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Hi guest!

So to start, you have to multiply the denominator by the conjugate.

\(\frac{2-3i}{-1+5i}\cdot\frac{-1-5i}{-1-5i}\)= \(\frac{-17-7i}{26}\)

The answer is \(\frac{-17-7i}{26}\)

I hope this helped you, guest!

Let me know if you have any questions!

:)

All of the shaded areas area ABOVE the line with negative slope.....AND INCLUDE the line (the line is solid)

sooo    y >= -2x+3

The line is included, so the answer must contain "=".

The shading is above, so the answer must contain ">".

Choice d.

Assuming that TWQ is a diameter, angle(PWT)  =  180^o - 128^o  =  52^o.

Assuming that PWR is a diameter, angle(TWS)  =  180^o - 31^o - 52^o  =  97^o.

Thus, arc(TS) is 97/360^th of the circumference of the circle:  (97/360)·2·pi·(4.5)  =         

Here is my attempt at this:
The word "HIGHMOON" has 8 letters. If you allow all letters to be permuted, in which case you will have "duplicates", you would get:

8! =40,320 permutations.
If you exclude duplicates, then you would have:
8! / 2!.2! =10,080 pemutations

However, in either case, you will have 2 "Hs" in your permutations, and since each letter appears an equal number of times in the total of ALL permutations, it therefore follows that in 2/8 =1/4 of ALL permutations, you will have 2 "Hs" next to each other. The other 6/8 = 3/4 of ALL permutations, they will NOT be next to each other. So, the answer is, I think, that in 3/4 or 75% of ALL permutations, they will NOT be together.
Note: somebody should check this. Thanks.

At the city museum, child admission is $5.90 and adult admission is $9.50. On Sunday, 149 tickets were sold for a total of $1095.10. How many child tickets were sold that day?

Im Stadtmuseum beträgt der Eintritt für Kinder 5,90 USD und für Erwachsene 9,50 USD. Am Sonntag wurden 149 Tickets für insgesamt 1095,10 USD verkauft. Wie viele Kindertickets wurden an diesem Tag verkauft?

Hello Guest!

\(C+A=149\\ 5.9C+9.5A=1095.1\\ C=149-A\\5.9(149-A)+9.5A=1095.1\\ 879.1-5.9A+9.5A=1095.1\)

3.6A=216

\(A=60\)

\(C=149-60\)

\(C=89\)

 89 child tickets were sold that day.

  !

How did you find x - y = 15? 

Solve for the unknown values.

Hello Guest!

\(x=180-95=85\\ y=180-50-(180-95)=45\)

  !

The smallest number is 2 and the largest number is 19.  Their difference is 17.

The solutions are x = 0, x = 2003, and x = 1/2003.

For k = 4, both equations become x = y, so this is the solution.

the second one 

"A pair of positive integers (x, y) satisfies the equation 31x + 29y = 1125. What is x + y?"

Write 31x as 30x + x

Write 29y as 30y - y

Then you can write 31x + 29y = 1125 as 30x + x + 30y - y = 1125  or  30(x+y) + (x-y) = 1125

Subtract x-y from both sides:    30(x+y) = 1125 - (x-y)

Divide both sides by 30:     x+y = 1125/30 - (x-y)/30 

Now 1125/30 = 37 + 15/30 so we have   x+y = 37 +15/30 -(x-y)/30  

If x and y are positive integers, the fractional terms on the right hand side must cancel each other out.

For this to happen we set (x-y) = 15, then we are left with 

x+y = 37

is it 2 - (3i/-1) +5i or (2-3i/-1+5i)?

Find the approximate volume of the figure below, composed of a cone, a cylinder, and a hemisphere. If necessary, round your answer to the nearest tenth.

3e + 4b = 485

5e + 3b = 460         Multiply this equation by - 1 1/3 to get

-20/3 e   - 4b  = - 613 1/3    add this equation to the top one    (see how we eliminated the 'b' variable?)

-11/3 e = -128 1/3

e    =   128 1/3   x 3/11 = 35 cents

SUb this value into one of the equtions to find the value of b

3(35) + 4b = 485

b = 95 cents

Now   x = 3y

15 years ago    (x-15) = 6(y-15)     or   x -15 = 6y-90      or x = 6y-75     Put this in for 'x' in the first equation

6y-75 = 3y

3y = 75

y = 25 y/o

x = 75 y/o

By the angle bisector theorem, the area of triangle BXA is 15*sqrt(2).

Thanks, Melody. I'll try watching the video and update you on my progress. 

Thanks for everyone's help! I really appreciate it. I got it. Have a nice day! :D

Thanks for your work! I got it. Please have a good day! :D

If:            h(x)  =  x⁹ + 9

and         g(x)  =  sqrt(x)

then  g( h(x) )  =  sqrt( x⁹ + 9 )

Thank you!

-4 + 3i      +     -2 -i      =    -6  + 2i

Not sure what you are supposed to graph,  but   -6 + 2i    would look like    -6 (for x)   and   + 2 for y   

          so graph    -6,2