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I think you're missing a picture :)

The "Think About It" name usually hints at an elusive trick to the question. There doesn't appear to be a trick anywhere; here's my best attempt:

If we arrange the players into two-player groups, we'll cut the players in half. 128 games have been played.

Here is the player to game progression:

(256,0)

(128,128)

(64,128 + 64)

(32, 128 + 64 + 32)

(16, 128 + 64 + 32 + 16)

(8, 128 + 64 + 32 + 16 + 8)

(4, 128 + 64 + 32 + 16 + 8 + 4)

(2, 128 + 64 + 32 + 16 + 8 + 4 + 2)

(1, 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1)

Fun fact: sum of powers of 2 starting from 2^0 up to 2^n = 2^n-1

Proof: our answer is 255.

Oh man... now I get the trick (think about it).

Hi AlgebraGuru,

I believe you have made a mistake, the question says 5x − y = 2, 2x + y = 7, not y = 9x - 3, y = -8x + 8.

This can be solved with trig and coordinate bashing (I got the impression that vectors may be the easier way). I graphed the red and blue lines as the lines in the problem, and the green line is a random line that's perpendicular to blue. The red and blue lines intersect at (9/7, 31/7); the green line intersects the red line at (4/9,2/9) and the blue at (14/5, 7/5). I used wolframalpha for the steps, but essentially you find all of the sides using distance formula, apply any one of the trig functions, then solve for the angle using inverse trig function. The result when we do this is 37.875 ≈ 38˚

Update: I just discovered that the formula is arctan((slope_1 + slope_2)/(1+slope_1*slope_2)) in degrees which gives the same answer :|

(now I wanna prove it 😅)

How do you delete a post?

For some reason, I can't see my own question. How do I fix it? I mean, I can see my answer, but not my question. I am really confused.

Let's find the slope of each line

y = 9x - 3         y = -8 + 8

And the slope of the first line is 9

And the slope of the second line is -8

And taking the tangent inverse of the second line, we have

tan-1(-8)  = -82.87°   We need to add 180° to this to get the correct angle = 97.13°

And taking the tangent inverse of the first line, we have

tan-1(9) = 83.66°

So.....subtrating the second result from the first, we have 13.47° = about 13°

To solve these types of equations, we usually have to isolate x. We do this by subtracting the right side from the left side.

\(100x^2 - x^2 + 20x - 8x + 1 - 16 = 0\)

\(99x^2 + 12x - 15 = 0\)

Why not divide by 3?

\(33x^2+4x-5=0\)

To factor the quadratic (assuming we can), we find two numbers that sum to 4 and multiply to (33 x -5). With some clever rearrangement, we get -11 and 15. Taking into account the leading coefficient and the factors of these two numbers, the quadratic factors as:

\((11x+5)(3x-1) = 0\)

 Thus, the solutions occur when any of the terms are 0, which means \(x=-5/11, 1/3.\)

Thanks!!

Since Bill buys at least one of each item, he has to spend at least 1+2+7=10 dollars. He has 40 dollars left to spend on jogs, so he can buy 5 more jogs (5x7=35) without going over budget. The remaining 5 dollars can be filled by buying jags.

The maximum number of jogs Bill can buy is 6.

The answer relies on minimizing all of the primes.

The smallest one-digit prime is 2.

The smallest two-digit primes are 11 and 13. 

\(2 \cdot 11 \cdot 13 = 286\).

It's 2013, I just went to Melody's profile and went to the first answer.

It think 2013 or 2014. But, it's just a guess.

Dunno

Correct option is 30

a,b are roots of x2−2cx−5d=0
⇒a+b=2c

and c,d are roots of x2−2ax−5b=0 
⇒c+d=2a
 

∴(a−c)+(b−d)=2(c−a)

⇒(b−d)=3(c−a)…(1)   
Since c is the root of x2−2ax−5b=0⇒c2−2ac−5b=0…(2)

Similarly a is root of x2−2cx−5d=0⇒a2−2ac−5d=0…(3)

On subtracting (3) from (2)
c2−a2=5(b−d)

⇒(c−a)(c+a)=5×3(c−a)……(from(1))
⇒c+a=15

∴a+b+c+d=2c+2a

=2(c+a)=2×15=30

1/2 * 8 * 4 = 16 units^2

Thank you soooooo much!!!!!! I can't thank you enough!!

We multiply infinity by infinity, and what will be the final answer? 

Infinity is a concept, not a number.  It cannot be used in multiplication.  

The answer will be infinity.

Infinity is not a number. It's much much greater than the largest number you can think of.

Infinity operations are important while solving limits.

Infinity + infinity= infinity

Infinity - infinity = not defined

Infinity × infinity = infinity

Infinity ÷ infinity = not defined.

|z| = 1.

9+36=45

45+16=61

the asnwer is 61 units^2

xy = 3/4.

Also, I forgot to metion

Two right triangles, ABC and ACD, are joined as shown. Squares are drawn on four of the sides. The areas of three of the squares are 9, 16 and 36 square units. What is the number of square units in the area of the fourth square?

Note that the diagram is not drawn to scale.

Thanks, but it's wrong. 😭

I only get one more try and it's due today. 😢

By Pythagoras, the area of the fourth square is 56.