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kobusy [5.1K]
2 years ago
7

Write the equation of each line in slope-intercept form and identify the slope. 4x=2+y

Mathematics
1 answer:
RideAnS [48]2 years ago
7 0

Answer:

y = 4x - 2

Step-by-step explanation:

Given: 4x=2+y

First, subtract 2 on both sides to isolate out y. (Slope-intercept form is y=mx+b)

Once subtracted, you get: 4x-2=y

Rearrange it, and you get: y=4x-2

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ASAP
rewona [7]

Answer: 90 people

Step-by-step explanation:

3 ladles per person = 150 people x 3

= 450 ladles full

450 ladles full = 5 ladles per one person = 450/5 = 90 people

8 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
Someone bought three t-shirts for $15 and nine $0. 90 each including tax how much did he spend
Goshia [24]

You multiply three( # of shirts) and 15.90 ( price)

The answer is $47.70 is how much he spend

6 0
3 years ago
Please help with this!!!!!!!! ASAP
Rom4ik [11]

Answer:

yes

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
PLEASE HELP due soon!I forgot how to do it omg
Flura [38]

Answer:

(3, -3) is correct

Step-by-step explanation:

-4 × 3 = -12. -12 + 9 = -3

8 0
3 years ago
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