Anonymous
asks:
The lengths of two sides of an isosceles triangle are 8 and 10. The length of the third side could be: a) 6, only .. b) 8, only .. c) 10, only .. d) 8 or 10

Since an isosceles triangle is by definition “triangle with at least two equal sides”, your answer is d) 8 or 10, because they could be 8,8,10 or 8,10,10, and it would in any case be still isosceles. Since we don’t have any indication of the equal sides being the longer ones or the shorter ones, we can’t say for sure whether they need to be 8 or 10 :)

-M

ryanandmath:

How to read math. You’d be surprised how far this will get you.

EDIT: Some corrections

Anonymous
asks:
David stands near a tree that casts a 35-ft. shadow, while David’s shadow is 10 feet in length. If David is 6 feet tall, how tall is the tree?

All you need is to do a proportion (you can also look at the question I just answered) 

So you now that a 6ft tall person casts a 10ft tall shadow, and a x tall tree casts a 35ft shadow

You can also write it as 6:10=x:35 -> (6*35):10 -> the tree has to be 21ft to fit your problem :)

-M

Anonymous
asks:
The scale on a map indicates that 1 2 3 inches represent 35 actual miles. i) How many miles does eight inches represent? ii) If the distance between two towns is 75 miles, how far apart are they on the map

Assuming that 3 inches are 35 actual miles (If I am assuming wrong please correct me, but I don’t really understand what you meant by “1 2 3 inches”), and you need to find out how much 8 inches would be, you just need to put down a proportion.

So you have that 3in:35m=8in:x

So you have (35*8):3= 93,(3)m, which fits, if you consider that 3in are 35m, so 6 inches would be 70m and 8 a bit less than 105m!

Then you need to know how much 75miles would be, and you do just the same thing. You put down the proportion this way

3in:35m=x:75m

So you have (3*75):35= 6,42~inches

Hope I helped!

-M

asks:
Is 2 a solution of 3x+5 ≥ 12?

Substitute!

3(2) + 5  ≥ 12 ?
6 + 5  ≥ 12 ?
11  ≥ 12 ?

No, 11 is not greater or equal than 12.

Anonymous
asks:
An airplane flies at a rate of 200mi/h. If the airplane has flown for 4 h, how many miles has it traveled?

distance=rate*time (I remember this as DRT i.e. “dirt”)

distance= (200 miles/hour)(4 hours)

800 miles (the hours cancel out)

-Nic :)

curiosamathematica:

The field axioms. Intuitively, a field is a set equipped with two operations, addition and multiplication, each of which make the set a commutative group. Furthermore, the operations are compatible by the law of distributivity.
(Edit: there is a typo in the 7th axiom, which should read (x · y) · z = x · (y · z), of course. Thanks for noticing, archonsandtaters!)

curiosamathematica:

The field axioms. Intuitively, a field is a set equipped with two operations, addition and multiplication, each of which make the set a commutative group. Furthermore, the operations are compatible by the law of distributivity.

(Edit: there is a typo in the 7th axiom, which should read (x · y) · z = x · (y · z), of course. Thanks for noticing, archonsandtaters!)

Check out this submission we got from

State Machines explained using a math video game

Hello! We built a state machine train set within the game world of Mathbreakers, and we’d love to show it to you! http://player.vimeo.com/video/98192528

Mathbreakers is a 3-D adventure-exploration game that currently teaches math in a very visual and tactile way to kids 7-12. We’re trying to push the upper bounds of the gaming platform, which is why we built the Turing trains ;-) We’ll be doing additional higher math experiments using the game in the near future!

The game is currently on Kickstarter — we hope you can check it out! https://www.kickstarter.com/projects/mathbreakers/mathbreakers-a-3-d-math-exploration-game

Anonymous
asks:
a company is shipping a product in a cardboard box. the box must have a height of 8 inches and a width of 6 inches to fit on the shelvs. what must the length be in order to have a volume of at least 500in squared?

Okay so volume is base x height x width. 

We know height and width and what it has to be equal to in the end.

So:
8 x 6 x “unknown” = 500
48 x “unknown” = 500
"unknown" = 10.4166666…

So the length much be at 11 inches to have a volume of at least 500in squared.

(This is assuming you need it rounded to a whole number and can’t have a length of 10.42 inches)

- Kendra

Anonymous
asks:
The amount of medication, in milligrams, in a patient’s bloodstream t hours after it has been administered is given bythe formula A = 8(6.85)-0.36t. Find to the nearest tenth of an hour, how long it would take until only 0.1mg of the drug remains in the patient’s bloodstream.

Okay so your amount is equal to 0.1 mg and you need to find t. 

0.1 = 8(6.85)-0.36t
0.1 = 54.8-0.36t
-0.54.7 = -0.36t
151.944444… = t

We need to round this to the nearest tenth of an hour, so it will take 151.9 hours :) 

I hope this helps, if not, feel free to ask again.

- Kendra