#x^2-7x+10
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redallia.bsky.social
Meanwhile, we can have more easily resolved ambiguous states:

(x² - 7x + 10):0 ↔ ⋈{(x-2), (x-5)}

A is the composite polynomial, T is the target state of zero for the equation, ⋈{(x-2), (x-5)} is a reconcilable set, and ↔ shows that these are equivalent states.
April 4, 2025 at 8:13 PM
nathanday.bsky.social
I had a great time today at #MathsConf38.
I particularly enjoyed @ljohns6.bsky.social's workshop about connecting concepts.

At the end we were challenged us to come up with a question featuring the expression 𝑥² − 7𝑥 + 10.

Here's what I came up with.
The masses of 28 parcels are represented in the histogram. Find x. An image of a histogram with: • the first bar covering 0 < m < 3 kg and with frequency density 2; • the second bar covering 3 < m < 7 kg with frequency density 1; • the third bar covers 7 < m < x kg with frequency density x
June 21, 2025 at 5:56 PM
nathanday.bsky.social
I think these questions need a tag! Maybe #x^2-7x+10?
@ljohns6.bsky.social
The masses of 28 parcels are represented in the histogram. Find x. An image of a histogram with: • the first bar covering 0 < m < 3 kg and with frequency density 2; • the second bar covering 3 < m < 7 kg with frequency density 1; • the third bar covers 7 < m < x kg with frequency density x Find an expression for the value of the 𝑛th square to be shaded in. A bag contains 𝑥 counters. Three of the counters are green. Two of the counters are red. The rest of the counters are blue. Pete takes a counter from the bag and replaces it. Liza then also takes a counter from the bag. Find an expression for the probability that Pete’s counter was blue and Liza’s counter wasn’t red. A right-angled triangle with a horizontal hypotenuse of length 7 and a height of sqrt(10). x is labelled as the distance from where the height meets the hypotenuse to the corner of the triange. The question says to find x.
June 21, 2025 at 7:54 PM
mathmisery.bsky.social
we can do a bunch of inspection. y = 2x^2 + x from the 1st eq. the 2nd eq becomes (2x^2 + x)*x^2 + 7x = 10. by inspection x = 1 solves it and so y = 3. another solution is x = -2 making y = 6. and both give x + y = 4. eq 2 is also y = (10 - 7x)/x^2, so eq 1 and 2 coincide in two spots (1,3), (-2,6)
September 21, 2025 at 7:31 PM
wyrdingstudios.com
Anybody good at algebra want to have a go at this and tell me if it’s solvable with the information provided? Feral Teenager thinks it isn’t, and I can’t make sense of it either. The test had a lot of badly written questions. 🤬

(This was the only one she couldn’t do, and she’s mad about it.)
A photograph of a multiple choice question from a math test. The question is “Samantha made a mistake while trying to solve this problem. Which step did Samantha do incorrectly?” followed by a table containing the steps in question: 7x - 35 = 2x + 15 Step 1 7x - 2x - 35 = 2x - 2x + 15 Step 2 5x - 35 + 35 = 15 - 35 Step 3 5x = 50 Step 4 5x ÷ 5 = 50÷5 x= 10
June 27, 2025 at 10:04 PM
swampudlian.bsky.social
2 of the last 3

All of 2022: 45 times
All of 23: 82 times
Jan 24: 11 times
Feb 24: 7x
Mar 24: 8x
Apr 24: 5x
May 24: 9x
Jun 24: 12x
Jul 24: 10 times
Aug 24: 12 times
Sept 24: twice
24 so far: 76 times
On pace for 111.3 in 2024

#ZeroOutTheGrid

#Wordle 1175 X/6

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September 6, 2024 at 4:49 AM
mrlevmaths.bsky.social
Think this one works! Really fun #x^2-7x+10 challenge @ljohns6.bsky.social
#MathsToday
June 21, 2025 at 10:13 PM
nathanday.bsky.social
I'm now enjoying the idea of
a) For each question, show that x^2-8x+48=0
b) Change each question so that x^2-7x+10=0
June 21, 2025 at 9:02 PM
covidchronicles.bsky.social
Day 1008—COVID is Airborne.

So I built myself a computer fan MERV13 Corsi-Rosenthal Box—Unlike brand-name purifiers, no part of it is proprietary, all components can be replaced. It's quieter—so quiet!—cheaper & 100% portable (12 hour battery life). Biggest win in a while.

#COVID #CleanAir
Maple/Cedar CR BOX Build: I cut scraps of 1/2" maple plywood into strips that ended up being too narrow for the fans and filters to fit "inside" the body of the box. ("Doh!") So I ended up making channels out of leftover cedar with my table saw (using a dado blade), and gluing them onto the plywood (having also previously glued in backing strips so that I'd have more than the 1/2 inches to attach the channels to. Much more complicated than I wanted, but in the end I gotta say: it doesn't make for a bad look at all! The inside is entirely sealed with caulk except for the top two cedar channels—they top off the filters snugly thanks to a strip of foam tape on the inside wall of the box (see picture). My (lack of) process is why I didn't flair this as a tutorial. I just went for it and kept modifying the build as I went. I intend to make a second box (for 20x20x1 filters, using 6 fans—3 on top, 3 on one side) and for that I'll simply cut dados for the filters into a piece of 2x10. Mitering the 2x10 at 45 degrees, gluing it up and presto! A second build is why many of the components listed below were ordered in packs. Some were sourced outside of Amazon (and I made my purchases before the Canadian boycott began) but I added links merely as a reference. #CleanAirCrew #LongCOVID #COVIDisAIRBORNE #StillCoviding Parts list: (2x) 3M Filtrete MPR 2200 (16x25x1) 1-inch Premium Furnace Filters — 88.80$ (4-pack) (7x) Noctua NF-P12 redux-1700 PWM, High Performance Cooling Fan, 4-Pin, 1700 RPM (120mm, Grey) — 17.95$ (Each) (7x) 120mm PC Fan Grill Guard, Metal Slivery Black — 11.99$ (10 Pack) (1x) DC to 4Pin/3Pin PC Fan Cable Splitter: Goes from DC 5.5mm x 2.1mm Female to two (2x) 4 Pin/3 Pin PC Fan Power Cables (11.8in/30cm) — 14.99$ (2 Pack) (1x) 4-Way PWM Fan Splitter Cable - Allows you to connect up to four 4-Pin/3-Pin PWM fans to a single 4-pin motherboard fan header — 11.99$ (2 Pack) (1x) 3-Way PWM Fan Splitter Cable - 4 pin fan splitter cable connects 3 computer case fans to a single 4-pin motherboard fan header. (12 inches long) — 10.39$ (2 Pack) (1x) DC 12V 5A Power Supply 60W AC Adapter 100-240V 50-60Hz AC to DC Converter 12 Volt 5 Amp Power Adapter Transformer with 5.5mm x 2.5mm DC Outlet Plug — 14.71$ (1x) Self Adhesive High Density Foam Insulation Tape 1In x 1/8In x 33Ft — 10.66$ (33 Feet) (1x) 4 inch Hole to Hole Center Cabinet Handles (Overall Length is 4-1/2 inch) Matte Black Stainless Steel Kitchen Cabinet Pulls — 23.99$ (5 Pack) (1x) 3/4 Inch Flexible Silicone Rubber Cable Cord Grommet/Pass Through (Black) — 7.98$ (10 Pack) Optional: Battery Powered/Portable (1x) Anker Prime Power Bank, 27,650mAh 3-Port 250W Portable Charger (provides 12.5 hours on one charge) — 169$ (1x) USB C Male to 12V 3A DC 5.5 x 2.1mm Male (3FT) — 14.99$ (2 Pack) #CRBox #COVIDisAIRBORNE #CleanAirCrew
June 13, 2025 at 9:36 PM
arithmaticks.bsky.social
I keep forgetting to take pictures of cool things we do in #mathstoday to share… so I’ve recreated on notes app 😂
Today Y10 were looking at expanding double and triple brackets and absolutely smashed it. So we spent the last 10 mins working “in reverse” as a taster for their next lesson…
Two questions with gap fills for working in reverse at the end of expanding double brackets lesson, leading to “factorisation” ready for the real deal in their next lesson! 1) gap fills for constants in (x+_)(x+_) = x² +2x + 3x +7 2) gap fills in (_+_)(_+_) = x² +5x __x -10 Two questions with gap fills for working in reverse at the end of expanding double brackets lesson, leading to “factorisation” ready for the real deal in their next lesson! 1) gap fills in (_+_)(_+_) = x² + __ + ___ +12 given that the missing terms in the RHS sum to +7x 2) gap fills in (_+_)(_+_) = x² + __ + ___ -15 given that the missing terms in the RHS sum to -2x
September 10, 2025 at 8:53 PM
swampudlian.bsky.social
2 consecutive and 4 of the last 7

All of 2022: 45 times
All of 23: 82 times
Jan 24: 11 times
Feb 24: 7x
Mar 24: 8x
Apr 24: 5x
May 24: 9x
Jun 24: 12x
Jul 24: 10 times
Aug 24: 7 times
24 so far: 69 times
On pace for 107.0 in 2024

#ZeroOutTheGrid

#Wordle 1161 X/6

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August 23, 2024 at 10:06 AM
nathanday.bsky.social
This one took some work... but I quite like it.

#x^2-7x+10
René invests £1000 in a savings account for two years. The savings account pays interest at a fixed rate, compounded annually, but also gives a £1 loyalty bonus at the end of the second year. The total amount of interest René receives in the second year is 7% bigger than in the first year. Find the two possible interest rates for the account.
June 22, 2025 at 7:10 AM
ljohns6.bsky.social
Yes! Yes we do!!! I have a 5 hour train trip in a bit.....🚆
I wonder what I will be spending the time doing 🤔
What a fantastic idea! Watch this space!
#x^2-7x+10
June 22, 2025 at 5:53 AM