Which of the following side lengths can form a triangle? a. 2 in, 3 in, and 7 in b. 21 cm, 23 cm, and 44 cm c. 12 mm, 36 mm, and 53 mm d. 14 ft, 17 ft, and 30 ft

The sum of the length of the two sides of the triangle must be greater than the length of the third side.

A.

2 + 3 = 5 < 7 NOT

B.

21 + 23 = 43 < 44 NOT

C.

12 + 36 = 48 < 53 NOT

D.

14 + 17 = 31 > 30

14 + 31 = 45 > 17

17 + 31 = 48 > 14

CORRECT

D. 14 ft, 17 ft, and 30 ft

the answer would be c:   ax + b = ax + c

step-by-step explanation:

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)