It was recently estimated that homes without children outnumber homes with children by seven to five. If there are 3564 homes in the county, how many of them are homes without children

2079

Step-by-step explanation:

Homes without children outnumbers homes with children by about 7 to 5 ;

If number of children = 3564

Number of homes without children :

Expressing the relaship interms of ratio :

Without children : with children = 7 :5

Total ratio = 7 + 5 = 12

Number of homes without children:

(7 / 12) * 3564

0.5833333 * 3564

= 2079

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

⭐⭐

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.