Hernandez has 17 tomato plants that she wants to plant in rows. she will put 2 plants in some rows and 1 plant in the others. how many different ways can she plant the tomato plants?

There are 17 total plants of tomatoes, lets count case per case assuming that the order does not matter (because we don't have any information about if the plants are indistinguishable or anything like that)

1) 17 rows with one plant each.

2) 15 rows with one plant, one row with two

3) 13 rows with one plant, 2 with two plants

4) 11 rows with one plant, 3 with two plants

5) 9 rows with one plant, 4 with two plants

6) 7 rows with one plant, 5 with two plants

7) 5 rows with one plant, 6 rows with two plants

8) 3 rows with one plant, 7 rows with two plants

9) 1 row with one plant, 8 rows with two plants.

So, if the order of these rows does not matter, there are 9 ways in which the plants can be ordered.

∠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.