Which of the following do not represent the measures of the sides of a triangle? A)57, 80, 24
B) 43, 133, 89
C) 5, 6, 7
D 20, 20, 30

Explanation:

For this answer choice, we have p = 43, q = 133, and r = 89. Note how p+r = 43+89 = 132, which is not larger than the third remaining side q = 133. Therefore, p+r > q is false and a triangle cannot be formed.

A triangle is only possible if and only if adding any two sides leads to a sum larger than the third side (triangle inequality theorem).

Put another way, we must have these three conditions hold true for a triangle to form:

If any of those three are false, then we cannot make a triangle with side lengths p,q,r

Let's go over choice C for an example in which we can form a triangle

p = 5, q = 6, r = 7

We can see that,

All three conditions are true, and therefore we have a triangle that is possible with side lengths p = 5, q = 6, r = 7. I recommend cutting out slips of paper with these lengths to try it out yourself, so you have a real world example to play with. Choices A and D are a similar story to choice C, so we can rule out all three of these choices.

the infinity sign

step-by-step explanation:

replace   with   27   and simplify.

10 , 27 , 10 , 70 , 10 , 35 , 10 , 48

step-by-step explanation: