The possible value of the third length is an illustration of Triangle inequality theorem
The possible third lengths are 4 units and 6 units
<h3>How to determine the possible length of the third side?</h3>
To determine the third length, we make use of the following Triangle inequality theorem.
a + b > c
Let the third side be x.
So, we have:
x + 6 > 3
x + 3 > 6
3 + 6 > x
Solve the inequalities
x > -3
x > 3
x < 9
Remove the negative inequality value.
So, we have:
x > 3 or x < 9
Rewrite as:
3 < x or x < 9
Combine the inequality
3 < x < 9
This means that the possible value of the third length is between 3 and 9 (exclusive)
Hence, the possible third lengths are 4 units and 6 units
Read more about Triangle inequality theorem at:
brainly.com/question/2403556
Answer: Andy has 41 books
Erica has 82 books
Clay has 56 books
Step-by-step explanation:
Let x represent the number of books that Andy has.
Let y represent the number of books that Erica has.
Let z represent the number of books that Clay has.
Andy, Erica, and Clay have a collection of books totaling 179 books. This means that
x + y + z = 179 - - - - - - - - -1
Erica has twice as many books as Andy. It means that
y = 2x
Andy has 15 fewer books than Clay. It means that
x = z - 15
z = x + 15
Substituting y = 2x and z = x + 15 into equation 1, it becomes
x + 2y + x + 15 = 179
4x = 179 - 15 = 164
x = 164/4 = 41
y = 2x = 2×41 = 82
z = x + 15 = 41 + 15 = 56
1.) 5x + 10y = 15 => x + 2y = 3 => 3x + 6y = 9
2.) -9x - 12y = 6 => 9x + 12y = -6 => 3x + 4y = -2
3.) -2x + 4y = -5 => 2x - 4y = 5 => 4x - 8y = 10