Part (1)
n is some positive integer. Let's say for now that n is even. So n = 2k, for some integer k
This means n-1 = 2k-1 is odd since subtracting 1 from an even number leads to an odd number.
Now multiply n with n-1 to get
n(n-1) = 2k(2k-1) = 2m
where m = k(2k-1) is an integer
The result 2m is even showing that n(n-1) is even
------------
Let's say that n is odd this time. That means n = 2k+1 for some integer k
And also n-1 = 2k+1-1 = 2k showing n-1 is even
Now multiply n and n-1
n(n-1) = (2k+1)(2k) = 2k(2k+1) = 2m
where m = k(2k+1) is an integer
We've shown that n(n-1) is even here as well.
------------
So overall, n(n-1) is even regardless if n is even or if n is odd.
Either n or n-1 will be even. If you multiply an even number with any number, the result will be even.
=======================================================
Part (2)
n is some positive integer
2n is always even since 2 is a factor of 2n
2n+1 is always odd because we're adding 1 to an even number. The sequence of integers goes even,odd,even,odd, etc and it does this forever.
-----------
Another way to see how 2n+1 is odd is to divide 2n+1 over 2 and you'll find that we get (2n+1)/2 = 2n/2+1/2 = n+0.5
The 0.5 at the end is not an integer, so there's no way that (2n+1)/2 is an integer; therefore 2n+1 is odd.
What two products would you add to find 713x48
9514 1404 393
Answer:
40·713 and 8·713
Step-by-step explanation:
When this multiplication is carried out "by hand", the usual sum of partial products is ...
8·713 + 40·713
Answer:
5704, 28520
Step-by-step explanation:
First find the product of 713 x 48 which is 34224. Next, we find the two products to do so we first add 713 x 8 = 5704.Then,we multiply 713 x 40 which is 28520. This strategie is multiply by the ones then by the tens and add them together to find the your answer.
12.
Bharathi borrows an amount of 12500 al 12% per annum for 3 years at a simple inters
and Madhuri borrows the same amount for the same time period at 10% per annum
compounded annually. Who pays more interest and by how much?
Answer:
Step-by-step explanation
For bharathi
Principal,P =Rs 12500
Simple interest Rate,R = 12%
Time period,n = 3 years.
Simple Interest, SI at 12% for 3 years =
(12500×12×3)/100
= Rs 4500
For Madhuri
Principal,P =Rs 12500
Compound interest Rate,R = 10% p.a.
Time period,n = 3 years.
Amount when interest is compounded annually
C.i=A-P
C.i=(1+R/100)^3-p
=12500((1+10/100)^3-12500
=12500(11/10)^3-12500
=[(125×11×11×11)/10×10×10]-12500
=16637.50-12500
=4137.50
Bharathi pays more interest and Rs (4500 - 4137.50) = Rs 362.50 more.
The number of miles a car can drive varies directly with the number of gallons of gas in
the car. If the car can go 81 miles on 3 gallons of gas, how many gallons does the car
need to go 378 miles?
Answer:
14 gallons
Step-by-step explanation:
Answer:
14 gallons
Step-by-step explanation:
solve for z: -4 - (z - 6) = 12
Answer:
z = -10
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
-4 - (z - 6) = 12
Step 2: Solve for z
Distribute negative: -4 - z + 6 = 12Combine like terms: -z + 2 = 12Subtract 2 on both sides: -z = 10Divide -1 on both sides: z = -10Step 3: Check
Plug in z to verify it's a solution.
Substitute: -4 - (-10 - 6) = 12Subtract: -4 - (-16) = 12Simplify: -4 + 16 = 12Add: 12 = 12Here we see that 12 does indeed equal 12.
∴ z = -10 is a solution of the equation.
Answer:
z = -10
Step-by-step explanation:
-4 -(z+6)=12
2-z=12
-z =12-2
ans= z = -10
Solve for x in the following angle relationship. Please also identify the type of angles given:
answer options
O x= 10, corresponding
O x = 4, corresponding
O x = 10, alternate interior
O x = 4, Same side interior
9514 1404 393
Answer:
x= 10, corresponding
Step-by-step explanation:
Corresponding angles are in the same direction from their respective intersections. Here, the angles are both northwest of the point where the lines cross. The angles are corresponding.
__
Corresponding angles are congruent, so we have ...
10x +10 = 110
10x = 100 . . . . . subtract 10
x = 10 . . . . . . . . divide by 10
Geena is meeting her brother at a cafe on Bradford Rd and Blanco Rd. She is currently on the corner of Lafayette Ave. and Blanco Rd.
Her brother tells Geena that the shortest route is straight down Blanco Rd.
Geena disagrees. She thinks the shortest route is down Lafayette Ave., turn onto Smith St., then on Blanco Rd. until she reaches the cafe.
Who is correct? What is the difference in the two routes?
Answer:
THEY ARE BOTH IN DIFFERENT PLACES??
Answer:
.25
Step-by-step explanation:
PLS ANSWER ASAP!!!!!
The temperature is dropping at a rate of 2.5 degrees for 4.25 hours. How much did the temperature change?
Group of answer choices
A.) -10.625 degrees
B.) -6.75 degrees
C.) 10.625 degrees
D.) 6.75 degrees
Answer:
A
Step-by-step explanation:
Answer:
The correct answer would be A.
Can someone plzz answer this!!?
Answer: B Angle Side Angle
Step-by-step explanation:
Since line AB and CD are parallel angles D and A are congruent by the alternate interior theorem and both angles AOB and DOC are congruent by the vertical angle theorem and it already shows line OC and line OB are congruent.
Find the value of all angles
Answer:
Step-by-step explanation:
This means that <C and <F are congruent.
So 2x - 15 = x + 15 Add 15 to both sides
2x-15+15=x+15+ 15
2x = x + 30 Subtract x from both sides
2x-x=x-x+30
x = 30
I've taken the bottom 2 angles to be equal. The lettering says they
are
4x - 3y = 13
8x - 6y = 26
Solve systems of equations through elimination method please!
Answer: 0 = 0
Many solutions
Step-by-step explanation:
4x - 3y = 13
8x - 6y = 26
-2(4x - 3y = 13)
-8x + 6y = -26
8x - 6y = 26
You can cross them all out and you’ll get 0 = 0 which also means many solutions
Given: 4d=1/3(c-d) Proof= c=13d
Proof:
Multiply both of the sides by 3. You would get 12d = c - d. Add d on both sides, and you would get c = 12d
Here, we are required to proof c = 13d from 4d=1/3(c-d)
Ultimately, c = 13d (proof)
We have;
4d=1/3(c-d)Cross product
4d × 3 = c - d
therefore, By collecting like terms;
C = 12d +d
and Ultimately, c = 13d ......
Read more:
https://brainly.com/question/21406377
HELP ASAPPP!!! !!!! PLEASE
Answer:
B.
Step-by-step explanation:
for decimals, you start with tenths, so it would be thousandths
HELP ASAP PLS AND THANKS!!!!
Answer:
The first one
23·4 1 6 +37·4 1 6 HOW DO I DO THIS?!?!?
Answer
60.832
Step-by-step explanation:
Combine the numbers
HOPE THIS HELPS YOU....
Joshua uses his thermometer and finds the boiling point of ethyl alcohol to be 75o C. He looks in a reference book and finds that the actual boiling point of ethyl alcohol is 80oC. What is his percent error?
Answer:
the percent error is 6.25%
Step-by-step explanation:
The computation of the percent error is shown below:
Percent error is
= (Experimental value - accepted value) ÷ (experimental value) × 100
= (80 degrees - 75 degrees) ÷ (80 degrees) × 100
= (5 degrees) ÷ (80 degrees) × 100
= 0.0625 × 100
= 6.25%
hence, the percent error is 6.25%
We simply applied the above formula so that the correct value could come
And, the same is to be considered
Answer:
6.25
Step-by-step explanation:
I just did this
Brainliest!! Pls help
Answer:
its c
Step-by-step explanation:
that one is shaded down other one is shaded up (up = greater)( down= less)
The total bill at a restaurant was $52.50. If you want to tip the waitress 15%, how much tip should you leave?
A. $7.87
B. $7.88
C. $78.70
D. $78.75
Answer:
B
Step-by-step explanation:
52.50*0.15=7.875
7.875 rounded is 7.88
hope this helps :3
if it did pls mark brainliest
Answer:
B)$7.88
Step-by-step explanation:
15% = 0.15
52.50 x 0.15 = 7.875
Round to the nearest hundredth
$7.88
question is in the picture
Answer: d,f
[tex]-x\geq 4\\=> x\leq -4[/tex]
=> all the values are d and f
Step-by-step explanation:
(-4, 12) and (-7, -3)
(Write an equation of the line in point slope form that passes through the giving points)
Answer:
5
Step-by-step explanation:
Use the slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{-3-12}{-7-(-4)}[/tex] = [tex]\frac{-15}{-3}[/tex] = 5
3f+7=1
Plz write explanation
Answer:
f = -2
Step-by-step explanation:
3f + 7 = 1
or, 3f = 1 - 7
or, 3f = -6
or, f = -6/3
or, f = -2
True or False: A function must have a different output for each input.
Answer:
True
Step-by-step explanation:
for every X there can be on Y
that doesn't necessarily go the other way around, but that's not what the problem is asking, so whatever.
Nathan goes to the store and buys 4 shorts and 3 shirts for 85.5$. He later goes to the same store and buys 3 shorts and 5 shirts for 115$. What is the price for each shirt and each shorts?
cAn SOmeOnE PLeAse HELp ME WIth Math
Answer: B
Step-by-step explanation:
I did this last year so I can recall how to solve it :p
(barely)
Adelaide has a credit card with a company that charges $3.00 for every day a payment is late. If she paid $492.93 for a bill that is 3 days late, how much was the bill without the late fee?
Which one should I choose
Answer:
Third one
C.
Step-by-step explanation:
Evaluate the expression when a=14 and b=6. 5b/32a2
Answer:
28/16071 as a decimal 0.00174226...
Step-by-step explanation:
Hope this helps!
Help please!! If you can't see the photo well just let me know <3
Answer: The second one and fourth one.
Step-by-step explanation: did this already and got it right :)
Crystal bought b boxes of cookies to bring to a party. Each box contains 18 cookies. She decides to keep two boxes for herself. She brings 90 cookies to the party. Which equation can be used to find the number of b boxes Crystal bought?
A) 2b − 18 = 90
B) 18b − 2 = 90
C) 18b − 36 = 90
D) 36 − 18b = 90
Answer:b
Step-by-step explanation:
she took 2 boxes and there is 18 per box 18 times b = 90
Question 1 of 10
Which of Saturn's moons has an atmosphere that is most like Earth's?
O A. Pandora
B. Atlas
Ο Ο
C. Titan
O
D. Europa
SUBMIT
Answer:
The answer is Titan
Step-by-step explanation: the atmosphere of Titan is similar to earth's atmosphere because Titan's atmosphere is mostly made up of nitrogen and so is Earth's atmosphere.
If you ever see a cheetah coming to you Don’t PANIC it should be going up to you very fast get ready and when it comes pound it in the chest and get up on your toes and act to be tall and the cheetah will be scared of you and shoutout to evansandre2007 and vc538720 for my 1st and 2nd Friends add me and thank me For more
Answer:
you would have to be still!
Step-by-step explanation:
