Answer:
the cyclists rode at 35 mph
Step-by-step explanation:
Assuming that the cyclists stopped, and accelerated instantaneously at the same speed than before but in opposite direction , then
distance= speed*time
since the cyclists and the train reaches the end of the tunnel at the same time and denoting L as the length of the tunnel :
time = distance covered by cyclists / speed of cyclists = distance covered by train / speed of the train
thus denoting v as the speed of the cyclists :
7/8*L / v = L / 40 mph
v = 7/8 * 40 mph = 35 mph
v= 35 mph
thus the cyclists rode at 35 mph
<span>The expression given (27x^2)z/(-3x^2)(z^6), can be simplify as below:
By properties of powers, if you have the same base, you can substract the exponents. Then:
=(</span>27x^2)z/(-3x^2)(z^6)
=-9z/z^6 (As you can see: x^2-2= x^0=1)
=-9/z^5 (Then, z^6-1=z^5)
<span>
Therefore, the answer is: The exponent on the variable z is 5.</span>
Answer:
Step-by-step explanation:
The power station is located 5 miles west and 6 miles north of the center of town. So if we try to locate the above points on a Cartesian plane. The co-ordinates of these points will be (-5,6).
And it is also mentioned that a power outage affected all homes and businesses within a 3 mile radius of the power station. So if we plot all the furthest points from the station affected by the power outage it will be a circle of radius 3 miles and center at (-5,6).
The equation of a circle with center (a,b) and radius r is given by :
Hence the equation of the resulting circle will be: 
Answer:
Kadeem will take 0.166 h more to complete the course.
Step-by-step explanation:
The speed is the rate at which the distance changes, when the speed goes up the distance changes more quickly, therefore if the distance is the same and the speed is higher the one who will take longer is the one that has less speed. In this case the one who will take longer to drive the 25 miles is Kadeem, since he's driving at 50 mph. In order to calculate how much longer we need to calculate the time at which each of them complete the course, this is shown below:
time = distance/speed
For Kadeem:
time = 25/50 = 0.5 h
For Quinn:
time = 25/75 = 0.334 h
The difference between the is 0.5 - 0.334 = 0.166 h.
