Write an informal negation for each of the following statements. Be careful to avoid negations that are ambiguous. Some suspicions were substantiated. 1. All suspicions were substantiated. 2. All suspicions were unsubstantiated. 3. Some suspicions were unsubstantiated. 4. There is at least one suspicion that was unsubstantiated. 5. There is at least one suspicion that was substantiated. slader

See below

Step-by-step explanation:

To write informal negations, change the existential quantifiers "some, there exists" for universal quantifiers "All, for every" and viceversa. Then write the informal negation of the statement after the quantifiers:

1) Some suspicions were unsubstantiated.

2) Some suspicions were substantiated.

3) All suspicions were substantiated.

4) No suspicions were unsubstantiated. Equivalently, Every suspicion was substantiated.

5) No suspicions were substantiated. Equivalently, Every suspicion was unsubstantiated.

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.