Solve. Enter your answer as a mixed number. The driving distance from the sports arena to Kristina's house is 11 7 10 miles. The distance from the sports arena to Luke's house is 5 2 10 miles. How much greater is the driving distance between the sports arena and Kristina's house than between the sports arena and Luke's house? The driving distance between the sports arena and Kristina's house is miles greater than between the sports arena and Luke's house.

Step-by-step explanation:

From the sports arena to Kristina's house =

From the sports arena to Luke's house =

Subtract Luke from Kristina

There's a confusing but easy way to solve this. However, I'm going to convert into improper fractions to make it easier.

To convert to improper fraction, take the whole number, multiply it by the denominator and add it to the numerator. All over the same denominator.

Subtract them.

Convert to mixed number by dividing.

65/10=6

60

----

5

The 6 is the whole number, 5 the numerator and 10 the denominator. Remember the negative sign that we had.

5 and 10 can be simplified

5/5=1

10/5=2

Our final answer would be:

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

191 students play sports and ninety-seven 10th graders were surveyed.

step-by-step explanation: