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Sorry, I didn't see the "<", I just rounded...

Check out your information.

13   + 4 p    =   49  + 3p    solve for p

p = 36

cost will be    13 + 4(36) = $________

 m < 15.87... 

Actually,    m = 15   is the largest integer value of m such that the equation 3x^2 - mx + 21 = 0 has no real solutions.

ugh...

When I wanted to click "Show Preview", they deleted my answer...

So... here we go again:

\(\frac{\mbox{Total number of all possible solutions}}{\mbox{Total number of all solutions}}\)

In the set, we can choose 100 numbers \(\Rightarrow\)\(\frac{n}{100}\), where n is a positive integer.

From those 100 numbers, ( 100 / 2 = ) 50 numbers are divisible by 2.

From those 50 numbers,

50 / 6 = 8 mod 2 \(\Rightarrow\) 8 numbers

are divisible by 6.

Subtract both numbers \(\Rightarrow\) 50 - 8 = 42 numbers, so

42 / 100 = 21 / 50 .

Thus, our answer is 21 / 50.

ok, thanks for the help. 

What have you done so far? 

Just substitute for x, y, z, expand the brackets and cancel down.

You're just left with the number 3.

Put the number into polar form \(\displaystyle (1/2,\pi/2), \)  (abbreviated).

We're finding a root so the number has to be put into its multivalued form, \(\displaystyle (1/2,\pi/2+2k\pi), k=0,1,2,...\)

\(\displaystyle z=(1/2,\pi/2+2k\pi)^{1/2},k=0,1,\\=(1/\sqrt{2},\pi/4+k\pi),k=0,1,\\ =(k=0),(1/\sqrt{2},\pi/4)=(1/2+i/2),\\ \text{or }(k=1),(1/\sqrt{2},5\pi/4)=(-1/2-i/2).\)

Equate the two:

 x^2 + 4x + 6 = 2x^2 + 7x - 4

Simplify:

x^2 + 3x -10 = 0

Factor:

(x-2)(x+5) = 0

So the two roots (x-values) are:  x = 2 and x = -5.  These are c and a, respectively.   

thx for your help!!!

Sorry BuilderBoi.  :)

oh if you have a free geogebra account you can save you pics online.

For posting all of my pics I used Gyazo.  It is like an onle version of 'Snip'

Gyazo has a free and a paid version.  They are the same except the paid version lets you store as many pics as you want but the free one stores only the most recent few.  I am not sure how many becasue I have the paid version.

I do not think Gyazo is the best online storage of pics, I expect there are many to chose from. This forum saves in Tinypics I think if you use the provided one.  But i used to find the link to tinypics was often broken, so Gyazo has been a better for me.  

Thanks! I've used it in class before, but I didn't know you do such stuff with it lol! (You misspelled my name btw.)

Hi BilderBoi,

Thanks!

I use a free program called GeoGebra.  It takes a while to get the hang of, just do simple things to start and your knowledge will build. 

Here is a download page.  I didn't know that there were all these ones to choose from.  I just use Classic 6.

I don't think there used to be so many when i dowloaded mine.  ://

ABCDE is NOT a regular pentagon so your logic is incorrect.

That's a cool drawing, how did you make it?

Equal chords are subtended from equal angles. at the centre

We have 4 equilateral triangles.  

together that make an angles at the centre of  4*60 = 240degrees

The angle at the centre remaining for the last tirangle is 120 degrees.

The Apothem for the 4 congruent trianlges is   sqrt3

So their total area is  4sqrt3

The last triangle is isosceles with angles 120, 30,30

The length of the base is 2sqrt3 and the height is 1 so ther area is    sqrt3

So the total area is  5sqrt3 units     (which agrees with asin's answer.)

Here is the pic

\(ABCDE\) forms an irregular pentagon, which can be split into \(5\) triangles, each with an area of \(\sqrt3\), so the answer is \(\color{brown}\boxed{5\sqrt3}\). 

The smallest k that works is 72

The width of the interval is 16.

There are \(9 \times 10\times 1 = 90\) options. There are \(22\) numbers that work: \(136,176,216,256,296,336,376,416,456,496,536,576,616,656,696,736,776,816,856,896,936,976\)

Thus... the answer is \({22\over 90}= \color{brown}\boxed{11\over45}\)

Let's organize our information. 

_ _ 6

There are 9 * 10 ways to fill in the other two spots. (Because the first one can't be 0)

We check the first ones and we find that 

136

216

256 

works.

Each time the number grows by 40. 

So this is (999 - 136) / 40 = 863 / 40 = 21.575, but then you have to count 136, thus the probability that the number is divisible by 8 is 22/90 = 11/45.

⚡⚡⚡

ShockFish

Let the center of CD be O. From O to A and O to B, OA = OB = 2. Thus OAB is an equilateral triangle: Area = 1.732

Area of sector OAB = (1/6)(pi)(4) = 2.094. Area of segment AB = 2.094 - 1.732 = 0.362.

Area of semicircle with diameter AB = 1.571

Area of reqd shaded region = 1.571 - 0.362 = 1.209.