5 points A farmhouse shelters 10 animals. Some are goats and some are ducks. Altogether there are 36 legs. How many ducks and goats are there?​

2 ducks and 8 goats

Step-by-step explanation:

let goat be g

let duck be d

d + g = 10

ducks have 2 legs, 2d

goats have 4 legs, 4g

2d + 4g = 36

making d the subject in the first equation;

d = 10 - g

put in second equation

2(10 - g) + 4g = 36

20 -2g + 4g = 36

2g = 36 - 20

2g = 16

g = 8

if g is 8

d = 10 - 8

d = 2

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5