CalculatorUser

4ⁿ       with n being the number of 4s

a) Hint: Plus it in

\(\sqrt{5^2+12^2}\), then solve. You should get an integer as an answer

b) To do this problem, you can square both sides.

\(x^2+2xy+y^2=x^2+y^2\)

Then cancel out x^2 and y ^2

\(2xy = 0\)

Then solve

\(x*y=0\).

So when x and y multiplied together equaling 0 is when it can satisfy the original equation.

Examples: (0, 0)  (10, 0)    (0, 5)

Values of x and y that DO NOT satisfy the original equation is when they DO NOT multiply to 0

Examples (1, 1) (2, 3) (6, 9)

Thanks!

That is what I did, but there has to be a trick to do this without a calculator or internet

1) The answer is 61

I don't know why though! . I brute forced the problem...

Notice that triangle CDB is isoceles, with DB being the base. And ABC is isoceles.

I can assume you can use your knowledge on isoceles triangles and straight angles to figure out the answer. 

This problem uses isoceles triangles and sum of angles and vertical angles

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Lets see:

BAC is 28 degrees, and since ABCD is a rectangle, DAB is 90 degrees.

So that means DAC is 90 - 28 = 62 degrees.

That also means that DCA is 28 degrees because of vertical angle theorem (keep that in mind)

The sum of the angles of triangle DAQ is 180 degrees.

So since DQA is 90 degrees as given, and DAC is 62 degrees. 

Angle ADQ is 180 - 90 - 62 = 28 degrees.

Angle ADC is a right angle, so 90 - 28 = 62 degrees. QDC is 62 degrees.

And since DCA is 28 degrees,

Angle QDP is 62 - 28 = 34 degrees

I would just list the squares and double it and then reverse their digits too see if they are prime.

But looking at a list of primes, if available, is good too!

2) The two prime numbers have to be one away from each other.

So it is 2 and 3.

Lets check:

2 / (3+1)

3/ (2+1)

Yes, so P + Q is 5

D) At least 165

This problem is. To solve these types, I did:
 

250 + 215 = 465

465 - 300 = 165

So the answer should be D