In Exercises 17-20, describe the possible lengths of the third side of the triangle given the lengths of the other
two sides. (See Example 5.)
17. Sinches, 12 inches 18. 12 feet, 18 feet
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19. 2 feet, 40 inches
20. 25 meters 25 meters
In Exercises 21-24, is it possible to construct a triangle
with the given side lengths? If not, explain why not.
21. 6. 7. 11
22. 3, 6, 9
23. 28. 17. 46
24. 35, 120, 125

17. the sum of the lengths of any two sides of a triangle is always greater than the length of the third side

T=the third side

12+18>T

12+T>18

18+T>12

the first equation says that T<30

the second equation says that T>6

putting these together...

6<T<30

(Credit: Arthur D)

250

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1