Answer:
Jet= 420 mph Wind = 10mph
Step-by-step explanation:
The speed of the plane in a tailwind can be modeled by x+y where x is the speed of the plane and y is the speed of the wind. Dividing 1290 by 3 gets you the average speed of the jet in a tailwind, which is 430.
The speed of the plane in a headwind can be modeled by x-y where x is the speed of the plane and y is the speed of the wind. Dividing 1230 by 3 gets you the average speed of the jet in a tailwind, which is 410.
This can be modeled by a system of equations, where x+y=430 and x-y=410. Solving the equation you get x=420 and y=10.
So, the speed of the jet is 420 mph and the speed of the wind is 10 mph.
Answer: 69
Step-by-step explanation:
You can use simultaneous linear equations in two variables to solve this word problem.
Let Juwan's age be
![x - years](https://tex.z-dn.net/?f=x%20%20-%20years)
and Christy's age be
![y - years](https://tex.z-dn.net/?f=y%20-%20years)
Let us sum their ages and equate it to 92
![x + y = 92 - - - (1)](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2092%20-%20%20-%20%20-%20%281%29)
Ten years ago, Juwan's age was
![(x - 10)years](https://tex.z-dn.net/?f=%28x%20-%2010%29years)
and Christy's age was
![(y - 10)years](https://tex.z-dn.net/?f=%28y%20-%2010%29years)
By then Juwan's age was 3 times Christy's age
![(x - 10) = 3(y - 10)](https://tex.z-dn.net/?f=%28x%20-%2010%29%20%3D%203%28y%20-%2010%29)
Expand and simplify,
![x - 10 = 3y - 30](https://tex.z-dn.net/?f=x%20-%2010%20%3D%203y%20-%2030)
![x = 3y - 20 - - (2)](https://tex.z-dn.net/?f=x%20%3D%203y%20-%2020%20-%20%20-%20%282%29)
Put equation (2) in equation (1)
![3y - 20 + y = 92](https://tex.z-dn.net/?f=3y%20-%2020%20%2B%20y%20%3D%2092)
![4y = 112](https://tex.z-dn.net/?f=4y%20%3D%20112)
![y = 28](https://tex.z-dn.net/?f=y%20%3D%2028)
![x = 3(28) - 20 = 64](https://tex.z-dn.net/?f=x%20%3D%203%2828%29%20-%2020%20%3D%2064)
Juwan is 64 now
Answer:
$4261.71
Step-by-step explanation:
Montesquieu's annual payment is ...
(12 mo) × ($124.30/mo) = $1491.60
This is the 35% of the cost that is not paid by his employer. So, the total cost can be found from ...
$1491.60 = 0.35 × annual premium
$1491.60/0.35 = annual premium ≈ $4261.71
Given:
The figure of triangle ABC.
The area of the triangle ABC is D.
![m\angle B=\sin ^{-1}(\dfrac{m}{n})](https://tex.z-dn.net/?f=m%5Cangle%20B%3D%5Csin%20%5E%7B-1%7D%28%5Cdfrac%7Bm%7D%7Bn%7D%29)
To find:
The value of m and n in the given expression.
Solution:
Let h be the height of the triangle ABC.
Area of a triangle is:
![Area=\dfrac{1}{2}\times base\times h](https://tex.z-dn.net/?f=Area%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20base%5Ctimes%20h)
Where, b is the base and h is the height of the triangle.
![Area=\dfrac{1}{2}\times a\times h](https://tex.z-dn.net/?f=Area%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20a%5Ctimes%20h)
The area of the triangle ABC is D.
![D=\dfrac{1}{2}\times a\times h](https://tex.z-dn.net/?f=D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20a%5Ctimes%20h)
![2D=ah](https://tex.z-dn.net/?f=2D%3Dah)
...(i)
In a right angle triangle,
![\sin \theta =\dfrac{Perpendicular}{Hypotenuse}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3D%5Cdfrac%7BPerpendicular%7D%7BHypotenuse%7D)
![\sin B =\dfrac{h}{c}](https://tex.z-dn.net/?f=%5Csin%20B%20%3D%5Cdfrac%7Bh%7D%7Bc%7D)
[Using (i)]
...(ii)
We have,
...(iii)
On comparing (ii) and (iii), we get
![m=2D](https://tex.z-dn.net/?f=m%3D2D)
![n=ac](https://tex.z-dn.net/?f=n%3Dac)
Therefore, the required values are
.