can u pls help me with this question ​

Since 2⁵ = 32, and

2⁵ ≡ 32 ≡ 10 (mod 22),

we have

2⁵¹ ≡ 2 • 2⁵⁰ ≡ 2 • (2⁵)¹⁰ ≡ 2 • 10¹⁰ (mod 22)

Now consider 10¹⁰ (mod 22):

10 = 2 • 5

10¹⁰ ≡ 2¹⁰ • 5¹⁰ ≡ (2⁵)² • 5¹⁰ ≡ 10² • 5¹⁰ ≡ 2² • 5¹² (mod 22)

so that

2⁵¹ ≡ 2³ • 5¹² (mod 22)

Now consider 5¹² (mod 22):

5 and 22 are coprime, and ɸ(22) = 10 (where ɸ(n) is the Euler totient function). By Euler's theorem,

5¹² ≡ 5² • 5¹⁰ ≡ 5² • 1 ≡ 25 ≡ 3 (mod 22)

and so

2⁵¹ ≡ 2³ • 3 ≡ 24 ≡ 2 (mod 22)

Another, more tedious method: Start with smaller powers of 2 and look for a pattern.

2 ≡ 2 (mod 22)

2² ≡ 4 (mod 22)

2³ ≡ 8 (mod 22)

2⁴ ≡ 16 (mod 22)

2⁵ ≡ 32 ≡ 10 (mod 22)

2⁶ ≡ 2 • 32 ≡ 2 • 10 ≡ 20 (mod 22)

2⁷ ≡ 2 • 20 ≡ 40 ≡ 18 (mod 22)

2⁸ ≡ 2 • 18 ≡ 36 ≡ 14 (mod 22)

2⁹ ≡ 2 • 14 ≡ 28 ≡ 6 (mod 22)

2¹⁰ ≡ 2 • 6 ≡ 12 (mod 22)

2¹¹ ≡ 2 • 12 ≡ 24 ≡ 2 (mod 22)

2¹² ≡ 2 • 2 ≡ 4 (mod 22)

and so on, with a cyclic pattern of length 10. That is, [tex]2^{10k+1}\equiv2\pmod{22}[/tex] for any integer k ≥ 0. So 2⁵¹ ≡ 2 (mod 22).

Answer:

the one you have circled is correct

Step-by-step explanation:

Answer:

The fourth answer selection is the correct

Step-by-step explanation:

Yes, the two triangles have to sides and the angle in between congruent, so by the SAS theorem, they are congruent.

Therefore select the fourth option that gives the order of vertices of the second triangle similar to the order of vertices in the first one :

Triangle YXW  by SAS.

Notice that side YX is congruent to side QR,

and side RS is congruent to side SW.

Answer:

n<1

first graph

Step-by-step explanation:

subtract 5 from both sides

6n<6

divide by 6

n<1

please mark brainliest if correct

Answer:

x = 45

y = 60

z = 75

Step-by-step explanation:

We can create three different equations with the given variables:

x + y + z = 180

y + z = 3 x

z = y + 15

then we can use this last equation to substitute for 'z" in the second equation:

y + z = 3x

y + y + 15 = 3 x

2 y + 15 = 3 x

x = 2/3 y + 5

Then we can re-write the first equation in terms of y and solve for this unknown:

2/3 y + 5 + y + y + 15 = 180

2/3 y + 2 y = 160

8/3 y = 160

y = 3 * 160 /8

y = 60

Then   x = 2/3 (60) + 5 = 45

so x = 45

and finally:   z = 60 + 15 = 75

so  z = 75

Answer:

Step-by-step explanation:

Not congruent

Better to say that there is not enough information to say, "Triangles are congruent"

Answer:

-45 I think

Step-by-step explanation:

6 × (-7) - 3

-42 - 3

-45

Sorry if this is wrong

Answer:

i don't know . i did this in sixth grade and i failed

Step-by-step explanation:

Answer: B,D,E

Step-by-step explanation:

Answer:

2, 4, 5

Step-by-step explanation:

:)

Answer:

10  

Step-by-step explanation:

Answer:

Step-by-step explanation:

∠4 + ∠3 = 180

40 + ∠3 = 180

∠3 = 180 - 40

∠3 = 140

Answer:

f(-2) = 14

Step-by-step explanation:

f(-2) = 6(-2) 2 - 4

f(-2) = -12 + 2 - 4

f(-2) = -10 - 4

f(-2) = -14

Step-by-step explanation:

18 ..............hope it helps

Answer:

Step-by-step explanation:

first pay 100 = second pay 60

first pay ( 100 / 60 ) = second pay 1

first pay ( 100 / 60 ) * 36 = second pay 36

first pay 60 = second pay 36

[ Note : ( 100 / 60 ) * 36 = 60 ]

Answer:

A linear graph

Answer:

49.22 centimeters.

Step-by-step explanation:

7% of 46 is 3.22 which means you add 46 to 3.22and u get the answer 49.22

Step-by-step explanation:

Answer:

The tortoise can walk 0.25 feet per second.

Step-by-step explanation:

Convert inches to feet

Answer:

A tortoise walks 3 inches in 1 second. How many feet per second can the tortoise walk?

To answer the question, you need to write a conversion factor to convert  

inches to feet

The correct conversion factor has the inches in the  

denominator

The correct conversion factor has the feet in the  

numerator

.

The tortoise can walk  

0.25

feet per second.

by-step explanation:

hope this helps :)

If the train travels 744 miles in 3 hours then to determine the unit rate the train is traveling per hour you have to divide the miles by the hours, in this case (744 miles)/(3 hours). The final result concludes as 248 miles per hour.

Work Shown:

566,000 tweets = 1 hour

566,000 tweets = 60 minutes

566,000/60 tweets = 60/60 minutes .... divide both sides by 60

9,433.3 tweets = 1 minute

There were roughly 9,433.3 tweets per minute.

Answer:

4 to 7 *maybe

Step-by-step explanation:

Answer:

Divide 50,000 by 8.4...get that number and add it to the 50,000, divide again by 8.4 and add back, repeat until you reach 1,000,000... happy adding

Answer:

3.33in x3.83in

Step-by-step explanation:

Hello there pm34080075, I'm going to assume you are referring to a 19 ft 12in by 22ft 12in. If this is incorrect I will write out the steps so it should be an easy fix. The simplest thing we can do is convert all of our units to inches and then set up a ratio to find the dimensions on the blueprint.

With what we are given it should turn out to be roughly:

19ft 12in= 240in

22ft 12in= 276in

From this we can set up the simple ratio of [tex]\frac{1inch}{72in}[/tex] to find out the appropriate values This can be done by solving for x in:

[tex]\frac{1 inch}{72in}[/tex]  x  [tex]\frac{x}{240in}[/tex]

and

[tex]\frac{1 inch}{72in}[/tex]  x  [tex]\frac{x}{276in}[/tex]

After this is done we find that the dimensions on the blueprint will come out to 3.33in x3.83in

Hope this helps!

-HM

Answer: no

Step-by-step explanation:

algebraic expression for "a number , n, divided by 4 is 4. I

Answer:

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

A right triangle is 90 degrees

90-12-31=47

Answer:

The answer is C.

Step-by-step explanation:

Answer:

4.25

Step-by-step explanation:

Answer:

180 plants per row

Step-by-step explanation:

This is a division problem.

When he places 22,680 plants in 126 rows, he is dividing the 22,6980 plants by 126 rows.

22,680/126 = 180

Answer: 180 plants per row

Answer:

Step-by-step explanation

2x²+3x+5 roots means the zeros

So the method we will use is quadratic formula it's will tell us from the start whether this equation have a real solution no solution or one solution only calculating its discriminant

b²-4ac=3²-4(3)(5)

9-60=-51

If the discriminant is < 0 means the equation have no solution