The difference between two numbers is 13. twice the smaller plus three times the larger is 129

18 and 31

Step-by-step explanation:

Let the number be x and y and y be the smaller number

Given

condition 1:

difference between two numbers is 13.

Mathematical expression for this will be

x-y = 13 ( taking x as larger and y as smaller number)

=> x = 13+y   (1)

Condition 2:

twice the smaller plus three times the larger is 129

Twice the smaller is equal as 2y

three times the larger is 3x

according to question

3x+2y = 129

substituting value of x from equation 1 we have

3(13+y) +2y = 129

=> 39+3y+2y = 129

=> 39+5y = 129

=> 5y = 129 - 39 = 90

=> y = 90/5

=> y = 18

Thus, y = 18

and x = 13+y = 13+18 = 31

Therefore, two numbers are 18 and 31.

∠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.

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: