Points d, e, and f are not in a line. to construct a circle through points d, e, and f, begin by
drawing line segments de and ef. then construct the perpendicular bisectors of de and ef, and
name the point of intersection of the perpendicular bisectors o. how do you know that point o is
the center of the circle that passes through the three points?

join all the 3 points "d, e, f," forming the triangle "def."

let the midpoint of "ef" be "m" and the midpoint of "ed" be "n". (it's in the first picture)

now, join point "i" to "e, d and f."

since 'in" is both an altitude and median to triangle "eid," then triangle "eid" is an isosceles triangle, and "ie = id "

similarly, we see that "ie = if."

the conclusion : ie = id = ef.

now we know that o is the center of the circle with radius "ie" ( = id = ef)

(note : do refer the attachments ! )

final total: 63

step-by-step explanation:

60 times sales tax

60 times 0.05

3

60 + 3

63

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)