#combining like terms

[existinglimits]

Happy μ Year!

It's just a WIP, but I probably won't finish it. Happy New Year!

[math-journal2]

<— Unit 2 — Unit 3: Exponents— Unit 4 —>

Unit 3: Exponents

Part 1 —>

Related: Radicals

2025_4_23 Edit:

Location: Parentheses

Problem: bottom right

(2x+3)+(x-4) doesn’t match up with the work

Should be (2x+3)(x-4)

Properties of Exponents

Scientific Notation

*important for conversions

Combining Like Terms

Parentheses

Page 5

[math-journal]

Combining Like Terms

Like terms: must have exact same variable and exponent parts

Term: separated by addition or subtraction

Think of it like ducks and bats.

[blueskittlesart]

yay the hunger games!!! thank you for drawing book accurate katniss ough. love her. idk if you’re taking requests but peeta with his (her…) cane/prosthetic leg would be awesome. thats another plot point the movies need to die for 😭😭

more girlpeeta because im still on this train but you are so right that's another thing i will absolutely never forgive those movies for

[anghraine]

I know it's well-understood at this point that Kirk/Spock is much more of a nerd4nerd ship than a nerd/jock thing, but it's just been kind of percolating around my mind that both of them aren't just space nerds but space nerds who were personally bullied.

Like, 18-year-old Kirk was targeted by an older bully who combines "total asshole" with "the most grating man in existence":

MCCOY: Well, yeah, I'm beginning to feel a little bit picked-on, if that's what you mean. KIRK: I know the feeling very well. I had it at the Academy. An upperclassman there. One practical joke after another, and always on me. My own personal devil. A guy by the name of Finnegan. MCCOY: And you being the very serious young— KIRK: Serious? I'll make a confession, Bones. I was absolutely grim, which delighted Finnegan no end.

This was five years after Kirk survived a genocide, btw, and likely well before his stint as an Academy instructor known to be strict and demanding (which is the period the "stack of books with legs" description of him comes from). By the time he's 33, fifteen years after all this, it turns out one of his deepest fantasies is just beating the shit out of his bully, but only if he can do it According To The Rules (the replica of Finnegan sneers, "Always fight fair, don't you? True officer and gentleman, you").

Spock, meanwhile, is viciously targeted by his Vulcan peers for being biracial from at least age 5; he's described as being tormented by other boys by that age, and "at home nowhere except Starfleet." I think he'd have been 18 or 19 when he left for Starfleet and it's... the least bad of his options, but he seems to have spent his entire career among humans and being persistently subjected to raw racism and profound disrespect for his culture at every turn.

Like, their histories of being metaphorically shoved into lockers are not identical or anything, but I think it's interesting that they both have them.

[poorly-drawn-mdzs]

Los Chicos Peleandoooooo

[First] Prev <–-> Next

[skeletalheartattack]

for the past couple of days, i've been working on Boe's house in limbo and getting it to look close to how i've been picturing it in my head - here's a couple of shots so far showing off the exterior and interior, with the top screenshot being further along in progress than the other exterior shots.

[strangebiology]

Seraphim Angel Anatomy

What are our thoughts on the anatomy of a seraph angel with 6 wings? How does that work? (Outside of it being magic. Let's have fun with science.)

The biblical description of the six-winged Seraphim angels is super minimal (Isa 6:2, 6, with some interpretation here.) But let's just say for reasons they look like people with 6 wings.

To start: What is a seraph related to? In both biblical and Hazbin Hotel lore, it's implied that (maybe some?) angels can breed with humans, which suggests that they're mammals, and very close to humans. But...I wonder if that has to do with shapeshifting or other magic? Bible nerds chime in. It's also just as interesting/valid to consider bug anatomy, and I encourage bug artists to draw a human-ish body with wings attached in dragonfly or spider style or something.

A number of people have explored the concept of angel anatomy by looking at humans and birds, like DCRoleplays on Deviantart. I also recall this image by Uzlo on Deviantart pointing out that you need pectoral muscles to move your arms/wings, so...if you have two arms and two wings, all of which move independently, you might need four pecs.

Alternatively, here's an extremely cool gif by @squidlife-crisis showing a human ribcage with human arms, the keel of a bird, and what looks like layered pectoral muscles for arms and wings. So, rather than multiple visible chests, an angel with the skin on would appear to just have a bigger chest.

But now add MORE wings. Would we have a huge chest with lots of layers of pecs attached to the keel...and would you need to change the shape of the keel to handle so many attachments?

Or, is someone gonna draw Lucifer or the other seraphim with 8 pecs? Will it be me? For science, obviously.

What are your thoughts?

[catkin-morgs-kookaburralover]

storytime which my figs know about but whatever (and thanks to my beloved boundin for being all worired abotu me. sorry.)

so i had an assignment due yesterday. a care plan worth 15% of my grade for a double credit point unit. anwyay. i didn't touch it, for various reasons up to and including what i'm currently calling situational depression, and planned to get an extension.

fun fact: apparently you can't get extensions day-of, at least for that assignment.

i found this out at about 11am, due 8pm, having not even looked at assignment before then.

so of course i kind of panicked. just a little bit. and opened it up real quick. shifted to desk. put on the kettle and started digging around my music library.

there's this song i like, carpenters of course, "don't be afraid". i cycled through a few other songs before i got to that one, none of them helping me get into the zone.

(anyway i listened to "don't be afraid" on loop 108 times yesterday afternoon, putting it as the top number of plays on my music app, finally surpassing a particular movement of a beethoven sonata (13 second mvt) that has reigned as king for a couple of years. then towards the end, flagging, i switched to a combo of "road ode" and "a song for you (reprise)", because those two songs have to go together musically.)

i was already feeling awful physically because most of my intake the previous day had been cheese, so wheeee dairy and almost-diarrhea as well as reasonably severe stomach pain. stress was making me dissociate a bit as well.

so. caffeine time.

keep working. more caffeine time.

keep working. more caffeine, an unmeasured amount of sugar, and another couple of spoonfuls of coffee because why not. because of a mysterious headache (likely caused by a combination of too much coffee, no food, and dairy the previous day), took ibuprofen.

keep working. more coffee. more headache. more ibuprofen.

at that point i was entirely detached from my body, experiencing symptoms of a caffeine overdose and potentially ibuprofen overdose too (didn't exceed the maximum for ibuprofen in a day, but in that short a time yes, and certainly caffeine), and saying all the stuff that worried boundin. still working on the assignment though while feeling unreal to a complete degree, not just partial, and noting symptoms as an intellectual exercise. was not present in my body at all. oh, did i mention i hadn't eaten that day? i was also experiencing violent nausea.

keep working. song still on loop. headache reducing. time passed and the reaction i was experiencing began to fade. brother gave me chocolate at some point near the end.

completed and submitted assignment about five minutes before i had to go out for the evening. somehow not at all shaky but i could feel all my skin and was inclined towards giggling.

arrived at friends' house. mentor asked how my day had been. i began laughing, explained what my day had been doing, and ended up giggling helplessly. she looked Concerned++ as i hilariously recounted my accidental overdoses x2 and that i hadn't eaten anything except chocolate, sugar, caffeine and ibuprofen that day. i made many jokes throughout the meal but mostly restrained myself overall - i was self-aware enough to know how abnormally i was acting, but it was so hard to avoid these things. inclined to laughter the whole evening, though after eating actual food that didn't contain sugar it did settle a little. later in the evening i impulse-agreed to a thing saturday i didn't want to go to, noted the concerning level of impulsivity and restrained myself from agreeing to anything else.

was offered, and enthusiastically consumed, a quantity of cold roast potatoes, which definitely helped as well.

arrived home less inclined towards giggling, but still violently nauseous; managed to avoid throwing up by the barest of margins. practically inhaled bread and ham, which i found too sweet because it was housed in the same fridge as bananas; found peanut butter for the last slice of bread, which helped. still feeling very ill but suspected i needed it given all the everything - i think this was the right call.

went to bed, yoinked ransom, cuddled him forcibly and eventually managed to sleep, still feeling rather quite hyper.

this morning i am still slightly hyper and mildly unwell but fatigue is balancing the tendency towards impulsivity. am not going to consume either caffeine or ibuprofen today unless something drastic changes or something, and a hard ban on both refined sugar and dairy until i feel more normal again.

bit of a rollercoaster.

[perfectwitchcrown]

Ekuoto 81 thoughts

Spoilers below! CWs: references to abuse, suicidal ideation/suicide

Before this week's chapter I had been wondering how we might see the Dante and Vergilius fight resolve since Dante had so clearly expressed that this was the end of the line chapters ago and Bel had just been defeated, but I somehow did not expect this to be what happened… :’)

Tbh I think he’s going to live if only bc I think that there was a reason we were shown that Vergilius has healing powers when he kissed Charlotte chapters ago. Maybe this is just cope tho lmao. On the other hand, I’d be really interested to see Priest’s (and Barbara and Leah, who were in France with Dante) reaction to Dante being dead so I’m torn lol.

I think it's interesting how often Dante's advice to fall in love from the first chapter has come up in the series, and how tonally different Priest vs Dante treat that moment in this chapter. Dante sort of broods on it and considers it a curse he's left on Priest, whereas Priest kind of brushes it off to Imuri as uncool advice from an unreliable adult. On the other hand, I think it’s super interesting that Priest seems to consider the hug Dante gave him as having saved his life as a child. In chapter three, when Priest saves the children in the aquarium, he similarly gives them a hug.

I’m sure a lot of it has to do w most of his experience with adults throughout his life involved physical pain (the abuse he suffered from his father, the abuse he suffered from the church, etc) so like I am sure positive physical contact was not something he really experienced. But also, this moment in the first chapter comes after Priest breaks down about how hard he finds living--outside of Bel, who Priest had forgotten about at this point, Dante was likely one of the first adults that actually listened to his cry for help as a child and saw his idealization of religious martyrdom that was really, at its core, suicidal ideation.

Dante’s whole thing about being tired of chasing Vergilius is interesting too. It uses the same language as when he spoke of his failure to chase after Vergilius in chapter 20. Vergilius naming himself Vergilius is also such a "come follow me" move since Virgil was Dante’s guide in Inferno. Interested to see how this shift in the dynamic affects Vergilius.

Also excited to see what happens w Marco next chapter. His relationship w Priest seems fascinating to me bc it’s kinda hard to tell what level of distance they have from each other. Marco completely idolizes him, and it’s also been mentioned that he was present at the previous offscreen exorcism of Mammon prior to the start of the series, and he’s also visible in a flashback panel to that exorcism. They've known each other for like three years then so it's kind of interesting how obsessive Marco is and how little he actually knows about Priest as a person for having known him for all that time.

Even in the first chapter we're shown that Marco's understanding of Priest is completely misguided, where he assumes Priest's studying the bible when he's actually reading poetry by Goethe and Song of Songs (the second of which is in the bible, but the unifying theme between the works he's reading is romantic love. Also, this is the dorkiest form of romantic texts for him to be interested in LMAO).

Also can’t wait to see what goes down w Leah Barbara and the others. While Marco looks pissed, Leah looks more worried than anything else, and Mikhail looks sort of solemn. Daniel sort of has resting bitch face so idk what’s going through his mind. Last we saw of them all, Leah and Barbara very much dodged mentioning that Imuri is a demon and said to focus on fighting the witches first. Now that they’ve clearly finished with that, I wonder if they’ve told the rest or if they’re still hiding it. Either way Marco would be pissed since Priest did work with Bel.

Anyways, what a chapter, I'm so excited to see what happens next chapter. If Imuri and Priest have to be on the run from the church for awhile I wonder if Imuri's friend Cass from the file extras might finally make an appearance...

[shmorp-mcdurgen]

Aftermath

After waking up from a ten year stasis, Gordon finds himself back in the ruins of Black Mesa.

Notes: Hi half life fandom this is my first fic posted for HL. Also this is the first reveal of my HL au: Aftermath! So thats pretty neato, anyway hope you enjoy this short little prologue thing

Blackness was all he saw; darkness for miles, with pure nothingness filling the gaps. He couldn’t feel, see, or hear, and even trying to think of a single thing was proving to be a greater challenge than he’d expect. His thoughts blurred together into a sludge of meaningless ramblings, leaving him unable to process where he was, or how he got here. He had vague memories flashing in his mind, glimpses of concrete corridors and alien fauna. It was maddeningly barren, with the silence being enough to drive a man mad. How much time has passed since he arrived here? Has it been seconds? Days?  Time itself felt nonexistent at that very moment, simply a construct that meant nothing in this place. It felt as if he was in a dream, trapped in his own head as he traversed his own subconsciousness, floating in a vague void, unable to act or react to anything that could possibly be in there. He all but gave up hope of escaping this dark Hell he had found himself in, until he felt himself being pulled by an invisible force, and abruptly, there was light.

Gordon’s senses came back to him as fast as a train crash, the feeling of barely healed fractures and lacerations coming back to him as his nerves fired. Ringing flooded his hearing, with the HEV’s computer voice, an artificial voice he came to despise, sounding muffled and making it hard to process any of the words being said to him. He couldn’t move, his limbs feeling as if they were being pinned down by a massive weight, as if he was on the bottom of the ocean. The numbing pain shot up his legs and arms, though despite his wishes, there was no way he could even scream, with his throat tight and his vocal cords useless. He couldn’t bring himself to open his eyes, with the weakness draped across his body making even that menial action nearly impossible. He began to wonder if the infinite void he was in before would be better than reality, with the idea of feeling nothing rather than feeling everything to a painful degree seeming like a better option than what he was forced to bear.

As he laid on the rubble, he began to hear something new past the waning ringing; footsteps approaching him. Gordon desperately wanted to move, to protect himself from the new danger, yet as much as he tried, his limbs refused to budge. Soon he realized it was multiple sets of footfall coming near, and soon, he began to make out a voice.

The words slurred together in his mind, making the message hard to decipher, but a few words cut clearer than others:

“Breathing. Freeman. Alive. Help. Out.”

Gordon felt his limp body being moved, raised from the ground by someone, or something, being dragged across the concrete floor to somewhere else. Despite his foggy mind, Gordon couldn’t help but consider the worst; Xen creatures dragging him elsewhere to slaughter him as he did to them, and Military personnel taking him somewhere to question, torture, or even execute him were among the possibilities his short-circuting mind had come up with. However, before he could even do anything to try and prevent whatever fate might befall him, he felt himself drifting off, falling unconscious yet again.

He slowly stirred awake once again to hear the sound of an engine running and tires rolling across a gravel road. He was almost afraid to open his eyes, yet when he gained the strength to do so, his eyelids opened and he took a brief glimpse around. Through his blurred vision, he saw he was in the backseat of some sort of vehicle, laid across the seats. His metal HEV pressed against his body awkwardly, making any movement he could make uncomfortable. His head was supported with a wadded-up hoodie, and his body was covered by a thin blanket that had been thrown onto him. It was strange to see simple kindness extended to him, though he couldn’t help but wonder if it was a trick to make him let his guard down. He glanced towards the front seats, seeing the back of the drivers head, but not who was in the passenger seat. They were speaking to one another, but yet again the words fell out of Gordon’s grasp. He felt himself beginning to drift off again, and despite his wishes to stay awake, he grew limp as he fell unconscious yet again.

When Gordon next woke up, he was greeted with cold air around him. As he was pulled out of unconsciousness, he began to hear rhythmic beeping beside him; something he immediately recognized as a heart monitor. Gordon felt as if a weight was taken off of him, and when he gained the strength to open his eyes again, he saw the reason why. His HEV suit was missing, and he was instead wearing a pale blue hospital gown from what he could gather. He was laying in a bed, with its stiff mattress, albeit uncomfortable, feeling like heaven compared to laying on the cold concrete floors of Black Mesa. He saw bandages covering parts of his body, old blood seeping into them. Past his bed however, he could barely make out anything, with everything being blurry and hard to make out. He must have lost his glasses somewhere, but it was the least of his worries as the pain began to seep in. 

All his limbs felt sore, making it hard to move a single finger. His leg had a throbbing pain in his knee, and he felt as if he was being slashed with knives whenever he attempted to move his arms. His heart felt heavy and his lungs stinged with every breath. When was the last time he took a break to breathe? It felt like the days worth of fighting for his life hit him all at once, making him feel nearly paralyzed, and too tired to do anything to fight it. He began to wonder if it was best to be asleep; at least he wouldn’t have to think or feel. He began to wonder how he got here, racking his brain to try and bring up any clue of what had happened. The last thing he remembered before he woke up was being knee-deep in what he could assume was blood, staring up at something…he couldn’t even begin to describe. He killed the thing keeping the portal between earth and the border world open, so why did he feel so…empty? It felt as though his accomplishment meant nothing, as if he was missing something deep inside. He closed his eyes, attempting to fetch his blotted out memories for a shred of explanation, all before he shot his eyes open, a single image returning to his consciousness.

The man.

Gordon’s memories became clear as day when he remembered the man in the dull, navy blue suit. He remembered its unnaturally piercing eyes, staring deep into Gordon’s very being as if it was examining his very soul and regrets. He remembered its face, with it looking aged, yet it felt ageless at the same time. He remembered the unnatural way it stood, as if it was being held up with strings. He recalled the way it spoke to him as if it never spoke in its entire life before that very moment. He never got its name or its motivations, but something about remembering the man and its almost human facade caused his heart to skip a beat. Paranoia crept up in his mind, and the feeling of being watched began to be overwhelming. Something wasn’t right, as if something he didn’t see was coming after him. He needed to get out of here before it arrived.

Gordon forced his arms to move as he sat up in his bed, wincing before he turned to step out of bed, clasping the side of it with one of his shaking hands. As soon as he put weight on his leg, however, he collapsed onto the linoleum floor, ripping his IV out of his arm in the process. He let out a small squeak; the closest he physically could get to a scream, a pathetic noise that reminded him just how helpless he truly was at this moment. He pushed himself up as much as he could, arms shaking at the exertion, but he couldn’t get back onto his feet. As he tried to get off of the floor in vain, the door to the room opened, and a person appeared in the doorway. It was a nurse, coming into the room only to be greeted by Gordon unsuccessfully escaping his bed. She appeared surprised, immediately approaching him to help with getting him back onto the bed, despite his best tries to escape her grasp. She said a few things to try and comfort him, but Gordon couldn’t process the words before she quickly left the room, coming back with another doctor, presumably for help.

Gordon hated the fact he was back in the bed, with a new IV being attached and bandages being replaced. He wasn’t sure when the next threat would rear its head, and he needed to be prepared for when it did. Yet, he was all but incapable of doing anything of use, and he had to accept it. He could barely even move, less shoot a gun or swing a weapon at anything. 

“Dr. Freeman?”

Gordon was surprised to finally make out what someone was saying, looking up at the doctor who had just finished reattaching his IV. 

“You’re lucky to be alive,” He stated, almost smiling slightly. It was unclear if it was to try and make light of the situation or if it was relief. “Even more lucky to be awake right now. Though please, don’t try getting up again, alright? You might reopen stitches.”

Gordon stared at the doctor’s face blankly before leaning back and staring at the ceiling as the doctor continued talking.

“A couple of scavengers found you back at the ruins of Black Mesa, or, at least that's their story. You’ll have to speak with the police about the entire situation.” the doctor continued, “The Vortigaunt said you were lucky to be found in there, apparently had to drag you out of there.”

Gordon’s brows furrowed, not recognizing the word “Vortigaunt” despite the doctor bringing it up so casually. He looked back at the doctor with a puzzled look on his face. 

“I’m sure everyone will be happy to see you’re alive,” The doctor chuckled, trying to make light of the situation despite Gordon not reciprocating the cheerful atmosphere. “You’ve been gone for a long time, so a lot of us thought you would never return.”

Gordon’s puzzled expression turned to a look of borderline anger, wanting to ask so many questions but being unable to; he didn’t even know if the doctor knew sign language, and he didn’t have paper to write on, that is if he had the strength to hold a pencil.

“You look…upset,” The doctor said, his smile fading, “I can understand why, but if it brings you any comfort, you have hundreds of thousands of people who were wishing for your return. You’re a hero, you know.”

Gordon doubted that sentiment.

“We…believe you were in a coma, sir,” The doctor glanced at his nurse, as if he wanted help breaking the news, “...one that lasted ten years, so you're...lucky to be alive at all.”

The doctor continued to explain the situation, claiming that Gordon was lucky to have his brain still functioning despite being asleep for that long, but the words went through one ear and out the other. Gordon didn’t process the doctor trying to speak to him, only staring into the wall behind him as he leaned back in his bed. He didn’t even blink once as reality seemed to become meaningless, dissociating as his brain wouldn’t even allow him to process the time lost. To him, he was gone for a few mere moments, but an entire decade had passed in the time it took him to escape the void he was in for a brief, yet agonizing time. He wondered if his friends had forgotten about him, if they were even alive after the Resonance Cascade; they almost certainly believed he was dead at the very least. Gordon had been dead to the world for so long, he felt surprised anyone came to rescue him at all. After all, who would rescue the man who caused so much death in the span of a few days? Was he supposed to go back into normal society after everything? Was he supposed to be praised as a hero, despite the fact he was just a lowly scientist who just wanted to survive?

Gordon wished to go back to sleep. Being awake felt more agonizing than the temporary stasis ever did.

[vigilskeep]

one thing abt visibly chasind morrigan that’s super interesting is that it makes your ability to ask if flemeth is really her mother actually makes sense when it’s startling how fereldan flemeth looks and dresses when you’re brought there

[lets-try-to-be-normal-otakus]

Hi I have a desperate need for platonic soulmates stobin where she's sooo protective of Steve (and vice versa) and who he dates.

And like, her giving eddie the stink eye when he's a douche canoe (his attempt at flirting/getting over the munson doctrine).

Robin waking up in the middle of the night when steves sad and going over to comfort him. Eddie being able to help but doesn't soothe all of it and steve just needing robin. And like, steve getting out of bed with eddie when he feels robin needs him and eddie being sad but understanding and steve kissing him silly.

Steve having a locket or a watch or similar of both Robin and eddie on him 24/7. Of the fact that even though him and eddie aren't soul mates, they love eachother so fuckin intensely and desperately

And Steve's happy feelings about eddie transfer over and him and Robin being friends

[mc-tummy-blur]

And I’ll get you yet

I’ve got to make you mine

Just know I’m not the sinister type

Click for better quality

Check my pinned post to see links on how you can help the people in Palestine

[daily-whistlebreeze]

daily whistlebreeze until ap becomes PoV day 1586

When I say Apple and Flutter aren't The Best parents, I mean it. I do fully intend for them to fuck up raising Stretch and Rustle

[camelspit]

quick maruca drawings 💙

@skylilac @callas-pancake-tree @arson-anarchy-death @steal-nightmares-leave-dreams @neverseen-nevermore @abubble125 @purplesoup-lad-le @gay-otlc @thefoxysnake @keeper-of-the-lost-dadwin @ravs6709 @corruption-exe @kamikothe1and0nly @that-glasses-dog @presidentroarie @even-if-in-another-time @nyxpixels @slozhnos @katniss-elizabeth-chase @sofia-not-sophie @moontoastt @lemon-girl-in-devil-town @three-bunnies-in-a-trenchcoat @purpleunicycle @just-a-honey-badger @loverofallthingssmart @antisocialdork @tamsong @cutebisexualmess @tastetherainbow290 @gayupstraight @myfairkatiecat @famousinfamous @kale-of-the-forbidden-cities @oroshka @tw-5 @squishmallow36 @iggydancebreak @cosmxc-ars3hol3