Acircular jogging track forms the edge of a circular lake that has a diameter of 2 miles. johanna walked once around the track at the average rate of 3 miles per hour. if t represents the number of hours it took johanna to walk completely around the lake, which of the following is a correct statement?
a. 0.5< t < 0.75
b. 1.75< t < 2.0
c. 2.0 < t < 2.5
d. 2.5 < t < 3.0
e. 3 < t < 3.5

C. 2.0 < t < 2.5

Step-by-step explanation:

Diameter of track (D) = 2 miles, Average rate (A) = 3 miles per hour

A = distance/ time

time (t) = distance/A

distance around the track (circumference) = πD = 3.142 × 2 miles = 6.284 miles

t = 6.284miles/3miles/hour = 2.1 hour

Therefore, 2.0 < t < 2.5

slope is 35 and 20 miles is the y-intercept.

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4