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The expression simplifies to 6 - 3*3^(1/3).

Sorry, the answer choices got mixed up as well, here's the original problem.

If 3x−y=12, what is the value of 8x/2y?

A) 2^12
B) 4^4
C) 8^2
D) The value cannot be determined from the information given.

here's my solution. 

One way is to write

8x/2y

so that the numerator and denominator are writen with the same base. Since 2 and 8 are powers of 2, pluging in 2^3 for 8 in the numerator of 8x/2y gives

(2^3)x/2y

which can be written

2^3*x/2y (confusing)

Since the numerator and denominator of have a common base, this expression can be written as 2(3x−y). In the problem, it says that 3x−y=12, so can substitute 12 for the exponent, 3x−y, which means that

8x/2y=2^12

Heres a solution that I found. 

Multiply each side of the given equation by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:

24x^2+25x−47=(−8x−3)(ax−2)−53

You should then multiply (−8x−3) and (ax−2) using FOIL.

24x^2+25x−47=−8ax^2−3ax+16x+6−53

Then, reduce on the right side of the equation

24x^2+25x−47=−8ax^2−3ax+16x−47

Since the coefficients of the x^2 term have to be equal on both sides of the equation, −8a=24, or a=−3.

The final answer is B.

I'm sorry for the exponents and the fractions, I'm just new to latex and don't understand it.

100 ft^2 / ( 10 mem * 10 min) =   1 ft^2 /( mem_ min) 

100 ft^2 / ((1 ft^2 /mem_ min) * 15 mem ) = 6 2/3 min 

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2 - 2x^2 + 4x - 1.    

First, collect and combine like terms   

and arrange them as ax² + bx + c           (5x² – 2x² – 2x²) + (–2x + 6x + 4x) + (+8 + 2 – 1)    

                                                                  x² + 8x + 9    

The discriminant is b² – 4ac                     D  =  8² – (4)(1)(9)    

                                                                 D  =  64 – 36    

                                                                 D  =  28    

_.   

1.The class size must be between 10 and 15, and when arranged in a line, the only way to do so it in one line.

Well, how do we do that? Only if the number is prime! Why?

2. If the students are arranged in a grid the number of students is L x W, but its a single fill line, so either the length or width is one! So the number of students must be prime, since if it had other factors, there would be more available gride formation of students!  

3. The biggest prime between 10 and 15 is 13!

So 13 in our answer

:))

3. I'm assuming we are trying to find the value of \(\frac{8^{x}}{2^{y}}\)

Let's cite some equations that could help us in these equations. There are two main ideas we will be applying for this problem. 

\(a^{bc}=(a^{b})^{c}\) \(\frac{a^{b}}{a^{c}}=a^{b-c}\)

Now, let's focus on what we are trying to find. Let's simplify it a bit to get a better shot at figuring out our final answer. 

\(\frac{8^{x}}{2^{y}}=\frac{(2^{3})^{x}}{2^{y}}\)

This is where we apply the second equation stated. This allows us to put x and y into one exponent. 

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

Wait! We recognize this 3x - y from somewhere! The value was given to us in the problem! It was stated that \(3x-y=12\)

Thus, we plug in this value, we have

\(2^{12} = 4096\)

Thus, our final answer is 4096. 

Thanks! :)

Look at the image!

2. I don't have much time to explain...hopefully you understand my work...sorry

First, put everything on the right side into one fraction

\(\frac{24x^{2}+25x-47}{ax-2}=\frac{(-8x-3)(ax-2)-53}{ax-2}\)

Simplify the numerator on right side. 

\(\frac{24x^{2}+25x-47}{ax-2}=\frac{-8ax^{2}+16x-3ax+6-53}{ax-2}\) \(\frac{24x^{2}+25x-47}{ax-2}=\frac{-8ax^{2}+(-3a+16)x-47}{ax-2}\)

Since both have the same denominator, their numerators must be equal. 

\(24x^{2}+25x-47=-8ax^{2}+(-3a+16)x-47\)

Since the coefficients must correspond, we can right the equation

\(24x^{2}=-8ax^{2}\) \(24=-8a\) \(a=-3\)

Thus, b is the right answer. 

Thanks! :)

ummm...I would give a solid solution...but this was answered VERY well here.

1. https://www.doubtnut.com/qna/181168330

answer is d, btw :)

There's many ways to do this problem, but I prefer using Euler's Totient Function, mainly because when facing larger and more complicated numbers, listing is not going to do the trick. 

So here's the Totient Function. It essentially states that

\(\frac{\text{number we start with}}{\text{product of the prime factors}} \cdot \text{product of every prime factor -1}\) and this is our final answer

Thus, we can apply this to 20. 

We have \(20 = 2^2 * 5\)

2 and 5 are the two prime factors, so we have

\(\frac{20}{2*5} \cdot (2-1)(5-1) = 2 * 4 = 8\)

Thus, 8 is the final answer. 

If you want to learn more, here's another question that revolves around the equation. 

Let's set some variables and make some observations. 

Let's let \(d = a_2 -a_1\)

Now, let's note something important. Note that

\(S_5 = 5a_1 + (d + 2d + 3d + 4d) = 5a_1 + 10d\\ S_{10} = 10a_1 + (d + 2d + \cdots + 9d) = 10a_1 + 45d\\ S_{15} = 15a_1 + (d + 2d + \cdots + 14d) = 15a_1 + 105d\)

These observations are really important for us to solve the problem. 

Let's take two of these cases. We can write a system of equations, and we get

\(\begin{cases} 5a_1 + 10d = \dfrac15\\ 10a_1 + 45d = \dfrac1{10} \end{cases}\)

Now, we solve for a1 and d. 

Solving this system of equations, we get

\(d = -\dfrac3{250}\\ a_1 = \dfrac8{125}\)

Plugging this into S15, we get \(S_{15} = 15a_1 + 105d = -\dfrac3{10}\)

So -3/10 is our final answer. 

Thanks! :)

First, let's set up variables to solve this question. 

Let's let \(d = a_2 - a_1\)

The conditions in the problem give us the system of equations

\(\begin{cases} a_1 + d = -1\\ a_1 + 3d = \dfrac13 \end{cases}\)

Now, solving this equation, we get that

\(d = \dfrac23\) and \(a_1 = -\dfrac53\)

So the final answer is -5/3. 

Thanks! :)

Using prime factoriazation

36 = 2 x 2 x 3 x 3 

90 = 2 x 3 x 3 x 5 

385 = 5 x  7 x 11

2 x 2 x 3 x 3 x 5 x 7 x 11 = 13860 seconds  = 231 minutes 

Let's define the problem step by step to solve for the greatest possible percentage of questions Amy could have answered correctly.

### Solution By Steps

**Step 1: Analyze Amy's performance**

- Amy answered the first three questions wrong, but she answered all the other questions correctly.

- Therefore, the first three questions are incorrect for Amy, and all subsequent questions (starting from question 4) are correct.

**Step 2: Analyze Scott's performance**

- Scott answered exactly two questions wrong: the last question and the question before the last correct answer.

- This means Scott answered the second-to-last question wrong and also the last question wrong.

- All other 26 questions before these two wrong answers were correct.

**Step 3: Determine the overlap in wrong answers**

- We are told that Amy and Scott were both incorrect on exactly one common question.

- From Amy’s incorrect answers (questions 1, 2, and 3) and Scott’s incorrect answers (the last two questions), the only possible overlap occurs if Amy’s third wrong answer matches Scott's second wrong answer (i.e., the second-to-last question of the test).

- Thus, Amy's third wrong answer is the second-to-last question, which means she got question number \( n-1 \) wrong.

**Step 4: Calculate the total number of questions**

- Scott answered the last 26 questions before his last wrong answer correctly, and he got the last two questions wrong.

- Therefore, the total number of questions on the test is \( 26 + 2 = 28 \).

**Step 5: Count Amy's correct answers**

- Amy answered the first three questions wrong (questions 1, 2, and 3).

- Additionally, she also answered the second-to-last question wrong (question 27).

- Hence, Amy answered \( 28 - 4 = 24 \) questions correctly.

**Step 6: Calculate the greatest possible percentage of correct answers**

- Amy answered 24 questions correctly out of 28 total questions.

- The percentage of correct answers is calculated as:

\[
\text{Percentage} = \left( \frac{24}{28} \right) \times 100 = 85.71\%
\]

### Final Answer

The greatest possible percentage of the total number of questions that Amy could have answered correctly is **85.71%**.

Fill in the blanks with three distinct positive integers.    
1/___ + 1/___ + 1/___ = \frac{13}{12}    

                     1          1          1           39         13     

                  –––– + –––– + ––––  =  ––––  =  ––––    

                     1         18        36          36         12     

_.   

As an input:     On question 1 .....   everywhere you have the number '59'  that should be ' 5/9 '