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They didn't sell the same number of cookies.    

The problem says Max sold half as many as Jessica.  

_.

Normally, I wouldn't bother with an unsubstantiated claim like this,   

but there isn't anything good on television right now, so why not.  

The problem gives four answers to choose from.    

Let's try all of them.    

72 – 18 = 54     36 –   9 = 27      Same number left over?  No.

72 – 36 = 36     36 – 18 = 18      Same number left over?  No.  

72 – 24 = 48     38 – 12 = 26      Same number left over?  No.   

72 – 72 =   0     36 – 36 =   0      Same number left over?  Yes   

_.

Jessica sold 72 - 36 = 36 cookies. Since Max only baked 36 cookies, they must have sold the same number of cookies, so Jessica sold 18 cookies. The answer is A. 18.
 

Such a hard word problem.

Find the area of the equiangular octagon below.     

I think the dimensions don't work.  

If a side is 4, then the distance from the center to a side     

would be 2 + (4 / sqrt(2) ) which is 2 + 2.828 = 4.828, not 3.               

_.

This answer is WRONG!

I have not looked at the answer I am just editing to get rid of the unacceptable language .. Melody.

Jessica baked 72 cookies and sold x cookies. Max baked 36 cookies and sold half as many cookies as Jessica did. How many cookies did Jessica sell if they each had the same number of cookies left over?    

Call "n" the number of cookies they each had left over.    

                                                                72 – x  =  n         (1)     

                                                                36 – x/2  =  n      (2)     

Subtract (2) from (1)                                36 – x/2  =  0             

                                                                        x/2  =  36   

                                                                           x  =  72   

So                                                        Jessica sold 72 cookies    

                                                             Max        sold 36 cookies     

                                                             and neither had any cookies left over (i.e., n = 0).    

_.

Let's denote the interior angles of the hexagon as \( \angle A, \angle B, \angle C, \angle D, \angle E, \angle F \), where \( \angle A \) is the angle greater than \( 180^\circ \).

The sum of the interior angles of a hexagon is given by \( (6-2) \times 180^\circ = 720^\circ \). Therefore, the sum of the angles \( \angle A + \angle B + \angle C + \angle D + \angle E + \angle F \) should be equal to \( 720^\circ \).

Given that Noah measured the angles \( 71^\circ, 63^\circ, 99^\circ, 112^\circ, 107^\circ, \) and \( 99^\circ \), we can calculate the sum of these angles:

\[ 71^\circ + 63^\circ + 99^\circ + 112^\circ + 107^\circ + 99^\circ = 641^\circ. \]

Now, subtracting this sum from the total sum of interior angles gives us the missing angle \( \angle A \):

\[ \angle A = 720^\circ - 641^\circ = 79^\circ. \]

So, the missing angle measure is \( \boxed{79^\circ} \).

OMG! Look at this brainless bitch! He uses ChatGPT to answer questions far above his level and can't even do basic math such as this! Are you lazy or seriously fucking retarded?

 I can help you find the area of a regular octagon using the formula 2s2(1+√2), where s is the length of the sidehttps://www.vedantu.com/formula/area-of-an-octagon-formula. To use this formula, you need to know the value of s. From the image you provided, I can see that the octagon has a side length of 10 cm. Therefore, the area of the octagon is:

A = 2s2(1+√2)
A = 2 × 10^2 × (1 + √2)
A = 200 × (1 + √2)
A = 483.28 cm^2

The area of the octagon is approximately 483.28 square centimeters. I hope this helps you.

The following are the possible products for matrices:

Matrix multiplication: Two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Based on the given matrices, we can see that:

The product of QM is not defined because the number of columns in Q (1) is not equal to the number of rows in M (2).

The product of NM is not defined because the number of columns in N (4) is not equal to the number of rows in M (2).

The product of LP is not defined because the number of columns in L (2) is not equal to the number of rows in P (1).

The product of LQ is defined because the number of columns in L (2) is equal to the number of rows in Q (1).

Therefore, the correct answer is:

Product is Defined Product is not Defined ________________ _________________ LQ QM, NM, LP

By the way, you should send CPhill messages.  He'll be happy to help you, just like he helped me!

I have to confess that I committed a serious error in my calculations because I forgot to consider that a valid even-numbered exponent is 0. This means that there is one additional choice for each prime factor 2, 3, and 5. \(5 * 3 * 3 = 45 \) perfect square factors! I apologize in advance for this mistake!

this doesn;t work

Let D = (0, 0)

P =  ( 2,  6 - sqrt (4^2 - 2^2) )  = (2 , 6 - sqrt (12) )

C =  (4 ,0)

PC^2 =  (4 - 2)^2  + (6- sqrt (12))^2

PC^2 = 4 + 36 - 12sqrt (12) + 12

PC^2  = 52 - 12sqrt (12)

PC^2  = 52 - 24sqrt (3)  =   4 (13 - 6sqrt (3) )

PC = sqrt [ 4 ( 13 - 6sqrt (3) ) ] =  2 sqrt [ 13 - 6sqrt (3) ]  ≈  3.23

Please do not answer this question. It is from AoPS Beast Academy.

The following are the possible operations for matrices:

Addition: Two matrices can be added if they have the same dimensions.

Subtraction: Two matrices can be subtracted if they have the same dimensions.

Multiplication: Two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Scalar multiplication: A matrix can be multiplied by a scalar.

Transposition: The transpose of a matrix is created by exchanging the rows and columns.

Based on the given matrices, we can see that:

L and N have the same dimensions (2x2), so L - N is defined.

M and N have the same dimensions (2x2), so M - N is defined.

Q and P are not the same dimensions (1x2 vs. 2x2), so Q + P is not defined.

M and P are not the same dimensions (2x2 vs. 1x2), so M + P is not defined.

Therefore, the correct answer is:

Operation is defined Operation is not defined __________________ L - N M - N

Also, if you send a direct message to cphill, he'll be able to help you!

The prime factorization of 15 is 3 * 5. So, any integer that is a multiple of 15 must also be a multiple of both 3 and 5.

Let's consider the factorization of k! for some integer k. We can write:

k! = 2^(p1) * 3^(p2) * 5^(p3) * ...

where p1 is the number of times 2 appears in the prime factorization of k, p2 is the number of times 3 appears, and so on.

Now, the smallest possible value of k such that k! is divisible by 15 must have at least 2 factors of 3 and 1 factor of 5 (since these are the prime factors of 15). Therefore, we can write:

f(n) = 2a * 3b * 5c * ...

where a≥2, b≥2, c≥<0>1, and all other prime factors have exponent 0.

We can verify that f(360)=16, so this value of n satisfies the condition that f(n)>15. Therefore, the smallest value of n that satisfies the given condition is 360.

I apologize for the confusion. As you discovered, the diagram I created is intentionally NOT drawn to scale so that it looks as similar as possible to the original diagram. I figured that as long as points E and F were on the circle, then I could still go ahead and find the radius anyway.

I tried a similar procedure  as you, 3Mathketeers  and I got the  same answer.....but notice that a square of  5 will not fit  inside the  semi-circle      [a 4 x 5  rectangle will !! ]

In short, I believe that this is an impossible  problem as set up by the poster.....

AC is the hypotenuse

The circumradius =  (1/2) (hypotenuse)   = (3sqrt (3) / 2)  = (3/2)sqrt 3

The circumference  of O =    2pi * circumradius  =  2pi (3/2)sqrt (3) =   3 sqrt (3)  pi

First, perform the factorization procedure on 60. I am not sure how to show this properly, so I will do my best. I use the red color to distinguish a prime number factor.

\(60 = \textcolor{red} 2 * 30 \\ 30 = \textcolor{red} 2 * 15 \\ 15 = \textcolor{red} 3 * \textcolor{red} 5\)

Now, that we have found the prime factorization, we know that \(60 = 2^2 \times 3 \times 5\). However, we need the factorization of \(60^4\). We can accomplish this by doing the following:

\(60 = 2^2 \times 3 \times 5 \\ 60^4 = \left(2^2 \times 3 \times 5\right)^4 \\ 60^4 = 2^8 \times 3^4 \times 5^4\)

Now, we have the prime factorization of 60^4. In order for a number to be a perfect square factor, the factor would need an even-numbered power of all the factors 2, 3, and 5.

For the factor 2, the even-numbered powers possible are 2, 4, 6, and 8 for a total of 4 choices.

For the factor 3, the even-numbered powers possible are 2 and 4 for a total of 2 choices.

For the factor 5, the even-numbered powers possible are 2 and 4 for a total of 2 choices.

These choices are completely independent choices, so we can use the multiplication rule to find the number of perfect square factors of \(60^4 \). The number of perfect square factors is \(4 * 2 * 2 = 16\) perfect square factors.

Let the sides of the triangle =   2

Then AM = MB  =  1

And MN = 1

Let PM = NQ = x

Angle AMP  =120°

By the intersecting  chord theorem

AM * MB =  PM * MQ

AM * MB =  PM ( MN + NQ)

1 *    1 =    x ( 1 + x)

1 =  x + x^2

x^2  + x - 1  =  0  

x^2  + x   = 1               complete the square  on x

x^2 + x + 1/4  =  1 + 1/4

(x + 1/2) =  5/4                 take the  positive root of  both sides

x + 1/2 = sqrt (5) / 2

x =    [ sqrt (5)  - 1 ]  /  2 =   PM =   phi

By the Law of Cosines

AP^2  =   PM^2 +AM^2  - 2 ( AM * PM) * cos (AMP)               {cos AMP = cos 120° = -1/2 }

AP^2  =  phi^2  + 1^2  - 2 (1 * phi) (-1/2)

AP^2 =  phi^2 + 1 + phi          { 1 + phi  = Phi }

AP^2 =  phi^2 + Phi               { phi^2 + Phi =  2 }

AP^2 =  2

AP = sqrt (2) 

AP  / AM  =  sqrt (2) / 1  = sqrt (2)

Thanks for trying but those arent' the correct answers