Abag contains white marbles and yellow marbles, 57 in total. the number of white marbles is 3 more than 5 times the number of yellow marbles. how many white marbles are there?

I would guess and check. For example, let's say there are 15 yellow marbles. Multiply by 5 and add 3 to get 78, which means it's too much. Then I guessed 8. 8 times 5 plus 3 is 43. Then I added 8 to 43 to see how many total, which would make 51. Now it's to less. Then I guessed 10. Having 10 yellow means 53 white, which is 63 total. Too many again. Then I guessed 9. 9 yellow is 48 white, which makes a total of 57. So therefore, the answer is 48 white marbles.

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

∠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.