please help, brainliest will be given, thank you

Answer:

2730

Step-by-step explanation:

We want to determine the greatest common divisor of the elements of the set  [tex]S = \{ n^{13} - n \mid n \in \mathbb{Z} \}.[/tex]

We apply the Fermat's little theorem which states that if p is a prime number, then for any integer a, the number aᵖ − a is an integer multiple of p.

Now, [tex]n^{13} \equiv n \mod p [/tex] if p-1 divides 12.

Since the  of 12 are 1,2,3,4, 6, 12, the corresponding primes are 2, 3, 5, 7, 13.

Therefore, the gcd of the elements in [tex]2^{13}-2[/tex] and [tex]3^{13}-3$ is 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13.[/tex]

2*3*5*7*13=2730

Therefore, the gcd of the elements in set S is 2730.

Answer:60 degrees

Step-by-step explanation:BAC =90 Degrees

BAD= 30 degrees

Since BAD and DAC are complementary angles, they add up to 90 degrees

So, 90 degrees-30 degrees= DAC which is =60 degrees

HOPE IT WAS CLEAR

Angle DAC is determined to be 60 degrees as it is complementary to angle BAD, which measures 30 degrees.

According to the given information, angle BAD measures 30 degrees. It is stated that angle BAD and angle DAC are complementary angles, meaning they add up to 90 degrees.

To find the measure of angle DAC, we subtract 30 degrees from 90 degrees:
90 degrees - 30 degrees = 60 degrees.

Therefore, the angle DAC measures 60 degrees.

Learn more about complementary angles here:

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Answer:

∠ A ≈ 16.67°

Step-by-step explanation:

Using the Sine rule in Δ ABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values

[tex]\frac{8}{sinA}[/tex] = [tex]\frac{16}{sin35}[/tex] ( cross- multiply )

16 sinA = 8 sin35° ( divide both sides by 16 )

sin A = [tex]\frac{8sin35}{16}[/tex] , thus

∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{8sin35}{16}[/tex] ) ≈ 16.67° ( to 2 dec. places )

Answer:

140

Step-by-step explanation:

Sum of angles around a point = 360

So, if one angle 8 reflex and measures 220, it’s adjacent side measures.

360-220 = 140.

Hope this helps.

Good Luck

Answer:

435 pgs

Step-by-step explanation:

29 pgs per hr

29(15) pgs per 15 hr

435

Answer:

435 pgs

Step-by-step explanation:

29 x 15 = 435

Answer:

I am grade a man who is not in my life and I am 97 and the other is that 93inches is the urge for the pain of his life and I think that he is not a good person to be a

Answer:

2x=y

Step-by-step explanation:

Done

Answer:

8

Step-by-step explanation:

Answer:

(4x^2 +9) (4x^2 -9) =0

Step-by-step explanation:

16x^4 - 81 =0

Rewriting

(4x^2) ^2 - 9^2 =0

This is the difference of squares a^2 -b^2 = (a+b)(a-b)

(4x^2 +9) (4x^2 -9)=0

Answer:

PQ, N

Step-by-step explanation:

Just take the function, and wherever it says 'x', substitute '-3' .

Then it'll say  f(-3) = -2(-3)² - 7(-3) + 6 .  Surely you can solve that.

As my old Electronic Circuits professor used to tell us, back around 1962:

"If  

f(x) = -2x² - 7x + 6

then

f(cow) = -2cow² - 7cow + 6 ."

Of all the things I learned from him, this is the thing I remember most.  

Answer:

Solution,

[tex]f(x) = - 2 {x}^{2} - 7x + 6 \\ f( - 3) = - 2 \times {( - 3)}^{2} - 7 \times ( - 3) + 6 \\ \: \: \: \: \: = - 2 \times 9 - ( - 21) + 6 \\ \: \: \: = - 18 + 21 + 6 \\ \: \: \: = 3 + 6 \\ \: \: \: \: \: = 9[/tex]

hope this helps...

Good luck on your assignment..

Answer:

i'm sorry but the answer is 1.152

Answer:

[tex]1.152[/tex]

Step-by-step explanation:

[tex] \: \: \: \: \: 0.312 \\ + 0.14 \\ + 0.7 \\ =1.1 52[/tex]

hope this helps you.

Step-by-step explanation:

x5 - 4x + 7x3 + 8 + 9x3 + 7x2 - 10 - 2x5 + 7x4 - 3x + 8

Arranging

x5 - 2x5 + 7x4 + 7x3 + 9x3 + 7x2 - 4x - 3x + 8 - 10 +8

-1 + 7x4 + 16x3 + 7x2 - 7x + 6

7x4 + 16x3 + 7x2 - 7x + 5

Answer:

Cornor should divide the total length of the road on which there is traffic by the length of each of the cars

Step-by-step explanation:

The best calculation he can use is to divide the total length of the road on which we have the traffic by the length of each of the cars

Mathematically, the best way to go about this is to convert the miles to feet then divide by the length of each of the cars

Mathematically 1 mile = 5280 feet

so 5.5 miles will be = 5280 * 5.5 = 29,040 feet

It is this length we shall now divide by 12.5 ft

And that is 29,040/12.5 = 2,323.2

Which is approximately 2,323 cars

Answer:

2(t + 6) - 5

Step-by-step explanation:

If we are strictly following the directions, we first add t and 6 together:

t + 6

Then we multiply by 2 AFTER we add the 2 together:

(t + 6)2

At last, we subtract 5 from everything after:

2(t + 6) - 5

And we have our answer!

Answer:

2(t+6)-5

Step-by-step explanation:

The unknown number is t

=> Adding 6 will make it t+6

=> Multiplying by 2 will make it 2(t+6)

=> Subtracting 5 will make it 2(t+6)-5

Answer:

3m = 18

Step-by-step explanation:

9 + 12m = 6 + 15(m - 1)

9 + 12m = 6 + 15m - 15

3m = 18

Answer:

3m=18

Step-by-step explanation:

trust

Answer:

Third option.

Step-by-step explanation:

The coordinates are (1, 3)

x = 1

y = 3

Put x as 1, the output should be 3.

g(1) = 3(1)²

g(1) = 3(1)

g(1) = 3

The transformation of a function may involve any change. The function of the g(x) can be written as 3x². The correct option is C.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift

Stretching:

Given that f(x)=x², since the function g(x) is also similar to f(x), therefore, both the function are quadratic functions.

Since f(x) is streched vertically to form g(x), therefore, the function g(x) in terms of f(x) can be written as,

g(x) = k × f(x)

y = k × x²

Also, it is passing through the point (1,3), therefore, we can write,

3 = k × (1)²

3 = k

Thus, the function of the g(x) can be written as 3x².

Hence, the correct option is C.

Learn more about Transforming functions:

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Answer:

Step-by-step explanation:

Sequence (a),

Recursive formula of given sequence has been given as,

T(n) = 12 - n

First 4 terms of the sequence will be,

T(1) = 12 - 1 = 11

T(2) = 12 - 2 = 10

T(3) = 12 - 3 = 9

T(4) = 12 - 4 = 8

And 10th term of the sequence will be,

T(10) = 12 - 10 = 2

Sequence (b),

Recursive formula is,

T(n) = 5 - 2n

T(1) = 5 - 2 = 3

T(2) = 5 - 4 = 1

T(3) = 5 - 6 = -1

T(4) = 5 - 8 = -3

T(10) = 5 - 20 = -15

Sequence (c),

Recursive formula is,

T(n) = n² + 3

T(1) = 4

T(2) = 7

T(3) = 12

T(4) = 19

T(10) = 103

Sequence (d),

Recursive formula,

T(n) = 2n²

T(1) = 2

T(2) = 8

T(3) = 18

T(4) = 32

T(10) = 200

Answer:

AC = 90, AB = 90, CAB = 180

Answer:

Obi's age is 18 and Oba's age is 9

Step-by-step explanation:

Let Obi's age be x and Oba's age be y

Condition 1:

x = 2y -----------(1)

Condition 2:

(x-4) = 3(y-4)

=> x -4 = 3y-12

=> x - 3y = -9  -----(2)

Putting eq (1) in (2)

2y - 3y = -9

=> -y = -9

=> y = 9

Now,

x = 2y

=> x = 2(9)

=>  x= 18

Answer:

[tex]8\\4[/tex]

Step-by-step explanation:

Obi's age is [tex]x[/tex].

Oba's age is [tex]2x[/tex].

4 years ago, Obi's age was [tex]x-4[/tex].

4 years after, Obi's age is [tex]2x-4[/tex]

3 times more than Oba's, so [tex]3(x-4)[/tex]

[tex]2x - 4 = 3( x - 4)[/tex]

[tex]2x - 4 = 3x-12[/tex]

[tex]2x - 3x = -12+4[/tex]

[tex]-1x=-8[/tex]

[tex]x=8[/tex]

[tex]x-4\\(8)-4=4[/tex]

Answer:

280 kg

Step-by-step explanation:

279.98... so it rounds up to 280

Answer:

58kg

Step-by-step explanation:

127 pounds to kg is 57.606 kgs

divide pounds by 2.205

Answer:

The answer is C:  1

Step-by-step explanation:

Answer:

3n

Step-by-step explanation:

Answer: y=-64

Step-by-step explanation:

From the first sentence: the value of y varies directly with x:

y∝x

y=cx where c=variation constant

When y=40 x=-5

40=-5c

Therefore c=-8

To find y when x=8

y=cx where c=-8 and x=8

y=-8*8

y=-64

Answer: 151,200 combinations

Step-by-step explanation:

So we want to order the numbers 1, 2, .... , 9 in a:

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]

such that the sum in each row is an odd number.

if we add 3 odd numbers we have an odd number.

if we add 2 even numbers, and an od number, we have an odd number.

where the rows are in this case (1, 2, 3), (4,5,6) and (7, 8, 9)

We have 4 even numbers and 5 odd numbers, so one combination can be:

[tex]\left[\begin{array}{ccc}1&5&3\\4&7&6\\2&8&9\end{array}\right][/tex]

Now, we for this option we can:

permute the numbers in each row: c =3*2*1 options per row and permute the rows, also c = 3*2*1

So only for this combination we have: P = (3*2)^4 possible ways of writing it.

Now, let's find the different combinations of numbers, so you can expect that we will find a lot of combinations, now let's construct them:

Suppose that in the first row we have two even numbers and 1 odd, then for the first even number we have 4 options, for the second 3 options, and for the odd number 5 options, so we have 4*3*5 combinations.

For the second row we also want two even numbers and one odd.

For the first even number we have 2 options, for the second one, and for the odd number we have 4 options, so we have 4*2*1 combinations.

In the last row we want the other 3 odd numbers, so we have 3*2*1 combinations, this adds to:

C = (4*3*5)*(3*2*1)*(4*2*1) = 2880 combinations.

If we add the fact that the rows can interchange positions, we have other 3*2*1 combinations:

C = 2880*3*2 = 16,800 and if now we add the fact that the numbers in the first two rows can permute (it is not the same (2, 4, 5) than (2, 5, 4) or (4, 2, 5)) (this happens because in these two rows we have different types of numbers, while in the third one the permutations are already included)

So the thing that can change in the first two rows is the position of the odd number, can be first, second or third, so we have other 3 permutations for the two first rows:

C = 16,800*3*3 = 151,200  which is the total number of  different combinations.

Answer: There were 78 red apples at the party.

Step-by-step explanation:

This situation can be represented by the equation  

x + 3x + 2(3x) = 130    where x is the number of green apples, 3x is the number of  yellow apples and 2(3x) is the number  of red apples.

Now solve for x

x +3x +2(3x) =130

4x + 6x = 130

10x  = 130

x =  13  

Now we know that x is 13 so put it into the expression for red apples and solve for the actual number of red apples.

2 * (3*13)  = ?

2 * 39 = 78  

Answer:

A. 102

B. 78

Step-by-step explanation:

mEG = 360 - 258 = 102°

m∠EFG = 1/2 ( major arc - manor arc) = 1/2 (258 - 102) = 78°

Answer:

Step-by-step explanation:

1300 x 1.042 = $1354.6

Answer:

5,040 times

Step-by-step explanation:

Since there are 7 letters in the word glacier, and there is no set limit, the formula would look like this;

7x6x5x4x3x2x1

(and techinacally 0 counts as 1, but since any number x 1 is itself, it's unnecessary to put it in there)

All of this adds up to 5,040

(I also have acellus and I've already checked it and it's correct )

Answer:

5,040

Step-by-step explanation: