All categories

2 years ago

How do you solve 11=t+11.5-t?

Mathematics

1 answer:

Anarel [89]2 years ago

7 0

Answer:

Step-by-step explanation:

11=t+11.5-t

subtract 11.5 from both sides

-.5=t-t

-.5= 0

there is no solution to this problem

You might be interested in

Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64

tino4ka555 [31]

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

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.

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

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

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

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

46 2/3% of 28 please i need to know answer an work

Bogdan [553]

First, it would help to put 46 and 2/3 into an improper fraction: 140/3.

Then, since this is a percent, we put that improper fraction over 100: (140/3)/100 = 140/300.

Finally, we multiply this answer by 28 since "of" means multiply:

(140/300) * 28 = 196/15 = 13 1/15

8 0

3 years ago

Karen and Sara invent a game. They roll a number cube twice and read the two digits shown as a two-digit number. So, if Karen ge

Daniel [21]

1) 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 51 52 53 54 55 56 61 62 63 64 65 66
2) least number is 11
3) greatest number is 66
4) Yes they are equally likely because it’s a dice so it a 16.6 chance of u rolling a number

6 0

2 years ago

A complex number is a number that can be written in the form a + bi, where a and b are real numbers. In the complex number 4 + 2

IRISSAK [1]

Answer:

In the complex number 4 + 2i, 4 is the real part. In the complex number 4 + 2i, 2 is the imaginary part.

Step-by-step explanation:

The two parts of the complex number are called the real part and the imaginary part. The imaginary part is identified by its multiplier of i.

In the given number, the 2 is multiplied by i, so 2 is the imaginary part. The other part, 4, is the real part.

6 0

3 years ago

Read 2 more answers

A type of cell triples every hour. If there are 5 cells initially, which function can be used to

laila [671]

Answer:

T(t) = 5(3)(t)

Step-by-step explanation:

There are 5 cells initially.

And it triple every hour.

T0 =5

T(t) = T0(3t)

Each cell has it's multipling factor because it's Will be multipling by 3 every hour

T(t) = 5(3)(t)

4 0

3 years ago

How do you solve 11=t+11.5-t?​

How do you solve 11=t+11.5-t?