Which are the possible sides of a triangle ? a. 15, 9, 3 b. 6, 12, 19 c. 11, 6, 3 d. 4, 8, 10

Option d. 4, 8, 10

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Verify each case

case a) we have

15, 9, 3

Applying the triangle Inequality Theorem

1) 15+9 > 3

24> 3 > is true

2) 15+3 > 9

18 > 9 > is true

3) 9+3 > 15

12 > 15  > is not true

therefore

The set of lengths cannot be used to form the sides of a triangle

case b) we have

6,12,19

Applying the triangle Inequality Theorem

1) 6+12 > 19

18> 19 > is not true

therefore

The set of lengths cannot be used to form the sides of a triangle

case c) we have

11,6,3

Applying the triangle Inequality Theorem

1) 11+6 > 3

17> 3 > is true

2) 11+3 > 6

14 > 6 > is true

3) 6+3 > 11

9 > 11  > is not true

therefore

The set of lengths cannot be used to form the sides of a triangle

case d) we have

4,8,10

Applying the triangle Inequality Theorem

1) 4+8 > 10

12> 10 > is true

2) 4+10 > 8

14 > 8 > is true

3) 8+10 > 4

18 > 4  > is true

therefore

The set of lengths can be used to form the sides of a triangle

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

the solution is 12x-6y