All Answers 358101 Answers

You know GoldenLeaf, I have never seen anyone do simultaneous equations quite like that before. 

YES DRAGON THIS QUESTIONER NEEDS AN EXPLANATION!

Also look there.

factor 6x^2+11x-10 =

(3x - 2) (2x +5)

"Quotient" means "divide".....so we have

20/5 + 9 =

4 + 9  = 13

√(2.5)  = (2.5)^1/2  in exponential form.....

There are only three solutions to this problem......if he only needs a minimum of 6 notebooks.

He can buy no more than 2 of the $5 dollar notebooks. If he bought 3, he wouldn't have enough money for 3 more, even the cheaper ones !!!!

So, let the ordered pair x, y represent the number of $5 notebooks and the number of $2 notebooks, respectively. So we have:

(x, y) = (2, 4) ,  (1, 5),  (0, 6)......and as AT pointed out, buying 6 of the $2 ones would be the cheapest route.

-l1/3l - l-2/3l =

-1/3 - 2/3   =

-1

Nice answer AT....!!!

Here's another way.....

Notice that the midpoint "formula" is just ( [x₁ + x₂] / 2 , [y₁ + y₂ ] / 2  )....So, let's suppose we know (x₁, y₁)  and the midpoint - call it (m₁, m₂). Then, to find the other endpoint, (x₂, y₂),  we have (2m₁ - x₁ ,  2m₂ - y₁). The process would work in a similar manner if we were trying to find (x₁, y₁).

Basically, we're just "manipulating" the midpoint formula to find an unknown......!!!!

Hope that helps......

When you divide by a fraction, you flip the fraction and multiply it.

So: 60/5/3 = 60 * 3/5 = 180/5 = 36

Hmm don't know what you mean exactly by that, but it reminds me of this:

Basically using an infinite series this pattern will converge to 1/3 as n→∞.

Closest thing I could think of to your question.

Multiply both the numerator and denominator with the radical in the denominator. 

$$\frac{5}{\sqrt{3}} * \frac{\sqrt{3}}{\sqrt{3}}$$

I would like to add to the above answer.

Since you can't have 3.3 or 2.6 notebooks, the highest you could go would be 4 spiral and 2 three-ring notebooks for a total of $18. Or you could just buy 6 spiral notebooks for $12 which would be the most efficient use of the money...

First, imagine the following segment:

If you know the endpoint A and the midpoint B, then finding the other endpoint C is easy.

You would first have to find the change in X (ΔX) and change in Y (ΔY)when moving from point A to point B.

Lets give point A the coordinates (2,4) and point B the coordinates (5,8).

To find ΔX we subtract the X coordinate in point B from point A: ΔX=5-2=3 ΔX=3

To find ΔY we subtract the Y coordinate in point B from point A: ΔY=8-4=4 ΔY=4

To verify, simply add the ΔX and ΔY to the point A coordinates and you will get the coordinates of point B. 2+3=5 and 4+4=8

Since B is the midpoint, the distance between A and B is equal to the distance between B and C, which means the ΔX and ΔY are the same.

So take the coordinates of point B and add the ΔX and ΔY: 5+3=8 and 8+4=12

With that we find that the coordinates of point C are (8,12)

The GCF is $${\mathtt{4}}$$. Do you want the explanation?

Well this one can be solved with the Side-Angle-Side theorem.

Assuming the lamp post is at a 90 degree angle from the ground we have this:

Where B is the height of the lamp post, A is the length of the shadow, and b is the elevation of the sun casting the shadow.

The sum of the angles in a triange always add up to 180 degrees, so since we know two of the angles, the third is easy. 180 - 64 - 90 = 26 (Assuming the lamp post is angled 90 degrees relative to the ground.)

So far we have a=26 b=64 c=90 and A=8 B=? C=?

So the law of sines states that A/sin(a) = B/sin(b) = C/sin(c), therefore:

8/sin(26) = B/sin(64) = C/sin(90) = 18.25. (Fun fact: sin(90) = 1)

So solving for C: C/sin(90) = C/1 = C = 18.25

So now we have a=26 b=64 c=90 and A=8 B=? C=18.25

now to solve for B:  B/sin(64) = 18.25    B=18.25*sin(64) = 16.4

Finally all the cards are on the table: a=26 b=64 c=90 and A=8 B=16.4 C=18.25

So to answer the question, the height of the lamp post is 16.4 feet.

Thank you for supporting my answer, TakaHiroMaeda.

Sorry If it's spelled wrong.

A ratio would be something like 3 girls to 2 boys in a class or 5 losses to 1 win.

A rate is something per something else like miles per hour or gallons per minute.

Indeed, we will answer all the questions to the best of our abilities. However, we favour people who register. :]

So if you need an answer quickly, register. :]

In terms of the Borrower

$$(x+20)-18$$

In terms of Lender

$$(x-20)+18$$

s = # of spiral notebooks

t = # of three-ring notebooks

$$s + t \ge 6$$

$$2s + 5t \le 20$$ 

Sure go ahead.