Melody

The equation of a circle which has a center at (-5,2) can be written as Ax^2 + 2y^2 + Bx + Cy = 40

 Let r be the radius of the circle.

Find     A+B+C+r

\((x+5)^2+(y-2)^2=r^2\\ x^2+10x+25+y^2-4y+4=r^2\\ x^2+y^2+10x-4y=r^2-29\\ 2x^2+2y^2+20x-8y=2r^2-58\\ A=2,\quad B=20,\quad C=-8\\ 2r^2-58=40\\ r^2-29=20\\ r^2=49\\ r=7 \qquad \text{Since the radius must be positive} \)

You can do the addition. 

gueesstt. 

Please do not vote answerers down, especially not without given them an explanation.

The answer is wrong but I expect our guest was just trying to help. 

It is up to the asker to decide whether to accept the answer.

But you should not punish someone for trying to help.

On the student government ballot at Dusable High School,

the six candidates for president are listed first,          6!

followed by the four candidates for vice president,    4!

followed by the five candidates for secretary              5!

and ending with the three candidates for treasurer.    3!

In how many ways can the candidates be listed on the ballot?

now multiply all those together. 

Sounds good to me :)

Do you need help to learn how to write your questions into the forum properly?

I expect you can see that your LaTex coding is not rendering.

Use the Latex button on the ribbon. Copy your Latex in there WITHOUT the enclosing dollar signs.

Then we will all be able to read your questions as we are supposed to be able to.

When you present your questions properly, I for one, will be more likely to answer them. 

How many 3-letter words can we make from the letters A, B, C, and D, if we are allowed to repeat letters, and we must use the letter A at least once?

How many ways can the other 2 letters be chosen where order does not count?

There are 4 ways that the letters an be the same i.e.      AA,  BB,  CC,  DD

and there are 4C2=6 ways if the letters are not the same. Making a total of 10 ways.

So there are 10 combinations of letters, how many permutations of these are there

AAA   1 way

AAB, AAC, AAD      3 ways each     3*3=9  ways

ABB, ACC, ADD      3 ways each     3*3=9 ways

ABC, ABD, ACD       3*2=6 ways each     3*6=18ways

1+9+9+18 = 37 ways

1) Joshua has a ladder that is 12 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer.

OR

1.5 = 25% of x

1.5=0.25x

1.5/0.25=x

x=6

Thanks Juriemagic,

I have not seen this before but I will take your word for it :))

Find the least common multiple of 9x^2-16 and 3x^2+x-4

\(9x^2-16=(3x-4)(3x+4)\)

\(3x^2+x-4\\=3x^2+4x-3x-4\\=x(3x+4)-1(3x+4)\\=(x-1)(3x+4)\)

So the lowest common multiple is

  \((3x-4)(3x+4)(x-1)\\ =(9x^2-16)(x-1)\\ =9x^3-16x-9x^2+16\\ =9x^3-9x^2-16x+16\\ \)