Prob 1) An owner raises a $60 coat by 40% then reduces it by 40%.. When raised by 40% you multiply by 1 plus that.. so 60(1.4) = 84 Now when you reduce anything by a discount, you mult by that discount to get the discount amount.. 84(.4) = $33.60 discount.. so new price is 84-33.6 = $50.40 OR... another way .. preferred way... simply multiply the original price by (1-discount rate) to give you the new price so.. 84(1-.4) = 84(.6) = $50.40 just the same Once it is raised to 84, what discount must we apply to get it back to 60? I set it up like so.. 84(x) = 60.. but once we find x we need to subtract 1 from x to get the discount.. because same as above..original * (1-the discount rate) gives us the new price.. so to find the actual discount rate in this instance, we need to find x then subtract it from 1 to get the actual discount rate 60/84 = .714 or 71.4%.. so the discount rate is 1-.714 = .286 or 28.6%

∠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.

answer:   b

step-by-step explanation:

x2 = 16

x can not be a negative number because 16 is positive

the only answer would be positive 8  

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step-by-step explanation:

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