<span>Let x = the miles Jeanie ran
y = the miles Jeanie biked
T = 2 hours total time for the duathlon
v1 = 8.5 mph Jeanie's running speed and
v2 = 16 mph Jeanie's biking speed
But T = Jean's time she ran t1 + time she biked t2 I. e t1 + t2 = 2
So we have average speed v2 when she biked = distance (y) / time (t2)
Distance y = v2 * t2 = 16 * t2 and distance when she ran x = 8.5 * t1
Since she covered 27 miles while running and biking we have
x + y = 27
8.5t1 + 16t2 =27 ------(1)
t1 + t2 = 2 --------------(2)
The simultaneous equation gives us
t1 = 2/3 and t2 which is time she biked = 4/3
So 4/3 = 1 1/3. Which is 1 hour 20 minutes</span>
Answer:
1 / X² -4 = (- 1/4) / (X+2) + (1/4) / (X - 2)
Step-by-step explanation:
1 / x²-4 = 1 / (X+2) * (X-2)
1 / X²-4 = (A / X+2) + (B / X-2) = (AX - 2A + BX +2B) / X² -4
∴ 1 = (A + B) * X - 2 (A - B)
A + B = 0
- 2 (A - B) = 1
A - B = - 1/2
∴ 2A = - 1/2
A= - 1/4
B= 1/4
1 / X² -4 = (- 1/4) / (X+2) + (1/4) / (X - 2)
Answer:
T(x, y) = (x - 5, y - 6)
Step-by-step explanation:
The transformation T is a translation that creates an image P' of original point P by adding 5 to the x-coordinate and 6 to the y-coordinate of the original point P.
Now you want to transform point P' into point P, so you are undoing the first transformation. You need to do the opposite of what the transformation above does. You need to subtract 5 from the x-coordinate and subtract 6 from the y-coordinate.
Answer: T(x, y) = (x - 5, y - 6)
Answer:
from 3 o’clock until 3:20, the minute hand will move 1/3 of the way around the circle or 120 degrees. But the hour hand has also moved 1/3 of the way to the next number, or 10 degrees.