Eli read four more biographies than historical fiction book during the semester. he also read two fewer mysteries than historical fiction books. if he read a total of eleven books during the semester how many of each type of books did he read?

Eli read 3 historical fiction books , 7 biographies and 1 mystery book.

Step-by-step explanation:

Let x be the number of historical fiction books Eli read.

Then, Number of biographies he read = x+4

Number of mysteries he read = x-2

If he read a total of eleven books during the semester , then we have the following equation :

 (Subtract 2 from both sides )

 (Divide both sides by 3)

Therefore , Number of historical fiction books Eli read = 3

Number of biographies he read = 3+4=7

Number of mysteries he read =3-2=1

Hence, Eli read 3 historical fiction books , 7 biographies and 1 mystery book.

the number of biographies books that Eli read is 7

the number of historical fiction books that Eli read is 3

the number of mysteries books that Eli read is 1

Step-by-step explanation:

Let x represent the number of biographies books that Eli read.

Let y represent the number of historical fiction books that Eli read.

Let z represent the number of mysteries books that Eli read.

Eli read four more biographies than historical fiction book during the semester. This means that

x = y + 4

He also read two fewer mysteries books than historical fiction books. This means that

z = y - 2

If he read a total of eleven books during the semester, it means that

x + y + z = 11 - - - - - - - - - - - - 1

Substituting x = y + 4 and z = y - 2 into equation 1, it becomes

y + 4 + y + y - 2 = 11

3y + 2 = 11

3y = 11 - 2 = 9

y = 9/3 = 3

z = y - 2 = 3 - 2 = 1

x = y + 4 = 3 + 4 = 7

∠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.