Letaandbbe integers andda positive integer.(a) Prove that ifddividesaandddividesb, thenddivides botha+banda−b.(b) Is the converse of the above true? If so, prove it. If not, give a specific example ofa, b, dshowingthat the converse is false.

See step by step explanation.

Step-by-step explanation:

Recall that given two integers a, b, a divides b if there exists an integer k such that b = ka.

Let a,b,d be integers, such that d>0.

a) Suppose that d divides a and d divides b. Then, there exists such that and . Consider a+b and a-b. Replacing the previous equation, we have that

Since then and are both integers. Then, d divides both a+b and a-b.

b) It is false. Let a = 7, b = 5. Then d = 2 divides a+b (12) and a-b (2) but neither 2 divides 7 nor 2 divides 5.

answer: what are the following choices

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get