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This is what I got!!

side length | 17
circumradius | 289/30≈9.63333
inradius | 24/5 = 4.8
width | 16
height | 15
area | 120
perimeter | 50
interior angles | ((180 cos^(-1)(8/17))/π° | (180 cos^(-1)(8/17))/π° | (180 cos^(-1)(161/289))/π°)≈(1.081 rad | 1.081 rad | 0.9799 rad)
interior angle sum | 180° = π rad≈3.142 rad
exterior angle sum | 360° = 2 π rad≈6.283 rad

$3.97 / 500 =~0.00794 cents per page.

126 x 12 =1,512 page in all 12 copies of the report.

1,512 x 0.00794 =~$12 - the cost of the paper in all copies.

I can only think of 2 as follows:

1/3 + 1/6 = 1/2

1/4 + 1/4 =1/2

1/6 + 1/3 =1/2 - which is the same as the first.

Volume= 12 x 13 x 14 =2,184 square inches - Volume of first aquarium.

            = 28 x 33 x 35 =32,340 square inches - Volume of second aquarium

[32,340 / 2,184] x 2 = ~29 minutes and about 37 seconds.

If I understand your question, no matter what the value of x is, f(x) mod 15336 =216. So, the Greatest Common Divisor(GCD) = 216.

42/5 + 42/5^2 =8 + 1 = 9 zeros. Use the integer part only.

42! =1405006117752879898543142606244511569936384,000,000,000. As you can see 42! agrees with the first answer of having 9 zeros.

Exponential fit:

Notice that, because the fit was done using the log of y, we need to use the log version to determine the coefficient of determination.

Quadratic fit:

First of all, there are 14 diagonals, not 30 diagonals. This can be found by \(\dfrac{n(n-3)}{2}=\dfrac{7*4}{2}=14\) diagonals. Is the answer 28+42/182(5/13), because we can choose the first diagonal is 14 ways, the second is 13.   

Linear fit:

We can label x as the number of 7th and 8th graders, and x-50 as the number of 6th graders. So, we have x+x+x-50=3x-50=790 students. Therefore, 3x=840 students and x=280 students. We can solve for x-50, which is 280-50=230. Back again, we have 9/10(x-50)+7/8x+3/5x, which is just 9/10(230)+7/8(280)+3/5(280)=207+245+168=620 students.

If we add 2y to both sides, we get 3x+2y=10-7, 3x+2y=3. Since we are finding for 6x+4y, double both sides of the equation, so  6.

hi mirb, i see ur from aops xd. i cant answer the question, but stilll hi 

-noahdavid

This question has been asked before!!!

https://web2.0calc.com/questions/a-square-defg-varies-inside-equilateral-triangle

Now for the final part, we need to rearrange the eqution: \({y-14 = -2(x-1)}\) into slope-intercept form.

Slope-intercept form is in the form of \(y = mx + b\).

Rearranging our equation to look like this, we get:

\({y-14 = -2(x-1)}\),

\(y = -2(x-1) + 14\),

\(y = -2x + 2 + 14\)

\(y = -2x + 16\).

Therefore, our answer is \(\boxed{y = -2x + 16}\).

We can test this by inserting an ordered pair, let's say \((2,12)\).

\(12 = -4 + 16\),

\(12 = 12\)

Is this equation true? YES!!!!.. This tells us that our answer is correct!

So we know that our slope is \(-2\). 

Point slope form is in the form of \((y-y_1) = m(x - x_1)\).

Using our coordinate (I'm going to choose \((1 , 14)\) ), and plugging it into the formula, we get our point-slope form to be

\(\boxed{y-14 = -2(x-1)}\).

Okay, let's solve this one.

I would personally choose the coordinates \((1 , 14)\) and \((2 , 12)\), because they are going to make my life much easier than using coordinates that have decimals in them. Therefore, when we find the slope, we have zero rounding to do.

Now, we are going to use the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\) to find the slope, \(m\).

Plugging in our numbers, we get \(m = \frac{12 - 14}{2 - 1}\), which is equal to \(\boxed{-2}\).

CX = 12 : 4

CX = 3

BX/AX = CX/BX

BX² =AX*CX

BX² = 12*3

BX² = 36

BX = 6

I knew that. 

Thanks a lot!

I think this is what your teacher would want you to do

which is smallest:

2^(1/2), 4^(1/4), 8^(1/8)

\(2^{\frac{1}{2}}\\~\\ 4^{\frac{1}{4}} = 2^{2\cdot\frac{1}{4}} = 2^{\frac{1}{2}}\\~\\ 8^{\frac{1}{8}}=2^{3\cdot\frac{1}{8}}=2^{\frac{3}{8}}\\~\\ \)

3/8 is smaller than 1/2 so it will be the smallest one. 

\(P[\text{not get a hit in next 3 at bats}] = \\ \\ \left(P[\text{not get a hit in an at bat}]\right)^3 =\\ \\ \large \left(1-\frac 1 4\right)^3 =\left(\frac 3 4\right)^3 = \frac{27}{64}\)

This does assume that consecutive at bats are independent.

1.414     vs   1.414    vs    1.2968

They are all the same, but if you take a number's reciprocal and square it by the number, and the number is a power of 2, you get the square root of 2, NOT 1. This is because when you simplify the other equations, you get the square root of 2, every single time under these conditions. Remember, fractions as exponents are square roots to the power of the reciprocal of the fraction. Therefore they are all the same. Around 1.41421356237 ish, but the decimal never ends.

-MathCuber