Two tangents are drawn to a circle from an external point. If the measure of the major arc is 260º, what is the measure, in degrees, of the angle formed by the two tangents?

80degrees

Step-by-step explanation:

Using the expression to get the minor arc;

minor arc + major arc = 360degrees

minor arc + 260 = 360

minor arc = 360 - 260

minor arc = 100degrees (central angle)

Note that the central angle and that formed from the intersection of the tangents (X) are supplementary. Hence;

100 + X = 180

X = 180 - 100

X = 80degrees

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)