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Thank you guest!

Add 4 to both sides

x^2 = -7

square root of -7 is 

sqrt(-7) = 2.6457513110645906i

dunno, all I did was just solve, remember the answer is an imaginary number

x² is the first number

(x + 1)² is the second number

These numbers are consecutive.

(x+1)² - x² = 999       (they differ by 999)

Expand (x+1)² , then simplify.

x² + 2x + 1 - x² = 999

2x + 1 = 999

x = 499

Bigger number is 499 + 1 = 500

This is how you solve these problems.

The larger perfect square = 500^2 =250,000

The smaller perfect square =499^2 =249,001

250,000 - 249,001 =999 - difference

Hint:

General form of circle's equation is,

(x-h)^2+(y-k)^2=r^2

another hint

collect the x's in 1 barract and the y's in another barract added to it and move any number to the other side 

then complete the square for both x and y and don't  forget to add the same amount to the other side.

1. Input data entered: angle α, angle β, angle γ and height h
 alpha = 45° ; ; beta = 45° ; ; gamma = 90° ; ; h = 6 ;

 
2. From height h and angle α we calculate side a:
a = { h }/{ sin beta } = { 6 }/{ sin (45° ) } = 8.485 ; ; b = { h }/{ sin alpha } = { 6 }/{ sin (45° ) } = 8.485 ; 

3. From side a and angle α we calculate hypotenuse c:
 sin alpha = a:c ;  c = a/ sin alpha = 8.485/ sin(45 ° ) = 12 ; ; 
Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 8.49 ; ; b = 8.49 ; ; c = 12 ; ; 

4. The triangle area - from two legs
Area = { ab }/{ 2 } = { 8.49 * 8.49 }/{ 2 } = 36 Sq. units. 

Please help me

fast!

9 x 9 x 8 x 7 =4,536 such numbers.

When you say "coincide", do you mean when they are "on top of each other?".

If that is what you mean, then:

Every minute on a regular Clock, the hour-hand moves forward 1/2 minute, while the minute-hand moves backwords 5/6 minute.....So, since they are moving towards each other then:

1/2m + 5/6m =60 minutes.

Solve for m and m = 45 minutes(on a regular Clock).

So, the hour-hand will be: 1/2 x 45 =22.5 minutes on your faulty Clock. And:

5/6 x 45 =37.5 minutes (backwards) for the minute-hand. Or: 60 - 37.50 =22.50 when both hands will be on top of each other.

So 45 minutes will have passed on a regular Clock, or the time will be:12:45 pm.

Mod stands for "Modulus". Expand the number inside the bracket: (13314412157)^3 =2,360,293,389,988,491,779,694,252,033,893. Enter this big number into the calculator on this site followed by the "mod" 11, then press the = sign. You should get 8 as the remainder.

how did you get this answer and what does "mod" stand for?

(13314412157)^3 mod 11 = 8

No, you cannot make a Right Triangle, because: 26^2 ≠ 24^2 + 17^2. Your triangle would be described as "Acute Triangle".

No, not quite. 
You can compare interest rates when you convert them to "effective annual rates" in this case, which is much easier.
9% compounded annually = 9% effective annual rate.
2.25% compounded quarterly =1.0225^4 =1.0930833187890625 - 1 x 100 =9.30833187890625% - effective annual rate.
As you can see, 2.25% compounded quarterly is better than 9% compounded annually.
The equivalent quarterly compound of 9% compounded annually is: 1.09^(1/4) =2.177818% compounded quarterly, because:1.02177818^4 =~ 9% compounded annually.
In other words: 2.177818% compounded quarterly = 9% compounded annually.

Gavin is correct. This problem is about converting 9% per year to how many percents per quarter. The rate is still the same. It only differed in the time period. So, through dimensional analysis,

9% per year × (1 year / 4 quarters) = 2.25% per quarter

If he was asked to convert 9% per year to how many percents per quarter compounded quarterly, then you will not simply divide by four. This is because compounding is not linear.

Solve for x:
3^(4 x - 5) = 27^(-2 x - 10)

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(3) (4 x - 5) = 3 log(3) (-2 x - 10)

Divide both sides by log(3):
4 x - 5 = 3 (-2 x - 10)

Expand out terms of the right hand side:
4 x - 5 = -6 x - 30

Add 6 x + 5 to both sides:
10 x = -25

Divide both sides by 10:

x = -5/2

Whgat is the sum of the digits of 29999999^2?

1) If you mean the sum of = 29999999^2 =89,999,995,200,000,064?

The sum of 89,999,995,200,000,064=79

2) If you mean the sum of all digits from 1 to 89,999,995,200,000,064?

=60,299,994,000,000,133

If there are n people, you would count the number of handshakes as nC2.

nC2= \(\frac{n(n-1)}{2\cdot1}\)

If there were 10 people, there would be (10*9)/2=45 handshakes. Thats not enough, so lets try a bigger number. 12 people: (12*11)/2=66 handshakes so there were 12 people.

Solve 3^x + 4^x = 5^x    

x = 2    I don't have a formal proof, I just immediately flashed on a 3-4-5 right triangle. 

.

There are 6 letters so 6! (6*5*4*3*2*1) ways, except there are two Zs and 6! counts the Zs as different so you need to divide by 2.

6!/2 = 360 ways

Sorry I don't understand what you did here

Like what are some fo the rules I was supposed to do while solving?

1 2 3

let a=1

b=2

c=3

1+2+3=6

1*2*3=6