Last night, Roberto spent 90 minutes doing homework, 2/3 hour reading, and 540 seconds making his lunch for the next day. How many more minutes did Roberto spend doing homework than he did reading and making his lunch?

41

Step-by-step explanation:

Ok, so the time for homework is already simplified to minutes.

2/3 of an hour is x/60

60/3 = 20

20*2 = 40

so 2/3 = 40/60

40/60 = 40 minutes

[]

540 seconds is..

540/60

54/6=9

9 minutes

[]

40+9 = 49

90-49 = 41

So, he spent 41 more minutes on homework than on making lunch and reading.

d

step-by-step explanation:

d

∠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.