In the form of a paragraph, explain in complete sentences, your answers to the following questions. include the final answer in your explanation. complete your work in the space provided or upload a file that can display math symbols if your work requires it. lisa is an avid runner and is training for a marathon. this week, over a span of six days, she ran a total of 38.4 miles. the distances, in miles, that lisa ran throughout the week are as follows: 3.2, 7.5, 9.8, 11.5, 2.9, 3.5. what was the average distance of each run? lisa's goal for this week is to run an average of 6 miles per day. how many miles does she need to run tomorrow (the 7th day) in order to achieve her goal of 6 miles per day for the week?

Lisa is an avid runner and is training for a marathon, so she runs everyday to achieve this purpose. In this way, she goes out to run for six days, so we have the following data set regarding the miles she runs:

1st day  = 3.2    miles
2nd day = 7.5    miles
3rd day  = 9.8    miles
4th day  = 11.5  miles
5th day  = 2.9    miles
6th day  = 3.5    miles

Finally, she ran a total of:

3.2+7.5+9.8+11.5+2.9+3.5 = 38.4 miles

What was the average distance of each run? 

This result can be get as the sum of each run (or the total of miles she run) divided by the numbers of days she ran.



Lisa's goal for this week is to run an average of 6 miles per day. How many miles does she need to run tomorrow (the 7th day) in order to achieve her goal of 6 miles per day for the week?

Let's name x the distance she must run tomorrow. Therefore, the equation for this purpose is given as follows:



∴

Isolating x:



∴ 

Therefore, she need to run:

in order to achieve the goal of 6 miles per day.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12