Answer:
33.9 m
Step-by-step explanation:
cos(32) = adjacent/hypotenuse
cos(32) = X/40
X = 40cos(32)
X = 33.92192385 m
Answer:
The usually speed of the bus is 50 miles/h.
Step-by-step explanation:
Let the usual speed of the bus be x mile/hour.
We know that


The bus travels 200 miles.
To reach its destination it takes time
h
This week however the bus leaves at 5:40.
The bus late 40 minutes

Now the speed of the bus is = (x+10) miles/h
The new time to reach the destination is
h
According to the problem,

![\Rightarrow 200[\frac{x+10-x}{x(x+10)}]=\frac{2}{3}](https://tex.z-dn.net/?f=%5CRightarrow%20200%5B%5Cfrac%7Bx%2B10-x%7D%7Bx%28x%2B10%29%7D%5D%3D%5Cfrac%7B2%7D%7B3%7D)
![\Rightarrow 200[\frac{10}{x^2+10x}]=\frac{2}{3}](https://tex.z-dn.net/?f=%5CRightarrow%20200%5B%5Cfrac%7B10%7D%7Bx%5E2%2B10x%7D%5D%3D%5Cfrac%7B2%7D%7B3%7D)
⇒2(x²+10x)=200×10×3
⇒x²+10x = 3000
⇒x²+10x -3000=0
⇒x²+60x-50x-3000=0
⇒x(x+60)-50(x+60)=0
⇒(x+60)(x-50)=0
⇒x= -60,50
∴x=50 [since speed does not negative]
The usually speed of the bus is 50 miles/h.
Answer:
__
0.2676 or 0.268
Step-by-step explanation:
53 ÷198
Answer:
5y + 15x = 25, 9x - y = -4
Step-by-step explanation:
The standard form is Ax + By = C. We can make this simple by first creating the slope intercept equations of both questions:
1. y = (-3/5)x + 5
2. y = 9x + 4
For the first one, we must first get rid of the denominator by multiplying everything by 5, so we get 5y = -15x + 25, and then you can add 3x to both sides to arrive at your first standard eqn, 5y + 15x = 25.
For the second, all you need to do is swap the y and the 4, subtracting both y and 4 from each side, arriving at 9x - y = -4