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ser-zykov [4K]
3 years ago
9

Help please!!!!! :) its kind of hard for me..

Mathematics
2 answers:
AleksAgata [21]3 years ago
7 0
A 1 inch button is 5/8 inches longer than a 3/8 inch button. Just count from the 1 inch mark to the 3/8 inch mark.
adoni [48]3 years ago
5 0
It would have to be 5/8.

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Taylor went shopping for a new camera. Sales tax where she lives is 4.5%. The price of the camera is $28. Find the total price i
Alja [10]

Answer:

I think the answer would be 29.30 . good luck ^^

7 0
3 years ago
Find the difference between 900 and 246
Svetlanka [38]
The answer is 900-246=654
4 0
3 years ago
Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64
tino4ka555 [31]

a.

x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}

By Fermat's little theorem, we have

x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5

x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7

5 and 7 are both prime, so \varphi(5)=4 and \varphi(7)=6. By Euler's theorem, we get

x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5

x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7

Now we can use the Chinese remainder theorem to solve for x. Start with

x=2\cdot7+5\cdot6

  • Taken mod 5, the second term vanishes and 14\equiv4\pmod5. Multiply by the inverse of 4 mod 5 (4), then by 2.

x=2\cdot7\cdot4\cdot2+5\cdot6

  • Taken mod 7, the first term vanishes and 30\equiv2\pmod7. Multiply by the inverse of 2 mod 7 (4), then by 6.

x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6

\implies x\equiv832\pmod{5\cdot7}\implies\boxed{x\equiv27\pmod{35}}

b.

x^5\equiv3\pmod{64}

We have \varphi(64)=32, so by Euler's theorem,

x^{32}\equiv1\pmod{64}

Now, raising both sides of the original congruence to the power of 6 gives

x^{30}\equiv3^6\equiv729\equiv25\pmod{64}

Then multiplying both sides by x^2 gives

x^{32}\equiv25x^2\equiv1\pmod{64}

so that x^2 is the inverse of 25 mod 64. To find this inverse, solve for y in 25y\equiv1\pmod{64}. Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that (-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}.

So we know

25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}

Squaring both sides of this gives

x^4\equiv1681\equiv17\pmod{64}

and multiplying both sides by x tells us

x^5\equiv17x\equiv3\pmod{64}

Use the Euclidean algorithm to solve for x.

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that (-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}, and so x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}

5 0
3 years ago
Which figure best demonstrates the setup for the box method of finding the area of a triangle
Ivanshal [37]
Hi there! The third option shows us the best setup.

We can find the area of a triangle with the standard formula area = 1/2 * base * height.

To be able to fill in this formula, we need to have a base and a height. We can't easily find a triangle with given base and height, so we must look for another option.

We can also take the area of a square (length × width) and then divide the answer by 2. This is possible when we take the third setup. Hence the third answer is correct.
4 0
3 years ago
Read 2 more answers
|-19+9|/3-|14-22|/9<br> give me an answer
MArishka [77]

Answer:22/

9

= 2 4/

9

≅ 2.4444444

Step-by-step explanation:

Add: -19 + 9 = -10

Absolute value: abs(the result of step No. 1) = abs(-10) = 10

Divide: the result of step No. 2 / 3 = 10 / 3 = 3.3333333333333 = 10/

3

Subtract: 14 - 22 = -8

Absolute value: abs(the result of step No. 4) = abs(-8) = 8

Divide: the result of step No. 5 / 9 = 8 / 9 = 0.88888888888889 = 8/

9

Subtract: the result of step No. 3 - the result of step No. 6 = 10/

3

- 8/

9

= 10 · 3/

3 · 3

- 8/

9

= 30/

9

- 8/

9

= 30 - 8/

9

= 22/

9

6 0
2 years ago
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