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Here is an easy way:   Substitute in the given x,y value choices to see which set 'works'

AM = CM and BM = CM so AM = BM. So M is the midpoint of AB.

Triangle AMC is isosceles, so angles MAC and MCA are equal, call them alpha.

Triangle BMC is isosceles, so angles MBC and MCB are equal, call them beta.

Sum the angles in the triangle ABC, 2.alpha + 2.beta = 180, so alpha + beta = 90 = angle ACB.

Thanks Guest for showing me my error! I meant 1/8 x 7/4 =? That makes more sense now! 

Sorry if my additon error confused you.......

-Abi

giai he phuong trinh cho nao z ?

Xin chào người bạn đến từ Việt Nam!

giai he phuong trinh cho nao z? Nó không tốn gì cả. Bạn không phải trả bất cứ điều gì.

  !

If x=0 what is the answer?

If x=1 what is the answer?

If x=  just a tiny bit less than 1,  what is the answer?

Try  x=1/4, x=1/3, x=1/2, x=2/3,  

What do you have so far?  

Please let guest asker answer this.

A square sheet of paper ABCD is folded such that B falls on the midpoint M of CD. In what ratio does the crease divide BC?

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The ratio is 21 / 35

(x + 4) + (3x - 2) = 180

4x = 178

x = 44.5          proof  ==>       (44.5 + 4) + (3*44.5 - 2) = 48.5 + 131.5 = 180

-i is not real. Thus, we square it. -i^2 = i^2 =-1. -1 is real. Thus, we square 1. After a whole chain of squaring 1 and -1, we end up eventually with 1, so the answer is 1.

I seem to have overlooked the 4,0,0,0 case... 

I might be wrong, but for the 2,1,1,0 case the number of ways should be the number of arrangements of 2,1,1,0 * number of ways to pick, and the number of arrangements is 4!/2! = 12, and the number of ways to pick the bracelets: 4C2 for the first pair, 2C1 for the second, 1C1, multiply, 6 * 2 = 12, then * 24 = 288, so perhaps the pair of 1s was left out in your solution?

Simplify \((1 + i\sqrt{3})^6 \)

Hello Guest!

\(\color{BrickRed}(1 + i\sqrt{3})^6\\ =(1 + i\sqrt{3})^2(1 + i\sqrt{3})^2(1 + i\sqrt{3})^2\\ = ( -2+i\cdot 2\sqrt{3}) ^2 \cdot (-2+i\cdot 2\sqrt{3})\\ =(-2^3-i\cdot 2^3\sqrt{3}) \cdot (-2+i\cdot 2\sqrt{3})\\ =\color{blue}64\)

  !

Your question asks how to multiply equations....but the numbers you provide are an addition....

1/8 + 7/4      to  ADD them , you need a common denominator

1/8 + 14/ 8   = 15/8 =   1 7/9

IF you want MULTIPLY them:

1/8 X 7/4   just multiply the numerators (top numbers) and multiply the bottom numbers

 = 7/32    

Consider the set of all points (x,y) in the coordinate plane for which one of the coordinates is exactly the square of the other. If we were to plot all such points, into how many regions would the resulting graph split up the plane?

Hello Guest!

\(y=x^2\\ y=\pm \sqrt{x}\)

The coordinate plane is divided into five planes by the graphs \(y=x^2\) and \(y=\pm\sqrt{x}\).

  !

Sorry, that's incorrect. The correct answer was 8.

https://web2.0calc.com/questions/question_139  

(This excellent work has been done by heureka)

Thanks!!!

😀

0.1x  -  1.6   =   0.2x  +  2.3

0.1x  -  0.2x   =   2.3  +  1.6

-0.1x  =  3.9

x  =  -39

By the angle sum/difference formula for cos,

cos(a - b)  =  cos a cos b + sin a sin b

And so...

\({\cos(\frac{\pi}{6}-x)}\ =\ \cos(\frac{\pi}{6})\cos(x)+\sin(\frac{\pi}{6})\sin(x)\\~\\ \phantom{\cos(\frac{\pi}{6}-x)}\ =\ \sin(\frac{\pi}{6})\sin(x)+\cos(\frac{\pi}{6})\cos(x)\)

Now we can see that

\(A\ =\ \sin(\frac{\pi}{6})\ =\ \frac12 \\~\\ B\ =\ \cos(\frac{\pi}{6})\ =\ \frac{\sqrt3}{2}\)

And so...

\(\dfrac{B}{A}\ =\ \dfrac{(\frac{\sqrt3}{2})}{(\frac{1}{2})}\ =\ \sqrt3\)    _

1  3  4  6  9  12  15  16  18  21  24  25  27  30  33  36  39  42  45  48  49  51  54  57  60  63  64  66  69  72  75  78  81  84  87  90  93  96  99  100  >>Total = 40 such numbers.

Probability = 40 / 100 =2 / 5

1- 100     100 choices

1   4   9  16  25   36  49  64  81 100 are the perfect squares     10 out of 100

Multiple of 3    there are 33    3 - 99        33 out of 100

1/8+7/4=1.875

😀

Just like the girl one you posted earlier

 Adjacent side is the shadow    14.3

Opposite side is the height

Tan 68 = opposite / adjacent

tan 68 = height / 14.3           Now use your calculator to find  tan 68   then multiply by 14.3 m for your answer....height=.......m

Abi.....PLEASE avoid just posting an answer with no explanation !   It is of no use to anyone actually wanting HELP trying to LEARN !!

Law of Cosines

DE ² = 12²  + 13² - 2 (12)(13) cos 59^o       Do the math on the right side ...then take the square root to find  DE

Tan is OPPOSITE side over ADJACENT side

   so opposite is   20   (or multiple of) = height

    adjacent   is 50  ( or same multiple of )= distance

1 - 

N mod 13 = 11

N = 13m  +  11, where m=0, 1, 2, 3.........etc.

5000 / 13 + 1 =385 integers that satisfy the congruence.

2 -

N mod 13 = 11

N mod 12 = 5, solve for N

Using "Chinese Remainder Theorem + Modular Multiplicative Inverse", we have:

N = 156m  +  89, where m =0, 1, 2, 3........etc.

5000 / 156 + 1 =33 integers that satisfy both congruences.