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The first step in this is to separate \(a^2\) from the rest of the function.

\(a^2-3a+9=0\) becomes \(a^2=3a-9\).

Now there is just one step to find \(a^3\). Can you take it from here?

To simplify polynomial fractions, you can factor and find canceling x-intercepts.

\(x^2-25 \over x^2+10x + 25\)can be factored in both the numerator and denominator. \(x^2 -25 \) becomes \((x+5)(x-5)\), and 

\(x^2+10x+25\) becomes \((x+5)(x+5)\).

From there you can get \((x+5)(x-5) \over (x+5)(x+5)\).

You can then eliminate one \(x+5\) from each part of the fraction, resulting in \(x-5 \over x+5\).

If no obvious factors are there, you can always use the quadratic formula to find them when the highest power is 2.

Hope this helps!

There may be an easier way to do this, but I would just go through the multiples and find them.

12, 15, 18, 21, 51, 81, 102, 105, 108, 111

114, 117, 120, 123, 126, 129, 132, 135, 138, 141

144, 147, 150, 153, 156, 159, 162, 165, 168, 171

174, 177, 180, 183, 186, 189, 192, 195, 198, 201

210, 213, 216, 219, 231, 261, 291, 312, 315, 318.

The graph of \(-3^x-5\) includes all real numbers less than -5. As the exponent becomes increasingly negative, the first term approaches 0.

The answer should be option D.

Thanks! 

Ah, thanks. I do remember completing the square. 

they're word puns...

Medikin Joke:

pun: A loon full of sugar makes the medikin go down

normal: A spoon full of sugar helps the medicine go down (Mary Poppins)

Plant Joke:

pun: Hugh and only Hugh can stop florist friars

normal: You and only you can stop forest fires (Smokey the Bear)

The part my friend added to the plant joke:

pun: You're not Hugh when you're hungry

normal: You're not you when you're hungry (Snickers commercials)

Anyone who has jokes post them here!

There once was a group of monks who owned a flower shop. Business is kinda slow, so they travel around the world to find this rare flower. Unbeknownst to them, it was a man-eating plant. Every once in a while, a townsperson would go missing. They didn't know why but eventually found out why the people were missing. They had someone go get the plant, and it ate the person. They had the firefighters go get it, but it ate them all. The police too. Even the armed forces. They told everyone they could about a million dollars for whoever could get rid of the plant. So there's a man named Hugh, and he's pretty poor, so a million dollars is a lot to him. He goes to the monks' shop, walks in, and rips the plant to shreds without getting eaten. The moral of the story is Hugh and only Hugh can stop florist friars. 

My friend added this part:

Somehow the monks got another plant, and of course, they wanted Hugh to save them. He invested all of his money in stock, but then the stocks fell dramatically, so he was poor and couldn't have lunch. He agrees to help the monks again. He walks up to the doors and says "I got this". He walks in and gets eaten! The second moral? You're not Hugh when you're hungry.

There once was a group of monks who owned a flower shop. Business is kinda slow, so they travel around the world to find this rare flower. Unbeknownst to them, it was a man-eating plant. Every once in a while, a townsperson would go missing. They didn't know why but eventually found out why the people were missing. They had someone go get the plant, and it ate the person. They had the firefighters go get it, but it ate them all. The police too. Even the armed forces. They told everyone they could about a million dollars for whoever could get rid of the plant. So there's a man named Hugh, and he's pretty poor, so a million dollars is a lot to him. He goes to the monks' shop, walks in, and rips the plant to shreds without getting eaten. The moral of the story is Hugh and only Hugh can stop florist friars. 

My friend added this part:

Somehow the monks got another plant, and of course, they wanted Hugh to save them. He invested all of his money in stock, but then the stocks fell dramatically, so he was poor and couldn't have lunch. He agrees to help the monks again. He walks up to the doors and says "I got this". He walks in and gets eaten! The second moral? You're not Hugh when you're hungry.

100-109, and then every ten, up to 190 so it's at 19

skip to 990 and it adds 19 every hundred, so it's at 171 ((19*8)+19)

there are no others after that because it goes to 999, so the answer is option D.