Just checking if the two questions are correct

63. The right answers are (a) y < 0 and (e) |y| > 1

64. Yes, you're right, answer is A. 7 1/5.

Step-by-step explanation:

Question 63.

In x * y = z, we know that x is positive, that z is negative and we know the absolute value of x is greater than the absolute value of z.

How can a positive number (x) be turned in a negative number (z) through multiplication?  By multiplying it by a negative number (y).

So, if y is negative...

we can safely say that y < 0 and that the |y| > 1.

We can say |y| > 1 because y can't equal 0 (because z > 0) and |y| can't be equal to 1 since |x| > |z|, if |y| = 1, then we'd have |x| = |z|.

Question 64.

You got your fractions addition right!

If we begin by calculating the total amount of onions the restaurant now has...

Then we split it into two equal buckets, we get...

Answer is then A.  

i dony know

step-by-step explanation:

∠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.