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This was answered... 

https://web2.0calc.com/questions/please-help_46059

I think only n =1    and  n= 2   and n = 4 , 8 , 12    ...multiples of 4

If they won 4/11 of the 132 games, they would have lost 7/11 of the 132 games. 7/11 * 132 = 84

Out of natural numbers, the answer is trivially 0. So trivially that clearly you actually care about positive integers instead. Out of those, the answer is 11111111100 (nine ones and then two zeros).

Reasoning: 225 = 25 * 9. Thus, every multiple of 225 is a multiple of 25, and its last digits will be either 00, 25, 50, or 75, according as to the multiplying factor's residue modulo 4. Out of these, only the first is acceptable, so we must multiply 225 by a multiple of 4, which is to multiply 9 by a multiple of 100.

Thus, the problem reduces to the smallest multiple of 9 which is all 1s and 0s, with two zeros tacked onto the end. As is well known, to be a multiple of 9 is to have digits which add up to a multiple of 9 (by consideration of the fact that 10 = 1 modulo 9); thus, the smallest (positive) answer is nine ones followed by two zeros.

Thanks!!

Ay nice

(1) The first term can be labeled as x, the second x + y, third x + 2y, and so on. The 13th would be x + 12y, and the 1st would be just x.

\(x + 12y = 29 \\ x = 5 \\ 12y = 24 \\ y = 2\)

The 15th term would be x + 14y,

\(x + 14y \\ 5 + 14(2) \\ 5 + 28 = 33\)

So the 15th term would be 33.

(2) The numbers do not show, but here: https://artofproblemsolving.com/wiki/index.php/1986_AIME_Problems/Problem_6

A hemisphere is basically half of a sphere. The regular formula for the SA of a sphere is \(4\pi r^2\), but *1/2 so the surface area of the hemisphere is \(2\pi r^2\). Plugging in 2.5, 

\(2\pi \cdot2.5^2 \\ 2\pi \cdot 6.25 \\ 12.5\pi\)

So $12.5\pi$ is the surface area

By stars and bars, the total number of possible vote totals is C(52,4) = 270725.

By stars and bars, the total number of vote totals is C(51,3) = 20825.

Thank you!

I really liked your matching-up with constants and variables! +1

TYSM! They were all correct :D

Please help on this question, I need help too :)

Rearrange the equation into slope-intercept form,

\(-3y = -2x+12 \\ y = \frac{2}{3}x -4\)

The line we are looking for is perpendicular meaning that it's slope is the negative and reciprocal of $\frac{2}{3}$,

\(y = -\frac{3}{2}x + b\)

We know it passes through (-3, 5) so we can plug that in,

\(5 = \frac{9}{2} + b \\ b = \frac{1}{2}\)

So our final equation for the line we are looking for is \(y = -\frac{3}{2}x + \frac{1}{2}\)

We can start off my multiplying the first equation by $xy$,

\(2y+2x=30xy \\ x + y = 15xy\)

Our second equation has the same exact left side, so our right sides are equivalent too.

\(10 = 15xy \\ \frac{10}{15} = xy \\ \frac{2}{3} = xy\)

So $xy = \frac{2}{3}$

We can start off by multiplying \(x^2-7x+10\) on both sides which cancels out the denominators.

\(5x+16 = A \cdot (x-5) + B \cdot (x-2) \\ 5x+16 = Ax-5A + Bx-2B \\ 5x+16 = (A+B)x - 5A - 2B\)

Because -5A-2B will not result in something in terms of x, we can ignore it and 16. So we are left with,

\(5x = (A+B)x \\ A+B = 5\)

So A+B = 5.

We can plug in each of the given values to find a, b, and c. 

When x = 0, the ax^2 and bx term are 0, so c must be 0.

When x = 1, we have the equation a + b = 2, (no c because it is 0).

Finally, when x = 2, we have the equation 4a + 2b = 5.

Simple system of equations, and in the end we get a = 0.5 and b = 1.5. So the final equation is,

\(0.5x^2+1.5x\)

Plugging in 3, 

\(f(3) = 0.5\cdot 9 + 1.5 \cdot 3 \\ f(3) = 4.5 + 4.5 \\ f(3) = 9\)

So our final answer is 9.

\(\)

similar problem: https://web2.0calc.com/questions/help_43170

First we can find the LCM of 13, 17, and 19 which is 4199.

\(x = \frac{4199}{13}\\ y = \frac{4199}{17}\\ z = \frac{4199}{19}\)

You can do the rest from here.

(1) odd

(2) null

(3) increasing and invertible

Let $a_1$ equal Bart's madeleines, and let $a_2$ equal Jeff's madeleines.

$a_1 + 57 = a_2$

$\left(1-\frac{3}{5}\right) a_1 = \frac{1}{4} \cdot \left(1-\frac{2}{3}\right) a_2$

$\frac{2}{5} a_1 = \frac{1}{12} a_2$

$24 a_1 = 5 a_2$

$24 a_1 = 5(a_1 + 57)$

$24 a_1 = 5 a_1 + 5 \cdot 57$

$19 a_1 = 5 \cdot 57$

$a_1 = \frac{5 \cdot 19 \cdot 3}{19}$

$a_1 = 15$

$a_2 = 15 + 57 = 72$

$\frac{2}{3} a_2 = \frac{2}{3} \cdot 72 =  24 \cdot 2 = \boxed{48}$

2x - 5 >= -x + 12

-17 >= -3x

x <= 17/3

Interval: $(-\infty,17/3]$

lol sorry i got it wrong, just noticed it

OP plz change the best answer

My answer was supposed to be:

\(12^2+x^2=(12+16)^2\\x^2=640\\x=\sqrt{640}=8\sqrt{10}\)

and then multiply by 2