ilorty

The question is not hard at all: it's funny how some people don't get the similarity between this and the Pythagorean theorem!

The formula for right triangle: c^2 = a^2 + b^2

Formula for distance between opposite points of rectangular prism: d^2 = x^2 + y^2 + z^2

See how simple it is? It probably faster than the time it takes for me to open my front door! (Really, that creature is super unruly, maybe oil will help)

Do you really want an answer? An answer you want, an answer you get.

Using the formula, we see that the diagonal squared is:

d^2 = 3^2 + 4^2 + 12^2

Evaluate:

3^2 + 4^2 + 12^2 = 9 + 14 + 144 = 167

Now root that:

And....your answer is sqrt(167)

maybe if you paid attention in class (I am assuming they gave a lecture) you would have known this simple formula. you could even do a quick google search!

maybe I finally entered my house after hours of trying to swing the door open...

:)

We need to sharpen our trig skills, because believe it or not, this problem involves trig!

Anyways, I assume we are allowed to use calculators. 
 

This calls for "casework", though not much of counting...

We first need to figure out a "not so specific" range for quarters. We see that:

25 - 17 = 8

Which means, she can have from 1 to 8 quarters, but that is not specific enough. We also need to calculate the total amount of dimes she has:

0.1 * 17 = 1.7

Now, we can start:

If there were 1 quarter:

Not possible: not enough for the minimum amount of money

If there were 2 quarters:

Not possible: not enough for the minimum amount of money

If there were 3 quarters:

Not possible: not enough for the minimum amount of money

If there were 4 quarters:

Not possible: not enough for the minimum amount of money

If there were 5 quarters:

Not possible: not enough for the minimum amount of money

If there were 6 quarters:

Not possible: not enough for the minimum amount of money

If there were 7 quarters:

Not possible: not enough for the minimum amount of money

If there were 8 quarters:

Not possible: not enough for the minimum amount of money

so leave your answer blank.

BUT!

We could have saw from before whether there would have been enough money or not!

If we multiply: 8 * 0.25 = 2, and add that to 1.7, we get 3.7. Not possible.

What I don't understand about this problem is: If they literally said that Akana had some dimes and quarters, and they said that this was true, why did they give a possibility of "not possible"? Akana, you probably discovered Roman Numeral 0.

:)

In my opinion, there's no point of that extra triangle, maybe just there as a red herring...

Thanks! Maybe I'll practice my explaination skills, so that it won't be that hard to understand my answers....

deleted

:)

When the customer recieves both gift cards (i wish i were that guy! who doesn't like free money?), it would be the LCM of 20 and 45. Then we could do some math, and voila! the answer

LCM (20, 45)

How to do this? Let's go back to what we learned in third grade: GCF and LCM (or was it fourth? it has been such a long time...)

This one isn't hard: we don't need to use the "prime factorization method", we can use the "list out the numbers" method we learned:

20: 20, 40, 60, 80, 100, 120, 140, 160, 180

45: 45, 90, 135, 180

So, now we know that the 180th customer got 2 gift cards

But we are not done yet! We need to know how many people have recieved the gift card!

Let's get some counting ready!

There are 9 $10 (90 total) gift cards, and 4 $15 (60 total) gift cards, so add that together, and we have a total of $150 worth of gift cards.

Here are the answers, for your conveniance:

1. 180th person

2. $150 worth of gift cards

:)

(x+1)/(x-2)≥(x+3)/(x-4)

Move the right to the left:

(x + 1) / (x - 2) - (x + 3) / (x - 4) >= 0

Find the LCD:

(x + 1)(x - 4) / (x - 2)(x - 4) - (x + 3)(x - 2) / (x - 4)(x - 2) >= 0

Combine the two fractions:

(x + 1)(x - 4) - (x + 3)(x - 2) / (x - 4)(x - 2) >= 0

Multiply both sides by (x - 4)(x - 2):

(x + 1)(x - 4) - (x + 3)(x - 2) >= 0

Expand:

x^2 - 3x - 4 - (x^2 + x - 6) >= 0

Distribute negative:

x^2 - 3x - 4 - x^2 - x + 6 >= 0

Combine like terms:

-4x + 2 >= 0

Subtract 2:

- 4x >= -2

Divide - 4:

x <= 1/2

:)
 

who is the owner???