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3 years ago

15

Simplify the expression.

1 answer:

Kobotan [32]3 years ago

6 0

Answer:

5.1

Step-by-step explanation:

(-44.288-31.6)/ -3.1(6-1.2) Open the bracket below with -3.1

(-44.288-31.6)/(-18.6+3.72)

(-75.888)/(-14.88) The minus sign cross each other out

=5.1

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Find the interval between: 8:40 pm and 9:30 am

jonny [76]

Answer:

12 hours 50 minutes

Step-by-step explanation:

8:40 pm to 9:30 am

8:40 pm to 8:40 am = 12 hours

8:40 am to 9:30 am = 50 minutes

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3 years ago

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Write the equation of a line passing through (5,2) parallel to y=4x-3

choli [55]

Y=4x-18 is the parallel equation

Y=mx+b Substitute
2=4(5)+b Multiply by 5
2=20+b Substract 20 in both sides
-18=b

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4 years ago

you play games where you score -6 points on the first turn and on each of the next 3 turns. what is your score after those 4 tur

dybincka [34]

I believe the answer is -24

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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

The graph of the function f(x) is shown. Which graph represents the function f(2x)

slava [35]

Answer:

It should be the top left graph where there is point (1,1) and (-1, -1) y = 1/x

Step-by-step explanation:

from the original graph, I see:

f(x) = 2/x because f(2) = 1 = 2/2

f(1/4)= 2/(1/4) = 2

...

so then f(2x) compresses f(x) horizontally by a factor of 2

so f(2x) = 2/(2x) = 1/x

8 0

3 years ago