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
![speed=\frac{distance}{time}](https://tex.z-dn.net/?f=speed%3D%5Cfrac%7Bdistance%7D%7Btime%7D)
![\Rightarrow time = \frac{distance}{speed}](https://tex.z-dn.net/?f=%5CRightarrow%20time%20%3D%20%5Cfrac%7Bdistance%7D%7Bspeed%7D)
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
![= \frac{2}{3}h](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2%7D%7B3%7Dh)
Now the speed of the bus is = (x+10) miles/h
The new time to reach the destination is
h
According to the problem,
![\frac{200}{x}-\frac{200}{x+10}=\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7Bx%7D-%5Cfrac%7B200%7D%7Bx%2B10%7D%3D%5Cfrac%7B2%7D%7B3%7D)
![\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:
15
Step-by-step explanation:
Given that a1 = 6
an = 3 + 2(an-1),
Substitute n = 2 into the formula
a2 = 3 + 2(a1)
a2 = 3 + 2(6)
a2 = 3+12
a2 = 15
Hence the second term of the sequence is 15
Bruh thats hard but still ill give it a try promises me you going to thanks me
g*f = (2x -6)*(-4x+7) = -8x2 + 14x + 24x - 42 = -8x2 + 38x - 42
<span>Then, (g*f)(1) = -8 (1)2 + 38 (1) - 42 = -12</span>
Answer:
y = -
x - 11
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 10, - 7) and (x₂, y₂ ) = (- 5, - 9)
m =
= -
, hence
y = -
x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 5, - 9 ), then
- 9 = 2 + c ⇒ c = - 9 - 2 = - 11
y = -
x - 11 ← in slope-intercept form