance of both cars using:
![Distance = Speed * Time](https://tex.z-dn.net/?f=Distance%20%3D%20Speed%20%2A%20Time)
For Car 1:
![Distance = 26 * h](https://tex.z-dn.net/?f=Distance%20%3D%2026%20%2A%20h)
![Distance = 26h](https://tex.z-dn.net/?f=Distance%20%3D%2026h)
For Car 2:
![x^{2} Distance = 52 * (h - 2)](https://tex.z-dn.net/?f=x%5E%7B2%7D%20Distance%20%3D%2052%20%2A%20%28h%20-%202%29)
Open bracket
![Distance = 52h - 104](https://tex.z-dn.net/?f=Distance%20%3D%2052h%20-%20104)
When car 2 meets up with car 1, they are at the same distance.
So:
![26h = 52h - 104](https://tex.z-dn.net/?f=26h%20%3D%2052h%20-%20104)
Collect Like Terms
![26h - 52h = -104](https://tex.z-dn.net/?f=26h%20-%2052h%20%3D%20-104)
![-26h = -104](https://tex.z-dn.net/?f=-26h%20%3D%20-104)
Solve for h
![h = \frac{-104}{-26}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B-104%7D%7B-26%7D)
![h = 4](https://tex.z-dn.net/?f=h%20%3D%204)
<em>Car 2 will catch car 1; 4 hours from the start</em>
Answer:p = 28.36
q = 31.78
Step-by-step explanation:
Considering the smaller right angle triangle, with 50° as the reference angle, the opposite side is q and the adjacent side is 55 - p
Applying the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side
Tan 50 = q/(55 - p)
1.1918(55 - p) = q - - - - - - - - - 1
Considering the bigger right angle triangle, with 30° as the reference angle, the opposite side is q and the adjacent side is 55
Applying the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side
Tan 30 = q/55
0.5774 = q/55
q = 55 × 0.5774
q = 31.757
Substituting q = 31.757 into equation 1, it becomes
1.1918(55 - p) = 31.757
65.549 - 1.1918p = 31.757
1.1918p = 65.549 - 31.757
1.1918p = 33.792
p = 33.792/1.1918
p = 28.36
Step-by-step explanation:
24% of 800 ➡ 800 ÷ 100 × 24 = 192
75% of 1000 ➡ 1000 ÷ 100 × 75 = 750
Answer:
x = 0.25 or 1/4
Step-by-step explanation:
Answer:
x = 18; y = 20
Step-by-step explanation:
6.
Triangles KLM and KNO are similar, so the ratios of the lengths of corresponding sides are equal.
KL/KN = LM/NO
10/30 = 6/x
Cross multiply.
10x = 6 * 30
10x = 180
x = 18
KL + LN = KN
10 + y = 30
y = 20