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: 72.8%
Step-by-step explanation:
This is a geometric sequence of the form:
a(n)=(x+3)(-2x)^(n-1) because each term is -2x times the previous term...so
a(8)=(x+3)(-128x^7)
a(8)=-128x^8-384x^7
Answer:
rotational symmetry of 60 degrees around the origin - yes
rotational symmetry of 120 degrees around the origin - yes
Step-by-step explanation:
A regular hexagon has 6 congruent angles
the the angles created on the line of symmetry are equal to 60 so the angle of rotational symmetry is 60 degrees.
The regular hexagon, like stated before, has 6 congruent angles so the order of symmetry is 6
Here is a visual from basic-matematics
