Prove that: 27^4-9^5+3^9 is divisible by 25
PLEASE HELP QUICK!

Answers

Answer 1

Answer:

19,683

Step-by-step explanation:

Answer 2

[tex]27^4-9^5+3^9[/tex] is divisible by 25

The expression is given as:

[tex]27^4-9^5+3^9[/tex]

Express all terms of the expression as a base of 3

[tex]27^4-9^5+3^9 = (3^3)^4-(3^2)^5+(3^9)[/tex]

Remove the brackets

[tex]27^4-9^5+3^9 = 3^{12}-3^{10}+3^9[/tex]

Factor out 3^9 from the expression

[tex]27^4-9^5+3^9 = 3^9(3^{3}-3^{1}+1)[/tex]

Evaluate all exponents

[tex]27^4-9^5+3^9 = 3^9(27-3+1)[/tex]

Simplify

[tex]27^4-9^5+3^9 = 3^9(25)[/tex]

The above equation means that:

[tex]27^4-9^5+3^9[/tex] is the product of 3^9 and 25.25 is a factor of [tex]27^4-9^5+3^9[/tex].

Hence, [tex]27^4-9^5+3^9[/tex] is divisible by 25

Read more about factors and multiples at:

https://brainly.com/question/15560501


Related Questions

points A, S, Q, and R are ___

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Answer:

both please brainlist me

Peter spent 32.50 at the ball park Marty spent 5times as much money as Peter spent Callie spend at the ball park

Answers

Answer:Callie spend 162.5 and Peter spent 32.5 = total 195

Step-by-step explanation:32.5 x 5 = 162.5

32.5 + 162.5 = 195

Answer:

the direct answer is 195....

If H be the H.M. between a and b.
prove that 1/H-a + 1/H-b = 1/a+1/b​

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2x+y=6
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Y=-2x+6
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Answer:

Draw the perpendicular bisector of each line of each line.

Step-by-step explanation:

Because this is a right triangle, the circumcenter will always be located at the midpoint of the hgypotenuse.   Locate those coordinates and you have the circumcenter.

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Answer:

y points are 0, 1, 2, and 3 for x points 0, 2, 4, 6

Step-by-step explanation:

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At the toy store, Caleb and his younger brother, Gabe, each used money they had saved to buy Motor Mystery boxes. The convertibles are their favorite cars to get! Out of the 30 cars in Caleb's Jumbo box, 12 were convertibles. Out of the 10 cars in Gabe's Mini box, 4 were convertibles. Did the boxes have the same ratio of convertibles to total cars yes or no​

Answers

Answer:

Answer: Yes

Step-by-step explanation:

Ratios

Caleb's Jumbo box has 30 cars, 12 of which are convertibles.

This gives a ratio of 12:30. The equivalent fraction of this ratio is:

[tex]\frac{12}{30}[/tex]

This fraction can be simplified by dividing both parts by 6:

[tex]\frac{2}{5}[/tex]

Thus Caleb's ratio of convertibles is 2:5.

Gabe's Mini box has 4 convertibles out of 10 cars. This gives a ratio of 4:10.

Simplifying by 2, the ratio is 2:5.

It's clear that both boxes have the same ratio of convertibles to total cars.

Answer: Yes

3x+8=3x+____


Which value could you write in the blank above that would make the equation have one solution?
a.2x


b.8


c.7

Answers

Answer:

2x

Step-by-step explanation:

Think about it. Adding 8 would make the equation: 3x+8=3x+8. That has infinite solutions.  if you made it 7, it would be 3x+8=3x+7, which is impossible.  

Therefore, it must be 2x, which would make the equation 3x+8=5x.

Let's check: 3x+8=5x

                     8=2x

                     4=x

All good.

Find the value of each expression in simplest form
14 1/5 - 5 5/6

Answers

The answer should be 8 11/30

Please help please help

Answers

Answer:

1: A

2:C

3: B

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5:16

6:1

PLS HELP!!!!! OR I FAIL!!!
The graph of g(x), shown below, is a vertical shift of the graph of f(x) = 2*
Write the equation for g(x).

Answers

Answer:

C

Step-by-step explanation:

+1 shifts the function up 1

Is 150% of 36 less than 100, greater than 100 but less than 150, or greater than 150?
150% of 36 is


HELP!!

Answers

Answer:

no 150% of 36 is 54

Step-by-step explanation:

its 54 btw

please help real quick, least to greatst, math

Answers

Answer:

-1,-0.5,1/4.

Step-by-step explanation:

Please mark me brainliest I need it!!!! Please!!!

Answer:

-1, -0.5, 1/4,

Step-by-step explanation:

-1 is the least since it's a negative one whole, -0.5 follows since it's half of one whole and it's negative, 1/4 after since it's positive.

THIS MAY OR MAY NOT BE RIGHT SORRY IF NOT

how many times can 3 go into 10000

Answers

Answer:

3333 times

Anymore and you'll have extra

May I have brainliest please? :)

Determine if the two triangles are congruent. If they are, state how you know.

Answers

Rules for congruency .

Decide whether the change is an increase or a decrease, and find the percent change. Original number = 35; New number = 16.... PLS LEAVE A STEP BY STEP EXPLANATION

Answers

Answer: 60 decrease or 150 decrease

Step-by-step explanation:

The Clark County Sheriff’s Department schedules police officers for 8-hour shifts. The beginning times for the shifts are 8:00 a.m., noon, 4:00 p.m., 8:00 p.m., midnight, and 4:00 a.m. An officer beginning a shift at one of these times works for the next 8 hours. During normal weekday operations, the number of officers needed varies depending on the time of day. The department staffing guidelines require the following minimum number of officers on duty:

Time of Day Minimum No. of Officers on Duty
8:00 a.m.–noon 7
Noon–4:00 p.m. 6
4:00 p.m.–8:00 p.m. 9
8:00 p.m.–midnight 7
Midnight–4:00 a.m. 4
4:00 a.m.–8:00 a.m. 6
Determine the number of police officers that should be scheduled to begin the 8-hour shifts at each of the six times to minimize the total number of officers required. If your answer is zero, enter “0”.

Starting Time Officers Starting
8:00 a.m.
Noon
4:00 p.m.
8:00 p.m.
Midnight
4:00 a.m.

Answers

Answer:

The number of policemen Officers starting each shift is given as follows;

Starting  Time           [tex]{}[/tex]             Officers Starting

8:00 a.m.                   [tex]{}[/tex]            3

Noon           [tex]{}[/tex]                          3  

4:00 p.m.                  [tex]{}[/tex]             6

8:00 p.m.                [tex]{}[/tex]               1

Midnight                 [tex]{}[/tex]               3

4:00 a.m.            [tex]{}[/tex]                   4

Step-by-step explanation:

The given parameters are;

The Time of the Day          [tex]{}[/tex]             Number of Officers

8:00 a.m. --- Noon                  [tex]{}[/tex]            7

Noon --- 4:00 p.m.           [tex]{}[/tex]                   6  

4:00 p.m. --- 8:00 p.m.           [tex]{}[/tex]            9

8:00 p.m. --- midnight          [tex]{}[/tex]               7

Midnight --- 4:00 a.m.           [tex]{}[/tex]              4

4:00 a.m. --- 8:00 a.m.            [tex]{}[/tex]            6

From the table, we have;

The total number of hours worked = (7 + 6 + 9 + 7 + 4 + 6) × 4 = 156 hours

The approximate number of policemen = 156/8 = 19.5 ≈ 20

Let a, b, c, d, e, and f be the number of policemen that start their 8 hour shift starting from 4:00 a.m.

Let b be the number of policemen that start their 8 hour shift at 4:00 a.m.

∴ a + b = 7, b + c = 6, c + d = 9, d + e = 7, e + f = 4, f + a = 6

Given that there are 6 variables, by noting that the maximum value of the variables will be about 5, and by trial and error, we have

a - c = 1

d - b = 3

c - e = 2

d - f = 3

a - e = 2

a - f = 1

Whereby a + b + c + d + e + f = 20

Therefore, we have;

b = 3, d = 6, f = 3, a = 4, c = 3, e = 1

Which gives;

Starting  Time           [tex]{}[/tex]             Officers Starting

8:00 a.m.                   [tex]{}[/tex]            3

Noon           [tex]{}[/tex]                          3  

4:00 p.m.                  [tex]{}[/tex]             6

8:00 p.m.                [tex]{}[/tex]               1

Midnight                 [tex]{}[/tex]               3

4:00 a.m.            [tex]{}[/tex]                   4

Please I beg you help me I need to turn this in right now

Answers

Answer:

D

Step-by-step explanation:

choose the graph of the function f(x)=1/2 times -2.

click on the graph until the correct graph appears.

Answers

Answer:

ur correct u got it.

Step-by-step explanation:

circular running track is ​1/5 of a mile long. Elena runs on this track, completing each lap in 1/15 of an hour. What is Elena's running speed?

Answers

Answer:

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Step-by-step explanation:

Answer:

3mph

Step-by-step explanation:


A plant is already 13 centimeters tall, and it will grow one centimeter every month.
Let H be the plant's height (in centimeters) after M months.
Write an equation relating H to M. Then graph your equation using the axes below.

Answers

Answer:

H = M + 13

Step-by-step explanation:

Each month will add 1 cm to the height which is 13

HELP PLSSSSSSSSSSSSS

Answers

Answer:

14 miles per hour

Step-by-step explanation:

49/3.5= 14

Hope this helps!  

pls mark brainliest if correct

Answer:

14 miles per hour because to find the speed, use the formula speed = distance / time. 49 / 3.5 = 14.

need help with this question please and thanks 100 points

Answers

I got you it is negative 4 and 2/3
Your answer is -4 2/3

- you have to do -42 divided by 9 and you get without going over -42. The closest you can get is -36. Now, with the remaining 6 would just be written bearing -4 as 6/9. Here, you have to simplify it, making it 2/3. Your answer is the -4 2/3

A washer and a dryer cost $965 combined. The washer costs $65 more than the dryer. What is the cost of the dryer?

Answers

Answer:

$450

Brainlyest if this is correct

Step-by-step explanation:

i just need a little help figuring this out

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Answers

x=70... do u need an explanation?

6. Find the value of x.
0
x
117°
660
a.
117
b. 297
c.
66
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Answers

Answer:

d.51

Step-by-step explanation:

Let the 3rd angle of the triangle be y. Then:

y+117=180

y=63

Then:

x=180-63-66

  =51°

i need help plz plz ​

Answers

Answer:

f(9) = 480 means that jason will have 480 after saving for 9 months

Jason will have 240$ after 3 months due to the fact that f(3) = 240

Jason will need to save 560 more dollers

Step-by-step explanation:

Andrew's fish tank measures
24 inches long, 10.5 inches
wide, and 13 inches high. What
is the volume of the fish tank?
MONS

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15 volume of the fish tank

HELPP MARKING BRAINIEST

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i believe the answer is a
No ive done this one already its C. brainlyest??
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