2. (a) Use a prove by contradiction to show that if a and b are nonzero integers such that a divides b and a + b is odd, then a is odd. (b) Prove that if n is a positive integer, then n² does not equal 2(mod 4).
Answers
a. Assume a is even, so a = 2k for some integer k. Now let a and b be integers such that a divides b and a + b is odd.
Since a divides b, b = an for integer n, and in turn b = 2nk, which means b is even and hence a + b is also even. But this contradicts our initial assumption, so a must be odd.
b. Let n be even, so that n = 2k for some integer k. Then
n² = (2k)² = 4k²
so that n² ≡ 0 (mod 4).
Now let n be odd, so n = 2k + 1 for integer k. Then
n² = (2k + 1)² = 4k² + 4k + 1
so that n² ≡ 1 (mod 4).
Therefore n² is never congruent to 2 (mod 4).
Related Questions
It is 9 kilometers from Charlie's house to the nearest mailbox. How far is it in meters?
Be sure to include the correct unit in your answer.
Answers
Answer:
Step-by-step explanation:
9,000 meters
Create 2 equations that are equivalent to 3x - 12 = 24
Answers
Answer:
1st equation: 3(12) - 12 = 24
2nd equation: 36 - 12 = 24
Answer:
3(12) - 12 = 24
Step-by-step explanation:
2/7 converted into a decimal then rounded to 3 decimal places.
Answers
Answer:
0.286
Step-by-step explanation:
Hope this helps
)) Type the missing numbers in this sequence: -3, -8, -13, -18,
Answers
Answer:
23
Step-by-step explanation:
first off if your to take away 3 from 8 you'd get five and the same goes for the rest
I.e
8-3=5
13-8=5
18+5=23
as 23 -18 would give you you 5
what is 1 1/2 of 150 and what is 1/2 of 180
Answers
Answer:
1 1/2 of 150 is 225 and 1/2 of 180 is 90
Step-by-step explanation:
1 1/2 of 150 basically means 1 1/2 x 150, which equals to 225. 1/2 of 180 means 1/2 x 180 which is 90.
Answer:
1 1/2 of 150 is "225" and
1/2 of 180 is "90"
Step-by-step explanation:
1 1/2 of 150 basically means 1 1/2 x 150, which equals to 225. 1/2 of 180 means 1/2 x 180 which is 90.
Hope this helps :)
Three business partners, Ren, Jaffary and Abel put money into a business in the ratio 2:3:4. From the profits they shared, Abel got 3400 dollars. How much did ren and Jaffary receive?
HELP GUYS PLS I HAVE 3 MIN TO GO
Answers
Answer:
Ren has 755.4
Jaffray has 1,133.1
Abel has 1,510.8
Decide where the first digit of the quotient should be placed. Do not complete the division. The first digit in the quotient of 1.593 ÷ 64 is in place.
Answers
9514 1404 393
Answer:
hundredths place
Step-by-step explanation:
When performing long division, the first digit of the quotient appears over the least significant digit of the first portion of the dividend that is greater than or equal to the divisor.
Here, when performing long division we compare ...
64 vs 1 . . . no quotient digit
64 vs 15 . . . no quotient digit
64 vs 159 . . . the first quotient digit appears with the same place value as the 9 in 1.59. That is, the first quotient digit will be 0.02, 2 in the hundredths place.
Answer:
hundreths place
Step-by-step explanation:
6.2 Margin of error and the confidence interval. A study of stress on the campus of your university using the College Undergraduate Stress Scale (CUSS) reported an average stress level of 1123 (a higher score indicating more stress) with a margin of error of 43 for 95% confidence. The study was based on a random sample of 400 undergraduates. a. Give the 95% confidence interval. b. If you wanted 99% confidence for the same study, would your margin of error be greater than, equal to, or less than 43
Answers
Using confidence interval concepts, it is found that:
a. The 95% confidence interval is (1080, 1166).
b. The margin of error would be greater than 43.
Item a:
The interval is the sample mean plus/minus the margin of error, hence:
[tex]1123 - 43 = 1080[/tex]
[tex]1123 + 43 = 1166[/tex]
The 95% confidence interval is (1080, 1166).
Item b:
The margin of error is direct proportional to the critical value.The higher the confidence level, the higher the critical value, and thus, the higher the margin of error.Hence: The margin of error would be greater than 43.
A similar problem is given at https://brainly.com/question/25675821
Anyone know the answer to this plz
Answers
Answer:
Domain: -10 < x < 10
Range: -2 < y < 8
Step-by-step explanation:
Hope this helps!
In grade 10, the ratio of boys to girls is 2: 3. There are 75 girls. How many are boys?
HELP PLEASE .. I WILL GIVE A BRAINLIEST !
Answers
Answer:
150
Step-by-step explanation:
The ration is 2/3 in this example means they are twice as many boys than girls. If boys = 2/3, than girls = 1/3.
So, to find the answer, you must multiply 75 by 2, which is 150.
You don't need this, but they are 75 + 150 = 225 boys and grils in grade 10.
2 short questions
Please help
Answers
Answer:
b c = 5.25p this is the answer
For the first problem shown the answer is number B.
It is B because we our always going up by $5.25
For our second one it isn't a function,
it isn't a function because it follows the same rule through-out it besides at the end of it.
Juan is paid a salary of $2400 biweekly. Find Juan's earnings per year. (use only numbers) $
Answers
Therefore to find Juan’s earnings, you multiply 26 by $2400
26 x 2400 = $62,400
Juan’s earnings per year is $62,400
8 m good wire how long is the wire in millimeters
Answers
Answer:
Converting m to mm
=> 1 m = 1000 mm
=> 8 m = 8000 mm
Therefore,
The wire will be 8000 mm long.
Hope it helps you...
Please mark as brainlliest!!!
Solve for x: -2(x + 3) = -2x - 6
A. 0
B. 3
C. All real numbers
D.No solution
Answers
Answer:
D.No solution
Answer:
C
Step-by-step explanation:
-2(x + 3) = -2x - 6 Remove the brackets
-2x - 6 = -2x - 6
Since the left and right sides are equal, any number will work.
If you wind up with a false statement, then there are no solutions.
2x + 4 = 2x + 7 Subtract 2x from both sides.
4 = 7
1.)Which of the following is a linear inequality in two variables?
a. 3x≤16
b. 3m-4m>5
c. 9q+4<12
d. 11+2t ≥ 3?
Answers
[tex] \large╚»★«╝ { \mathcal{Answer }}╚»★«╝[/tex]
The Correct option among them is B
[tex] \sf3m - 4n > 5[/tex]_____________________________________
The other options have one variable each, but according to the given question there should be two variables in the inequality.
The only choice satisfying the conditions is Option B
having two variables in it ( that is "m" and "n" )
[tex] ꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]
what is the domain and range?
Answers
Help me please ill mark you brainly
Answers
Answer:
The first one is -6x The second one is 18a to the power 3
Step-by-step explanation:
Four subtracted from x is less than 18.
Answers
Answer:
x - 4 < 18
Step-by-step explanation:
< means less than
> means more than
Can someone explain it step by step ?
Answers
Answer:
1. (x - 1) × (x + 3)
2. x = 3 and y = -2
Step-by-step explanation:
x² + 2x - 32x + 3y = 0; y = 3x - 11rewrite the equation:
y = 3x - 11; 2x + 3y = 0
solve y = 3x - 11 for the y:
y = 3x - 11
substitute 3x - 11 for y in 2x + 3y = 0;
2x + 3y = 0;
2x + 3y = 0
2x + 3 (3x - 11) = 0
11x - 33 = 0 (simplify both sides of the equation)
11x - 33 + 33 = 0 + 33 (add 33 to both sides)
11x = 33
11x/11 = 33/11 (divide both sides by 11)
x = 3
subtitute 3 for x in y = 3x - 11
y = 3x - 11
y = (3)×(3) - 11
y = -2
I showed one equation because the other is self explanatory, hope this helps.
Write money amounts using a leading zero if necessary & with 2 decimal places (For example: 0.80 or 0.72 or 1.23)
630 miles in 10 hours
miles per hour
donut hole per kid
24 donut holes for 8 kids
$
$3.50 for 5 lbs. of apples
$32 for a 14 2/9 km taxi ride.
per pound
per km
$
Answers
9514 1404 393
Answer:
63 mph3 donut holes per kid$0.70 per pound$2.25 per kmStep-by-step explanation:
In this context, "per" and "for" mean "divided by."
630 mi/(10 h) = 63 mi/h(24 dh)/(8 kid) = 3 dh/kid$3.50/(5 lb) = $0.70 /lb$32/(14 2/9 km) = $32/(128/9 km) = $(9/4)/km = $2.25 /kmSolve the following system using the elimination method
−8y+6x=36
6x−y=15
Answers
Answer:
a
Step-by-step explanation:
Answer:
C. (2, -3)
Step-by-step explanation:
Problem 3.2
The tires on a mining truck are 14 feet tall.
Is this measurement the diameter, radius, or
circumference?
Diameter
Radius
Circumference
Answers
Answer:
it is Circumference this is my answer
Answer:
circumfrence
Step-by-step explanation:
HELP! Can anyone help me i need help it this question
Answers
Average rate = distance / time
Rewrite distance as an improper fraction":3 1/3 = 10/3
Now you have 10/3 / 1/3
When dividing by a fraction flip the second fraction over and multiply:
10/3 x 3/1 = (10 x 3) / (3/1) = 30/3 = 10
Average rate was 10 miles per hour
HELLP ILL GIVE BRSINLY
Answers
m = 180 - CBE = 180 - [ 360 - BDC - BED - (180 - DCE - DEC)] = 180 - [ 360 - 90 -90 - (180 - 13*2)] = 154
P/s: 180 - DCE - DEC = CDE
ok done. Thank to me :>
Solve for x
5(x+8)=2x−7+8(x−1)
Answers
Answer:
x = 11
Step-by-step explanation:
5(x+8) = 2x - 7 + 8 (x - 1)
5x + 40 = 2x - 7 + 8x - 8
5x + 40 = 2x + 8x - 7 - 8
5x + 40 = 10x - 15
40 + 15 = 10x - 5x
55 = 5x
5x = 55
x = 55/5
x = 11
x=11
Step-by-step explanation:
5x+40=2x-7+8x-8
5x+40=10x-15
10x-5x=40+15
5x=55
x=55/5
x=11
help on math review edu
Answers
Answer:
Answer is A
Step-by-step explanation:
Subtract 47 from both sides to get 0
3x² - 18x - 42 = 0
Use Quadratic formula to get
[tex]3+\sqrt{23} \\3-\sqrt{23}[/tex]
Answer:
Step-by-step explanation:
a submarine is submerged to a depth of 650 feet below sea level the ascends 225 feet. Determine the current position of the submarine
Answers
Answer:
Step-by-step explanation:
Ascending means moving towards the surface.
So the submarine is 340 feet below sea level.
The submarine ascends 76feet.
∴
340
−
76
=
264
f
e
e
t
below sea level.
Answer: 425 feet
Step-by-step explanation:
650 - 225 = 425
ascend is positive
650 is technically negative
5. The coordinate increments from (4, 3) to (9, 7) are :
6. The coordinate increments from (- 6, - 4) to (12, - 9) are:
7. The coordinate increments from (10, - 7) to (14, - 9) are: are:
8. The coordinate increments from (- 47, - 10) to ( 17 , 8) are:
Answers
Answer:
the correct answer is 8
Step-by-step explanation:
Answer:
5. Is "+" 6. is "-" 7. is "+" 8. is "-"
Step-by-step explanation:
Given the following PARALLELOGRAM, find the measure of each angle below.
Answers
Answer:
m∠BEC = 65°
m∠DEC = 115°
m∠DAE = 78°
m∠ECD = 40°
m∠BAD = 118°
m∠ADC = 62°
Step-by-step explanation:
m∠BEC = 65°
Opposite angles formed by intersecting lines are congruent
m∠DEC = 180 - 65 = 115°
A straight line has a degree measure of 180
m∠DAE = 78°
Opposite interior angles of two parallel lines cut by a transversal are congruent
m∠ECD = 180 - [m∠DEC + 25] = 40°
Sum of angles inside triangle ECD has a measure of 180
m∠BAD = 78 + m∠ECD = 118°
Opposite angles of a parallelogram are congruent
2(m∠BAD) + 2(m∠ADC) = 360
118 + m∠ADC = 180
m∠ADC = 62°
Sum of angles inside a parallelogram = 360°
can someone plz help with this FAST
I WILL MARK BRAINIEST
Answers
Answer:
A. 1.56
Step-by-step explanation:
[0(3) + 1(9) + 2(10) + 3(2) + 4(1)] / [3 + 9 + 10 + 2 + 1]