christine runs 10 miles in 75 minutes. at the same rate, how many miles would she ru
i miles

 miles  [or, 9.2 miles]

Step-by-step explanation:

Complete Question:

Christine runs 10 miles in 75 minutes. At the same rate, how many miles would she ru n in 69 minutes?

Solution:

We need to find the unit rate first and then find our answer. To get unit rate, we need to know the number of miles she runs in "1 minute". So, we will divide number of miles by number of minutes, that is given. Hence:

That means in 1 minute, Christine runs 2/15th of a mile.

Now, we want to know how many miles she will run in 69 minutes. We simply multiply unit rate (2/15) by the number of minutes (which is 69). Thus we have:

In decimal, doing division, that is 9.2 miles

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0