You can put this solution on YOUR website!
, this is actually easier than trying to write a recursive formula. The recursive formula might look something like where .

You can put this solution on YOUR website!
I'm wondering if the developer of this site made some program to automatically post this message every several hours or so. Even then, it shouldn't be where the "unsolved problems" are, it should be contained in the instructions for posting problems.

You can put this solution on YOUR website!
-.201
-.204
-.21

You can put this solution on YOUR website!
Any k-by-k square where k is even. This is because we can divide up the k by k square into 2x2 squares, and if k is odd, this cannot possibly be done. Hence, find the number of 2x2, 4x4, 6x6, and 8x8 squares contained within the 8x8 square and add them (there should be a pattern).

You can put this solution on YOUR website!
10P4 = 10*9*8*7 = 5040

10C4 = (10*9*8*7)/(4*3*2*1) = 210

You can put this solution on YOUR website!
Choice C, because (2m - 1) is odd, so (2m - 1)^2 will always be odd.

You can put this solution on YOUR website!
The third side must be between 7 and 17. To see why, draw segment AB with length 12. Draw a circle with radius 5 around point B. You can connect vertex A to some point on the circle to obtain the third side.

You can put this solution on YOUR website!
The pattern is: add 2, divide by 2, add 3, divide by 3, add 4, divide by 4. To obtain the next number, we add 5 to the previous number to get 8.

You can put this solution on YOUR website!
1. If we let 2x and 2x+2 be two consecutive even integers, then their sum is 4x+2, which is 2 modulo 4. 146 is the only answer choice that is 2 mod 4, so B is correct.

2. We have x^2 - 2xy + y^2 = 0 --> (x - y)^2 = 0, x - y = 0. Hence x = y, answer choice E.

You can put this solution on YOUR website!
The expression is undefined when the denominator is zero and the numerator is nonzero (otherwise it is said to be "indeterminate").

We can set s^2 - 81 = 0, then s = 9 or -9.

You can put this solution on YOUR website!
Presuming you want slope-intercept form, if m is the slope and b is the intercept, it is simply y = 5x - 2.


Be careful that when you post questions, that you specify your variables clearly. Most tutors will know what m and b refer to, but there could be others who used different variables for slope and y-intercept when they learned it, e.g. y = ax + b.

You can put this solution on YOUR website!
Question does not make sense. Maybe if you said "Find a quadratic equation with 25 and 36 as the roots" it would make sense; even then, none of the answer choices are correct.

You can put this solution on YOUR website!
Assuming A is between 90% and 100%, we can set up an inequality (let x be the next test score):









Least possible score is 86.

You can put this solution on YOUR website!
The number of bills is two more than a multiple of 6, so 74 and 80 are the only possible choices given the first constraint. The second constraint implies that the number of bills is 2 more than a multiple of 4, so 70, 74, 78 are the only ones satisfying this. 74 is the only number satisfying both, so there must be 74 bills.

You can put this solution on YOUR website!
Note that n ≡ 2 (mod 3) because n can equal anything in {2, 8, 14, ...} and all of these numbers are 2 modulo 3. If n ≡ 2 (mod 3) then 7n ≡ 14 ≡ 2 (mod 3) (hence, the remainder is 2).

Try this with various values of n and you will see that the remainder is always 2.

You can put this solution on YOUR website!
Count the numbers in the set {-8000, -7996, -7992, ..., 8000}. Obviously we are not going to do this by hand so what we can do is make transformations to the set by adding 8004 to each element:

|{-8000, -7996, ..., 8000}| = |{4, 8, ..., 16004}| (here |S| denotes the number of elements in set S).

We can divide everything by 4.

|{4, 8, ..., 16004}| = |{1, 2, ..., 4001}|

There are 4001 numbers between -8000 and 8000 inclusive that are divisible by 4.

You can put this solution on YOUR website!
I don't know if this requires an elaborate explanation (however it could get deep into proving the change-of-base formula then deriving the Taylor series for logarithms, then proving Taylor's theorem in the first place, etc.).

Simply put, if you want to convert from base b to base 10 (so you can input it on your calculator), use the change-of-base formula:



Then it is easy to input it on a calculator.



Also, most graphing calculators can allow logarithms of bases other than 10 or e. They are quite expensive, though, but graphing calculators can do all sorts of functions such as sums/products, derivatives/integrals, limits, determinants of matrices, factorials, defining your own functions, etc.

You can put this solution on YOUR website!
The degree of a single-variable polynomial is the highest exponent that has a non-zero coefficient. In this case the degree is 4.

For multi-variable polynomials, the degree is the largest sum that is obtained by adding the exponents of the corresponding terms. For example, if



the degree would be 4+5 = 9.

You can put this solution on YOUR website!
Let the angles be 3x, 5x, 7x. Their sum is 180, so

3x + 5x + 7x = 180

15x = 180 --> x = 12

The largest angle is 7x, which is 7(12) = 84, choice C.

You can put this solution on YOUR website!
"Three more than the product of 8 and 7" is just a cheap, seemingly tricky way of saying "59." So all this problem asks is "The difference of 67 and an integer is 59."

If we let x be the integer, either equation could be true, depending on how the question is interpreted:

x - 67 = 59 --> x = 126
67 - x = 59 --> x = 8

You can put this solution on YOUR website!
We want a multiple of 3, and one that is 4 more than a multiple of 7. B, D, E are the only multiples of 3, and D is the only one four more than a multiple of 7, so D is correct.

You can put this solution on YOUR website!


If you were to graph y = x and y = |x| on a coordinate plane, they would intersect where x >= 0 and |x| is greater than x for negative x (which does not work here) Hence, the only values of n that satisfy are nonnegative values of n.

You can put this solution on YOUR website!
1. Statement is false because if we square both sides we get



which does not hold for all real a,b.

2. It must be multiplied by 3 - sqrt(3), not just sqrt(3). This is because the denominator becomes a rational number (applying difference of two squares).

You can put this solution on YOUR website!
Any number you can locate on a number line, e.g. 5, -3.8, sqrt(2), 0, pi/6, 25749, etc.

You can put this solution on YOUR website!
How does one get a red queen out of two dice rolls?

You can put this solution on YOUR website!
80 has nothing to do with it; you do not multiply -5*4*2. The ^2 means you square the expression, so if x is 4, then

(-5x)^2 = (-5*4)^2 = (-20)^2

(-20)^2 = 400, which is the correct answer.

You can put this solution on YOUR website!
Let a,b be the numbers

ab = 8933

(2a)(2b) = 4ab = 4(8933) = 35732

You can put this solution on YOUR website!
Add all three equations to get

2a + 2b + 2c = 3 + 5 + 8 = 16

The average of a,b,c is (a+b+c)/3, so if we divide both sides of the equation by 6 we obtain our desired result

(2a + 2b + 2c)/6 = 16/6

(a + b + c)/3 = 8/3

You can put this solution on YOUR website!
At most one queen, but how many cards are dealt (if they are even dealt)?

You can put this solution on YOUR website!
Assuming the family must answer all eight categories, there are eight ways to choose the first category. After this, there are only seven ways to choose the second category, since the original one cannot be picked again. Then there are six choices for the third category, and so on. The total number of ways is 8! = 8*7*6*...*1 = 40320.