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brilliants [131]

2 years ago

8

X+y=12 -x=-y-10 HELP thanks

1 answer:

Travka [436]2 years ago

4 0

do you have a picture or problem sentance that goes with that

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5/6 - 2/3 divide by 4/5

ollegr [7]

Answer:

5/24

Step-by-step explanation:

Start with the first part of the probelm 5/6 - 2/3

You need to find a common denominator of 6 and 3

common denominator= 6

so change 2/3 to 4/6

now you can subtract the top values

5/6-4/6

5-6=1

keep the denominator the same

= 1/6

Now divide 1/6 by 4/5

to divide you are going to multiply by the reciprocal so instead of 4/5 we are going to flip it to 5/4

1/6 x 5/4

5x1=5 and 6x4=24

= 5/24

8 0

2 years ago

Which of the following functions has a rate of change that stays the same?

aalyn [17]

Answer:

The answer is A because the rest are parabolas

5 0

2 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

2 years ago

Sammy opened a college savings account. She opened the account with $85, and then

MrMuchimi

Answer:

C. s= 85m + 45

Step-by-step explanation:

Given data

She opened the account with $85

and deposited $85

The equation that best models the relationship is

s= 85m + 45

Hence option C is correct

8 0

2 years ago

I need help with this no link pls

Naddika [18.5K]

Answer:

1. x = 36 equation is x + 2x + 9 = 117, then solve for x

2. x = 50 equation is x + x + 12 = 112, then solve for x

Step-by-step explanation:

4 0

2 years ago