1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gennadij [26K]
3 years ago
11

Prove the following statements: (a) For every integer x, if x is even, then for every integer y, xy is even. (b) For every integ

er x and for every integer y, if x is odd and y is odd then x y is even. (c) For every integer x, if x is odd then x 3 is odd.
Mathematics
1 answer:
Murrr4er [49]3 years ago
3 0

Answer and Step-by-step explanation:

(a) Given that x and y is even, we want to prove that xy is also even.

For x and y to be even, x and y have to be a multiple of 2. Let x = 2k and y = 2p where k and p are real numbers. xy = 2k x 2p = 4kp = 2(2kp). The product is a multiple of 2, this means the number is also even. Hence xy is even when x and y are even.

(b) in reality, if an odd number multiplies and odd number, the result is also an odd number. Therefore, the question is wrong. I assume they wanted to ask for the proof that the product is also odd. If that's the case, then this is the proof:

Given that x and y are odd, we want to prove that xy is odd. For x and y to be odd, they have to be multiples of 2 with 1 added to it. Therefore, suppose x = 2k + 1 and y = 2p + 1 then xy = (2k + 1)(2p + 1) = 4kp + 2k + 2p + 1 = 2(kp + k + p) + 1. Let kp + k + p = q, then we have 2q + 1 which is also odd.

(c) Given that x is odd we want to prove that 3x is also odd. Firstly, we've proven above that xy is odd if x and y are odd. 3 is an odd number and we are told that x is odd. Therefore it follows from the second proof that 3x is also odd.

You might be interested in
6tf & 10ft radius what the answer
guapka [62]
All you have to do is 3.14×6×10 Which is 188.4
4 0
3 years ago
WILL GIVE BRAINLIEST IF YOU GIVE AN EXPLANATION. In the packaging part of a warehouse, boxes of blue cups must be moved from the
Ugo [173]

Answer:

components: ⟨15, 75⟩, magnitude: about 76

I got this right edge 2020

3 0
3 years ago
Read 2 more answers
How many solutions does have 3x-6=3(x-2)<br>​
Anarel [89]

Answer:

Infinite.

Step-by-step explanation:

3x-6=3\left(x-2\right)

Expand:

3x-6=3x-6

Add 6 to both sides:

3x-6+6=3x-6+6

3x=3x

Subtract 3x from both sides:

3x-3x=3x-3x

0=0

No matter what x is, it doesn't affect the answer. Thus, the equation is true for all values of x.

3 0
3 years ago
A fitness club charges $25 per month as well as a one-time $80 fee of all new members which equation represents the cost in doll
madam [21]

Answer: So if you want to find the total cost (c) for a certain number of months (m) and it costs $35 per month, you just need to multiply the number of months by the cost per month. So

35m=c

If you want to see the units cancel

($35/month)(months)=$

The months will cancel out, and you will be left with total dollars.

Not sure about the second part of your question, but if you wanted to figure out how much it would cost to be a member for 6 months, you would just plug in 6 for m.

35(6)=c

c=210

So $210

Step-by-step explanation:

4 0
3 years ago
Math help please? There are 12 more toy cars than toy trucks in a box with a total of 38 toy cars and toy trucks. How many toy t
dlinn [17]
Let, the number of toy trucks = x
Then, number of toy cars = (x + 12)

Now, we have: x + x+12 = 38
2x + 12 = 38
2x = 38 - 12
2x = 26
x = 26/2
x = 13

So, there are 13 toy trucks in total.

Hope this helps!
7 0
3 years ago
Other questions:
  • Can someone help me solve for b? 2(b + 3) = 12
    5·2 answers
  • Two distinct integers, $x$ and $y$, are randomly chosen from the set $\{1,2,3,4,5,6,7,8,9,10\}$. What is the probability that $x
    6·1 answer
  • the ratio of roses to lilies in a flower arrangement is 3 to 5. how many roses would there be if there were 24 total flowers in
    11·1 answer
  • Every month, 7.00 is deducted from Jim's checking account. How much money is taking from his account for service fees in one yea
    15·1 answer
  • 2^(x-4) = 4a^(x-6) what is the value of x? ​
    14·1 answer
  • Four students received the following grades on their math quizzes. Which student could use the mode to show that she is doing be
    14·2 answers
  • Today only, a sofa is being sold at a 72% discount. The sale price is 218.40.
    7·1 answer
  • What is the solution to the system below? <br> y = -3x - 2<br> 6x + 2y = -4
    5·1 answer
  • Ram and his sister Kalpana win a prize of Rs 2000. They decide to share the prize in the ratio of their ages. Ram is 15 years ol
    5·1 answer
  • Definition of Identity property, Association property and communicative property please answer!​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!