prove that 5^(2n - 1) is divisible by 8

Answers

Answer 1

Your teacher must have made a typo somewhere. The expression 5^(2n-1) is not divisible by 8.

The expression 5^(2n-1) is composed of 2n-1 copies of "5" multiplied together. The key here is that 5 is the only unique prime factor of this number.

On the other hand, 8 = 2*2*2 = 2^3 showing that 2 is the only prime factor for this number. At this point, we can see that there's no way that 5^(2n-1) is divisible by 8. It all comes down to the clash of the primes 5 and 2 not matching up, and having nothing in common.

Let's consider a few concrete examples:

If n = 1, then 5^(2n-1) = 5^(2*1-1) = 5^1 = 5 which is not divisible by 8. The number 5/8 = 0.625 isn't an integer.If n = 2, then 5^(2n-1) = 5^(2*2-1) = 5^3 = 125 which is also not a multiple of 8. The number 125/8 = 15.625 isn't an integer.

I'll let you try other natural numbers for n, and you'll find that [tex]\frac{5^{2n-1}}{8}[/tex] isn't an integer.

Related Questions

3/4+5/6 divided by 2/3 in simplest form show work, please!
Thanks!

Answers

Answer:

2 [tex]\frac{3}{8}[/tex]

Step-by-step explanation:

3/4 + 5/6 (lowest common denominator = 12)

= 9/12 + 10/12

= 19/12

19/12 ÷ 2/3 (reciprocate 2/3 to replace division sign by multiplication sign)

= 19/12 x 3/2

= 57/24

= 19/8

= 2 [tex]\frac{3}{8}[/tex]

Hope this helps :)

This question is really bothering me: A restaurant has a square floor with an area of 324 m². Sketch the resaurant floor. What are its dimensions?

Answers

324= 18m

I am positive 18m is the correct answer, sorry if I am wrong. Make sure to check before submitting

The required dimensions of the restaurant is 18 by 18 meters.

Given that,

This question is really bothering me: A restaurant has a square floor with an area of 324 m². Sketch the restaurant floor. dimensions are to be evaluated.

What is surface area?

Surface area is defined as the collective region, whose mathematical expression can be formed.

here,

Let the sides of the square restaurant be a,
The area of the restaurant = area of the square
324 = a²
a = √324
a = 18 meters,

Thus, the required dimensions of the restaurant are 18 by 18 meters.

Learn more about surface area here:
https://brainly.com/question/2835293

#SPJ5

Sam bought a toy for $400 and sold it at a profit of 10% of the cost price. Calculate the SELLING PRICE of the toy.

Answers

Answer:

10% = 0.1 x 400 = 40

400 - 40 = 360$

3x9 is 27

9,18,27

if you need more support just ask me ;)

Answers

Answer:

genius confirmed?? O.o

Step-by-step explanation:

Manz is too goated on da stix

Wait what’s the question

ول
니,

If Susie takes a test with 50

questions and gets 4/5 of them

correct, how many questions did
she miss?

Answers

Answer:

Step-by-step explanation

4/5=40/50 50-40= 10.

M is the midpoint of PQ. MQ=5x+8 and PQ = 6x+56, find PM

Answers

Answer:

PM = 58

Step-by-step explanation:

The question tells us that the full line has a value of 6x+56. The midpoint divides this line into equal pieces. We are also given the value of half (MQ) of the line (5x+8). By subtracting 5x+8 from 6x+56, we can figure out the value of the other half of the line (PM).

This gives us the expression for PM: x+48

Now, since these are both the two parts of the midpoint, by definition, we know they're equal.

You equal both equations and get x=10

You plug in 10 as x in the expression we got for PM (10+48), which gives us the value 58.

The second hand of the clock is 3.7 cm long. Find the linear speed of the tip of the second
hand as it's passes around the clock face.
O 0.00646 cm per sec
O 172.03 cm per sec
O 0.387 cm per sec
2.87 cm per sec

Answers

Answer:

I'd look it up would probably work if not see if someone else might be able to help you out with this

Pls explain!!!
Pls and thank you

Answers

Answer:

A = L x W

A = 3 3/4 x 1 1/2

A = (you do the math, 3 3/4 x 1 1/2 : )

Step-by-step explanation:

Hope this helps! Please gie brainliest

Answer:

The formula to find the AREA of a rectangle is as shown A=l x w

L meaning Lenght, which in this case is 3 [tex]\frac{3}{4}[/tex] ft.

W meaning width, which in this case is 1 [tex]\frac{1}{2}[/tex] ft.

Now that you know what the length and the width are, you want to multiply them like the formula A = l x w

A= 3 [tex]\frac{3}{4}[/tex] x 1 [tex]\frac{1}{2}[/tex]

You want to create the fractions into a mixed number.

3 3/4 = 15/4

1 1/2 = 3/2

Now when you multiply it should look like this :

[tex]\frac{15*3 }{4*2}[/tex] or 15x3 / 4x2

This will get you the mixed number of 45/8

Then you can covert the mixed number to a whole number which will be

5 5/8

This will get you the final answer of 5 [tex]\frac{5}{8}[/tex] ft. This is your area.

I hope this helped.

under which circumstances will a right angle triangle have a line of symmetry give reasons

Answers

Answer:

x txrxrserfunvek ke r CPP

What is a strategy for dividing 428 by 107?

Answers

Answer:

Step-by-step explanation:

428÷107

Use the 1 st

digit 4 from dividend 428

107)1

107)428

Since 4 is less than 107, use the next digit 2 from dividend 428 and add 0 to the quotient

107)02

107)428

Use the 2nd

digit 2 from dividend 428

107)03

107)428

Since 42 is less than 107, use the next digit 8 from dividend 428 and add 0 to the quotient

107)004

107)428

Use the 3rd

digit 8 from dividend 428

107)005

107)428

Find closest multiple of 107 to 428. We see that 4×107=428 is the nearest. Now subtract 428 from 428 to get reminder 0. Add 4 to quotient.

107)0046

107)428

107)9990

Since 0 is less than 107, stop the division. The reminder is 0. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.

Quotient: 4

Reminder: 0

i need help cause i dont know this i was out of school that day

Answers

Answer:

0.315

Step-by-step explanation:

act like the fraction is a division problem divide 6 by 19.

this decimal is a repeating decimal so it will never end rounded to the thousandth place it is 0.315

Find the equation of a line that passes through (5,-3) and is perpendicular to y = x.

a) y=x+2
b) y=x-8
c) y=-x+2
d) y=-x-8

Answers

Answer:

Step-by-step explanation:

X is 5 and y is -3, so y is x minus 8, which is y=x-8

Solve for the value of y

Answers

8y-2 = 30 since that is a 90 degree and the above angle is 60 degrees. 90-60=30

8y=32
y=4

Given that the m < 60° and m < (8y — 2) add up to 90° because they are complementary angles:

We could simply establish the following formula to solve for y:

m < 60° + m < (8y — 2)° = 90°

60° + 8y — 2 = 90°

58° + 8y = 90°

Subtract 58° from both sides

58° — 58° + 8y = 90° — 58°

8y = 32°

Divide both sides by 8:

8y/8 = 32°/8

y = 4

Therefore, the value of y = 4°

Double check whether we derived with the correct answer:

m < 60° + m < (8y — 2)° = 90°

m < 60° + m < 8 (4)— 2° = 90°

m < 60° + m < 32 ° — 2° = 90°

m < 60° + m < 30° = 90°

m < 90° = 90° (True statement). Thus, we have the correct value for y.

Please mark my answers as the Brainliest if you find my explanations helpful :)

Solve the rational equation quantity 4 times x minus 1 end quantity divided by 12 equals eleven twelfths.
Answers:
x=2.5
x=2.7
x=3
x=4

Answers

Step 1 - write out the equation with numbers

4x - 1 divided by 1/12 = 11/12

Step 2 - multiply 12/1 to both sides

4x - 1 divided by 1/12 • 12/1 = 11/12 • 12/1

Step 3 - add 1 to both sides

4x - 1 + 1 = 11 + 1

4x = 12

Step 4 - divide 4 to both sides

4x/4 = 12/4

x = 3

Final answer

x= 3

Answer:

x=3 or C

Step-by-step explanation:

I just did the math and got it correct on my FLVS quiz

Which sequence shows The numbers in order from least to greatest?
(A.) -2/3, 1/2, -3/4
(B.) 1/2, -2/3,-3/4
(C.)-3/4, -2/3, 1/2
(D.)-2/3, -3/4, 1/2

Answers

Answer:33 as an answer

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

Kail and Toni rented a
moving truck for 9 hours
and paid $ 179.55. How much
did it cost per hour?
*Pls help!!*

Answers

Answer:

$19.95 per hour

Step-by-step explanation:

1. To find the cost per hour, we have to divide the total amount paid by the number of hours!

2. (Solving)

[tex]\frac{179.55}{9}[/tex] [tex]19.95[/tex]

Therefore, the answer is $19.95 per hour.

round 523 to the nearest ten

Answers

Answer:

523 to the nearest ten is 520

ratio x : y is 3: 1
Which of the following statements is correct?
A x 3/4 of y
B y is 1/3 of x
C x is 1/3 of y
D y is 1/4 of x

Answers

Answer:

Step-by-step explanation:

1+3=4

1 out of 4 =1/4

remember x is bigger than y

Help plsssssssssssssss

Answers

The first graph and then the third graph and then the fifth graph and then the 4th graph.

6x - 9 = 2x +7 what is x

Answers

Answer:

x = 4

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

6*x-9-(2*x+7)=0

Pull out like factors :

4x - 16 = 4 • (x - 4)

Solve : 4 = 0

Add 4 to both sides of the equation :

x = 4

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

and your answer is x=4

15. Find the values of y and y.
(18y+5)°(10r - 61)°(x + 10)°

Answers

This is the answer plz tell me if its wrong

If B is the midpoint of AC and AC = 40, what is the measure of BC?

BC =

Answers

Answer:

BC = 20

Step-by-step explanation:

Since B is the midpoint of AC , then

AB = BC = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × 40 = 20

Find the sets of numbers to which
belongs.
Select all that apply.
D A. integers
B. irrational numbers
C. natural numbers
D. rational numbers
E. whole numbers
F.
real numbers

Answers

Answer:

4/7 = 0.57142857……

Step-by-step explanation:

integer NO cause it has a decimal

irrational NO cause it can be written as a fraction

Natural NO cause it has decimals

Rational YES because it’s a fraction

whole NO cause decimals

Real YES cause it’s a number

I give brainlist pls help and don't use me for points

Answers

Answer:

search up different types of decimals and answer it to the same one that looks the same as the one on the paper .

Step-by-step explanation:

A. Yes because it’s a repeating decimal

B. No because it’s a decimal that neither terminates nor repeats.

C. No for the same reason as B

D. Yes because it’s a terminating decimal

Evaluate the expression when c=4 and d=8.
5c+d

Answers

I think it is helpful for you!!!!

Please make me brainliest..

Answer:

5c + d

putting value of c and d,

5 × 4 + 8

20 + 8

HOPE THIS HELPS YOU

HAVE A NICE DAY

please answer this, thank you so much!! <3 :D

Answers

Answer: The correct answer is: " 11 .1 " .

________

Step-by-step explanation:

Given:

" [tex]1.9h + 3.5 =[/tex] ? " ; Solve: when: " [tex]h = 4[/tex] " ;

________

To find the answer:

We plug in "4" for the value for " [tex]h[/tex] " ;

and performed the mathematical operations indicated.

________

→ " [tex]1.9h + 3.5 =[/tex] [tex](1.9*4) + 3.5 = 7.6 +3.5 = 11.1[/tex] " .

________

The correct answer is: " 11 .1 " .

________

Hope this is helpful to you!

Best wishes!

________

3 1/6 x 1/7 reduce to lowest terms

Answers

Answer:

19/42

Step-by-step explanation:

Plz help me do this math problem !

Answers

Answer:

ITS B

Step-by-step explanation:

well f and t are congruent and st and fl are congruent too and o has vertical angles. so I hope the answer is B

:))))

WILL GIVE BRAINLIEST- Geometric Proofs

Answers

Answer:

Angle ACE and Angle ABE are congruent because they both share a side of Line Segment AE

Step-by-step explanation:

2. A rectangle has an area of 12 square feet and a length of
5 feet. What is its width?

Answers

Answer: ¹²/₅ ft or 2.4 ft

Step-by-step explanation:

Area of rectangle = l × w

12 ft² = 5ft × w

w = ¹²/₅ ft or 2.4 ft

∴ the width is ¹²/₅ ft or 2.4 ft

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prove that 5^(2n - 1) is divisible by 8​

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prove that 5^(2n - 1) is divisible by 8