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The equation simplifies to \(44x^3+13x^2-24x-48=0\).

The solution for that is about 1, though not exactly.

See if you can figure it out yourself.

I'm not good at solving polynomials in the third degree.

1. Find all real numbers a that satisfy\(\frac{1}{64a^3 + 7} - 7 = 0\).

Move the seven to the right side.

\(\frac{1}{64a^3+7}=7\)

Multiply both sides by \(64a^3+7\).

\(1=448a^3+49\)

\(-48=448a^3\)

\(-3=28a^3\)

\(-\frac{3}{28}=a^3\)

\(a=-\sqrt[3]{\frac{3}{28}}\)

There is only one such real number.

2. Find all values of a that satisfy the equation\(\frac{a}{3} + 1 = \frac{a + 3}{a} + 1\).

Remove the 1:

\(\frac{a}{3}= \frac{a + 3}{a}\)

Multiply by 3a:

\(a^2=3a+9\)

\(a^2-3a-9=0\)

Solve using the quadratic formula:

\(\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \left(-9\right)}}{2\cdot \:1}\)

\(\frac{3\pm\sqrt{9-4\cdot-9}}{2}\)

\(\frac{3\pm\sqrt{9--36}}{2}\)

\(\frac{3\pm\sqrt{45}}{2}\)

\(\frac{3\pm3\sqrt{5}}{2}\)

You may choose what to do with that answer.

Simplify \(\sqrt[3]{576000 \cdot 4 \cdot 48}\).

Multiply the numbers:

\(576000\cdot4\cdot48=110592000\)

Cuberoot:

\(\sqrt[3]{110592000}=480\)

So 480 is the answer you are looking for.

I will assume that 'compounded continuously' means compounded annually. If this is not so, please tell me. Then

7500*1.029^14=11191.196 which rounds to $11190.

I will try a step-by-step solution. If the number is n, the equation is 

n-6=5(n+2)

n-6=5n+10

-6=4n+10

-16=4n

n=-4

Check:

-4-6=-10

5(-4+2)=-10

Therefore, -4 is the correct solution.

This can only have infinitely many solutions if both equations say the same thing. Let's work with the second one a bit.

6a+2b=k+3a+mb

3a+2b=k+mb

We now have each equation saying that 3a+2b is equal to something. If the two separate expressions are equal, then there will be infinitely many solutions. Set

k+mb=2.

If we make m=1, we get k+b=2, which varies based on b, so that cannot be it.

If we make m=0, we get k=2, which is a solution.

That simplifies to 15+2=17

The answer is -2.

25 cents

x+y=1.5

y=x+1

substitute in 

x+x+1=1.5

-1 form either side

2x=.5

/2    /2

x=.25

The perimeter of OSTQ is 55.

Assuming that x neq 1/2, simplify (12x^2 - 6x)*(4x - 2).  

I'm not sure about what you're asking, but I'll go ahead anyway. 

I would factor 6 out of the first expression and 2 out of the second. 

It would look like this                                   6 * (2x² – x) * 2 * (2x – 1) 

Moving the 2 over to the 6 it becomes      12 * (2x² – x)(2x – 1) 

You could take an x out of the first one.     12x * (2x – 1)(2x – 1)  

And so                                                        12x * (2x – 1)²  

I suppose that's as simple as I can get it,  

unless you want it multiplied out, but  

I don't think that would be simpler.  

Also I don't know what neq means,  

but I'm guessing it means not equal to.  

_.

Five times a number is divided by 7 more than the number.

If the result is 0, then what was the original number?

          5n  

       –––––  =  0 

        n + 7  

The only way this can happen is n = zero.   

_.

An aquarium tank is 1/6 full of water. When 2 gallons of water are added, the tank becomes 1/2 full. What is the total capacity of the aquarium tank, in gallons?  

Remember in step (2) that 3/6 is another way of saying 1/2. 

(1)  The tank starts out 1/6 full. 

(2)  Then 2 gallons makes it 3/6 full. 

(3)  So, 2 gallons added 2/6 of a tank.  

(4)  A full tank is 6/6 so the tank holds 6 gallons. 

_.

In a median, DG:DA = 1:3, where G is the centroid.  So the scale factor is 1/3.

We are not here to do your homework for you.

You said "6 times the largest of the seven integers"    

The problem said "21 times the largest of the seven integers" 

You solved a different problem from the problem that was posed.  

_.

I like it because it has expert answers and solutions.It's cool.

Since ∣a∣=∣b∣=∣a+b∣, we have ∣a∣2=∣b∣2=∣a+b∣2. This gives us the following equations:

a^2 = b^2 a^2 + b^2 = (a + b)^2

The first equation tells us that a and b are of equal magnitude. The second equation tells us that a2+b2=a2+2ab+b2, or 2ab=0. This means that a and b are either equal or opposite in sign.

If a and b are equal, then a/b=1. If a and b are opposite in sign, then a/b=−1. The sum of all possible values of a/b is therefore 1−1=0​.

Thank you! I'll let you know if the answer's correct and if so, thank you so much! It makes sense!

Factor \(y=-x^2+6x-5\): \((5-x)(x-1)\) You should be able to figure out what values of x put that equation equal to zero.

There are \(\pmatrix{8 \\ 2}=28\) ways to pick two balls simultaneously. 3 of them have both balls white. So, \(\frac{3}{28}\) is the probability. Given that information, try to figure out the second one on your own.

(a): The given expression is equal to \(\frac{\frac{n!}{k!(n-k)!}}{\frac{n!}{(k-1)!(n-k+1)!}}\) .

Cancel n! to get \(\frac{(k-1)!(n-k+1)}{k!(n-k)!}\)

Cancel \((k-1)!(n-k+1)!\) to get \(\frac{1}{k(n-k)}\).

(b): I agree that the answer is 17.