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kati45 [8]
3 years ago
8

Evaluate ƒ(x) = –4x – 5 for x = –1.

Mathematics
1 answer:
Alenkinab [10]3 years ago
7 0

Change your f(x) to y.(they are pretty much the same thing)

Plug in your -1 into the 'x' spot.

-4(-1)-5

multiply -4 and -1 to get 4(negative times a negative = a positive)

4-5

subtract.

-1

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Use strong mathematical induction to prove the existence part of the unique factorization of integers theorem (Theorem 4.4.5). I
valentina_108 [34]

Answer:

Lets say that P(n) is true if n is a prime or a product of prime numbers. We want to show that P(n) is true for all n > 1.

The base case is n=2. P(2) is true because 2 is prime.

Now lets use the inductive hypothesis. Lets take a number n > 2, and we will assume that P(k) is true for any integer k such that 1 < k < n. We want to show that P(n) is true. We may assume that n is not prime, otherwise, P(n) would be trivially true. Since n is not prime, there exist positive integers a,b greater than 1 such that a*b = n. Note that 1 < a < n and 1 < b < n, thus P(a) and P(b) are true. Therefore there exists primes p1, ...., pj and pj+1, ..., pl such that

p1*p2*...*pj = a

pj+1*pj+2*...*pl = b

As a result

n = a*b = (p1*......*pj)*(pj+1*....*pl) = p1*....*pj*....pl

Since we could write n as a product of primes, then P(n) is also true. For strong induction, we conclude than P(n) is true for all integers greater than 1.

5 0
3 years ago
On a recent trip to the convenience​ store, you picked up 3 gallons of​ milk, 6 bottles of​ water, and 8 ​snack-size bags of chi
SVETLANKA909090 [29]

Answer:

The answers to the question are as follows

A bottle of water costs  $2.00

A gallon of mik cots $4.10 and

A bag of chips costs $1.00

Step-by-step explanation:

To solve the question, it is important to note that it is a word problem hence we read the question carefully to clearly understnd and be able to interprete the message from any perspective

We list out the variables as follows

Number of gallons of milk = 3

Number of bottles of water = 6

Number of chips bags = 8

Bill before tax = $32.30

Price of a bottle of water = twice the price of a bag of chips

Price of a gallon of mlk  = $ 2.10 + price of a bottle of water

Therefore in order to find out how much each item costs let us call the price of  bottle of water $x say

This means that the price of a bag of chips = x/2 and

The price of a gallon of milk = x + $2.10

Therefore  we have by multiplying the prices of the items to their respective quantities and summing up

$(6x + 3(x+2.1)+ 8 x/2) = $32.3

This gives by expanding the values 6x+3x+6.3+4x =32.3

13x+6.3 =32.3

13x = 32.3 - 6.3 = 26

Dividing both sides by 13 gives

x = $2.00

This means that a bottle of water costs  $2.00

A gallon of mik cots $2.00+$2.10 = $4.10

A bag of chips costs x/2 which is equal to $2.00/2 = $1.00

8 0
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finlep [7]

Answer:

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Step-by-step explanation:

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yawa3891 [41]

Answer:

➩ 2,250 envelopes.

Step-by-step explanation:

Given that, Nicole buys 125 envelopes per box for her home office.

Therefore, She will have 18*125 envelopes in all

So, 18*125 is 2,250 envelopes

6 0
3 years ago
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