Answer:
20 mph
Step-by-step explanation:
Let speed of Train a = Va mph
Let speed of Train b = Vb mph
Va = Vb + 30
Let time taken for Train a = Ta
Let time taken for Train b = Tb
time taken = distance travelled/speed
Ta = 350/Va = 350/(Vb+30)
Tb = 140/Vb
But they both travel in the same amount of time.
So, Ta = Tb
![\frac{350}{v_{b} + 30}=\frac{140}{v_{b}}](https://tex.z-dn.net/?f=%5Cfrac%7B350%7D%7Bv_%7Bb%7D%20%2B%2030%7D%3D%5Cfrac%7B140%7D%7Bv_%7Bb%7D%7D)
Cross multiply
![350v_{b} = 140(v_{b} + 30)\\\\350v_{b} = 140v_{b} + 4200\\\\350v_{b} -140v_{b} = 4200\\\\210v_{b} = 4200](https://tex.z-dn.net/?f=350v_%7Bb%7D%20%3D%20140%28v_%7Bb%7D%20%2B%2030%29%5C%5C%5C%5C350v_%7Bb%7D%20%3D%20140v_%7Bb%7D%20%2B%204200%5C%5C%5C%5C350v_%7Bb%7D%20-140v_%7Bb%7D%20%3D%204200%5C%5C%5C%5C210v_%7Bb%7D%20%3D%204200)
Divide both sides by 210
![\frac{210v_{b} }{210} \frac{4200}{210} \\\\v_{b} = 20 mph](https://tex.z-dn.net/?f=%5Cfrac%7B210v_%7Bb%7D%20%7D%7B210%7D%20%5Cfrac%7B4200%7D%7B210%7D%20%5C%5C%5C%5Cv_%7Bb%7D%20%3D%2020%20mph)
4x²+4x-35=0
factor: (2x+7)(2x-5)=0
2x+7=0, or 2x-5=0
2x=-7 or 2x=5
x=-3.5 or x=2.5
I don't see any rounding necessary in this case.
when you factor ax²+bx+c, you take the two factors of a and the two factors of c, one factor of a times one factor of c, the other factor of a times the other factors, the sum of the two products make b.
in this case, the factors of 4 is 2 and 2, the factors of -35 is -5 and 7. I line them up in the following way:
2 -5
2 7
then I multiple them diagonally, the top left 2 multiplying the bottom right 7=14, and the other 2 multiplying -5=-10, 14 and -10 make a sum of 4.
if you don't get the desired sum, switch the factors up and down till you have the right combination. Note: Do not switch left and right.
I hope this makes sense to you.
Step-by-step explanation:
Use Pythagorean theorem here. To find the height, find the difference of the 2 y's. To find the length, find the difference between the 2 x's.
Length = x2 - x1
Height = y2 - y1
√length^2 + height^2 = distance
√5^2 + 5^2 = √50 = 7.07