By Euler's theorem, we have aφ(35) ≡ a24 ≡ 1 (mod 35).
Multiplying both sides by a12, we get (a12)·(a24) ≡ a12 ≡ 1 (mod 35), as desired.
To prove that a12 ≡ 1 (mod 35) for any integer a with gcd(a,35) = 1, we can use Euler's theorem.
Euler's theorem states that if a and m are coprime integers, then aφ(m) ≡ 1 (mod m), where φ(m) is Euler's totient function, which gives the number of positive integers less than or equal to m that are coprime to m.
In this case, since gcd(a,35) = 1, a is coprime to 35, so we can use Euler's theorem with m = 35.
We know that φ(35) = (5-1)(7-1) = 24, since the positive integers less than or equal to 35 that are coprime to 35 are precisely those that are coprime to 5 and 7.
Therefore, by Euler's theorem, we have aφ(35) ≡ a24 ≡ 1 (mod 35).
Multiplying both sides by a12, we get (a12)·(a24) ≡ a12 ≡ 1 (mod 35), as desired.
learn more about Euler's theorem
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a man sold two jeans at Rs 800. On one he gains a profit of 10 percent on other he loses 15 percent how he gain or loses in whole transaction
Answer:
1st jean:
100%-> 800
110%->880
880-800=80 ( earned)
-----------------------------------
2nd jean:
100%->800
85%->680
800-680=120(lost)
-----------------------------------------
120-80=40 (lost)
12. What type of triangle is shown?
Answer:
Scalene triangle, right triangle.
Step-by-step explanation:
To find out what type of triangle this is, we have to find x, so we set up an equation:
The sum of interior angles in a triangle add up to 180°
(2x + 15°) + (4x - 10°) + (x) = 180°
Open paranthesis:
2x + 15° + 4x - 10° + x = 180°
Combine like terms:
7x + 5° = 180°
Same to both sides
7x = 175°
x = 25°
We plug in x for each of the values:
2(25°) + 15° = 65°
4(25°) - 10° = 90°
25° = 25°
Because none of the angles are equal, that makes this triangle a scalene triangle, and since one of the angles is a 90° angle, that makes this triangle a right triangle
I hope this helped, let me know if you have any questions.
Kate deposited $1350 into a bank account that earns 3% simple interest per year. What is the total amount in the account after 2 years?
Answer:810$
Step-by-step explanation:
?/1350=3/100
1350*3=4050
4050/100=405
405 per year times 2= 810$
For the given expression, use the Commutative Property of Addition to enter an equivalent expression.
x + 19 =
Answer:
x+19=19+x
Step-by-step explanation:
heyy could you help me out with this question I have been stuck in this question??
Answer:
true, false, true that is the answer I belive
Hurry, it’s a test!!! Plz!
Raj estimated the sum of 214.73 and 9.6 by rounding each number to the nearest whole.
What was Raj's estimate and what is the actual sum of the numbers?
Enter your answers in the boxes.
Raj estimated the sum to be [ ]
The actual sum is [ ]
Answer:
estimate 215 answer 10
Step-by-step explanation:
URGENT!!! PLS GIVING BRAINLIEST!
A store is having a sale on walnuts and chocolate chips. For 2 pounds of walnuts and 3 pounds of chocolate chps, the total cost is $16. For 6 pounds of walnuts
and 5 pounds of chocolate chips, the total cost is $34. Find the cost for each pound of walnuts and each pound of chocolate chips.
Answer:
1 lb of chips cost $3.50
1 lb of walnuts cost $2.75
Step-by-step explanation:
c = $ chips
w = $ walnuts
System of Equations:
2w + 3c = 16
6w + 5c = 34
I multiplied the first equation by -3 to eliminate the 'w' terms to get
c = 3.5
I substituted 3.5 for 'c' to get 2.75 for 'w'
HELP HELP HELP PLSSS
Answer:
option. c. 720°
.....................
Answer:
720degrees
Step-by-step explanation:
-6=3x+3
Does anyone know this answer
Answer:
-1 :)
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
x = −1
15 points, 8-9 grade work
Polynomials
P(x) = 2x^4 + 3x^2 - 5x + 7
q(x) = -2x^2 + 4x - 3
calculation:
A. p(x) + q (x)
B. 2 • p (x)
C. p (x) - q (x)
D. 3 • p (x) + 4 • q (x)
E. p (x) • q (x)
F. (P (x) ) ^2
Answer:
A. p(x) + q (x) =2x^4 + 3x^2 - 5x + 7-2x^2 + 4x - 3 =2x⁴+x²-x+4
B. 2 • p (x)=2(2x^4 + 3x^2 - 5x + 7)=4x⁴+6x²-10x+14
C. p (x) - q (x) =2x^4 + 3x^2 - 5x + 7-(-2x^2 + 4x - 3 )=2x^4 + 3x^2 - 5x + 7+2x²-4x+3=2x⁴+5x²-9x-2
D. 3 • p (x) + 4 • q (x) =3(2x^4 + 3x^2 - 5x +7)+4(-2x^2 + 4x - 3 )=6x⁴+9x²-15x+21-8x²+16x-12=6x⁴+x²+x+9
E. p (x) • q (x)=sorry it is quite long.
F. (P (x) ) ^2this too.
-(7p+6)-2(-1-2p)
what is that simplified?
Answer:
-3p-40
Step-by-step explanation:
-(7p+6)-2(-1-2p)
-7p-42+2+4p
-3p-40
2X+1 -2X-8. Solve it
Kunal told Ana he was going to drop 10 dimes on the table. He said he would give her all the dimes where the "head" side was showing.How many dimes would Ana most likely get?
Answer:
10
Step-by-step explanation:
Whoever answers this question first gets brainly 2
The sample and h is the half-life, in days, of the substance. A sample contains 60% of its original amount of Fermium-257. The half-life of Fermium-257 is about 100 days. About how old is the sample? 52 days 60 days 74 days 136 days
Answer:
74 days
Step-by-step explanation:
The computation is shown below;
The proportion that remains left after d days is
p = (1/2)^(d ÷ 100)
In the case when the proportion is 60%
So,
0.60 = 0.50^(d ÷ 100)
Now
log(.60) = (d ÷ 100)log(.50)
100·log(.60) ÷ log(.50) = d = 74 days
Select the correct expressions.
Which expressions are equivalent to 3x + 2(x - 1) - 4?
3x + 2x - 2 - 4
5x -6
3(x-4)
3(x + 2) - 6
6(x - 1)
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John is measuring a piece of glass to fit in a triangular frame. he can only remember two sides of the brain, which are 6 cm and 11cm. Between what two numbers must the third side of the frame fall?
Answer:
yup right :)
Step-by-step explanation:
Answer: Your Correct
Step-by-step explanation:
Gordon types 2,964 words in 39 minutes. Find the unit rate.
Answer:
76 words per minute
Step-by-step explanation:
2964/39=76 words per minute
find the distance between j and k
Answer:
theres no picture...or points...
Step-by-step explanation:
Multiplying positive and negative fractions how do you do it
Answer:
I GOTCHU BAEE
Step-by-step explanation:
its just like regular negative numbers
but with fractions
see:
-7/12 x 1/2 = -7/24
negative negates the negative
negative negates the positive
positive keeps the positive positive
A yellow ball, a red ball, a white ball and a
black ball are placed in a barrel. Two balls
are drawn out of the barrel at random. What is the probability
that the yellow ball is drawn first?
Answer:
1/4 chance (this is equal to 25% as a percentage or 0.25 as a decimal)
Step-by-step explanation:
There are 4 balls and only one can be first. As there is only 1 yellow ball, there is 1/4 chance that the yellow ball is picked first.
At Pizza Pi, 12% of the pizzas made last week had extra cheese. If 6 pizzas had extra cheese, how many pizzas in all were made last week?
Answer:
50? maybe
Step-by-step explanation:
since half of the percentage was made it would also fall in for the other 88%.
im not 100% sure tho
The total number of pizzas is given as 50.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
The percent value of pizzas having extra cheese is given as 12%.
Suppose the pizzas made last week be x.
Then, as per the question the following equation can be written as,
⇒ 12% × x = 6
⇒ 12/100x = 6
⇒ x = 50
Hence, the number of pizzas that were made last week is given as 50.
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what is the value of the expression -3y/x
when x = 12 and y=-8
Step-by-step explanation:
here is your answerr.
Was it helpful?
comment down
If there is any kind of suspicious mistake
then sorry
If corresponding angles are on parallel lines, then their measure is the same _____.
always
never
sometimes
Step-by-step explanation:
always .
plz mark my answer as brainlist.hope this will be helpful to you
Answer: Always
Step-by-step-sumsum:
Please help me with this!!!!
Answer:
The answer is C
Step-by-step explanation:
Answer:
c is correct
hope it helped
There were 24 people invited to a pizza party. One-fourth of the people wanted sausage and olives. Three-fourths
wanted plain cheese. How many plain pizzas should Sam order?
18,16,14?
Answer:
the number of plain pizza does sam order is 18
Step-by-step explanation:
The computation of the number of plain pizza does sam order is shown below:
= Total people invited to a pizza party × plain cheese
= 24 × 3 ÷ 4
= 18
Hence, the number of plain pizza does sam order is 18
Use the distributive property to find the equivalent expression.
3(2 + x) =__+__x
Answer:
6+3x
Step-by-step explanation:
multiply each term in the parentheses by the outer term.
For a year, a chef from a restaurant collected data about the cost of strawberries and cherries in his local food market. this data is summarized in the table below. based on the data collected, select all of the statements that are correct.
Answer:
A Strawberries generally cost less.
D If the chef pays $6.00 for a pound of fruit, it is most likely cherries.
Step-by-step explanation:
A and D
LC
instrucciones: Resuelve lo que se te pide.
Ana preparo unos dulces
chiclosos. A los rojos les puso 3
cucharadas de azúcar por
cada lltro de agua, y en los
verdes 5 de azúcar por cada
dos litros, ¿que dulces estan
mas concentrados?
Answer:
los verdesestan mas concentrados
espero te ayude
6.) Resuelve: 6(X + 8) - 30 + 7 = 49
Answer:
x=4
Step-by-step explanation:
6(x+8)-30+7=49
6x+48-30+7=49
6x=49-48+30-7
6x=1+23
6x=24
x=[tex]\frac{24}{6}[/tex]
x=4
Step-by-step explanation:
Para resolver esto yo use una app llamada m a t h w a y
(sin los espacios) esta puede estar en varios idiomas, aunque esto se modifica segun el idioma en donde la uses.
6(x+8) -30+7 = 49 1. Simplifica 6(x+8) -30+7
6x+25 = 49 2. Mueve todos los términos que no
contengan x al lado derecho de la ecuación
6x = 24 (25 pasa restando por lo cual sería, 49-25
que es igual a 24.)
3. Divide cada término por 6 y simplifica.
x = 4
Espero esto haya ayudado!