Lukas wants to create a triangle with sides measuring 9 in., 13 in., and 15 in. he says that more than one triangle is possible given these side lengths. which statement about lukas’s claim is true?
a)lukas is incorrect. the side lengths satisfy the triangle inequality rule so one unique triangle can be drawn.
b)lukas is incorrect. the side lengths do not satisfy the triangle inequality rule so no triangles can be drawn given these side lengths.
c)lukas is correct. the side lengths satisfy the triangle inequality rule so multiple triangles can be drawn.
d)lukas is correct. the side lengths do not satisfy the triangle inequality rule so multiple triangles can be drawn.

A) Lukas is incorrect. The side lengths satisfy the triangle inequality rule so one unique triangle can be drawn.

Step-by-step explanation:

We know that unique triangles are triangles that do not have  an identical. This means there is not another  triangle that has the exact dimensions or shape.

Since 9+13=22>15

13+15=28>9

9+15=24>13

Thus given side lengths 9 in., 13 in., and 15 in. satisfy the triangle inequality.

We know that if we all three side lengths of a triangle then only one unique triangle can be drawn with the given side lengths.

Thus, A is the right answer. Lukas is incorrect. The side lengths satisfy the triangle inequality rule so one unique triangle can be drawn.

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