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Simplify to \(2x^2 - 16x + 3 + k\).

The quadratic has exactly 1 solution when the discriminant(\(b^2 - 4ac\)) is 0. 

This means we have the equation: \(256 - 4 \times 2 \times (3 + k) = 0\)

Solving, we find \(k = \color{brown}\boxed{29}\)

Let \(x = 0.43 \overline{54}\)

This means that \(100x = 43.\overline{54}\) and \(10,000x = 4354.\overline{54}\)

Subtracting the 2 gives us \(9900x = 4311\), meaning \(x = {4311 \over 9900} = \color{brown}\boxed{479 \over1100}\)

Subtract \({x - 5 \over x + 5} \) from both sides: \({9 \over x + 5} = {x-5 \over 2x}\)

Cross multiply: \(18x = x^2 - 25\) 

Subtract 18x from both sides: \(x^2 - 18x - 25 = 0\)

Use the quadratic formula: \(x = \color{brown}\boxed{{9 \pm \sqrt{106} }}\)

Using the distance formula yields: \(5 = \sqrt{({6 - 1})^2 + ({2 - b})^2}\). 

Simplifying this equation gives us \(25 = 25 + (2-b)^2\), meaning \((2-b)^2 = 0\). 

Can you take it from here?

 Point M is 12 units to the right of Point A, so it must be 12 units to the left of Point B. 

Can you take it from here?

oh nice. you should sign up.

Start with the fraction \({n \over 3}\). This is only terminating when n is a multiple of 3. 

Now, look at the \({n \over 1375}\) fraction. This is only terminating when n is a multiple of 11. 

So, every \(\text{lcm}(3,11) = 33\) integers, n will terminate. 

Thus, there are \(\lfloor {1000 \over 33} \rfloor = \color{brown}\boxed{30}\) integers that work. 

that was easy.

my answer shows an easier way for the percentage step. but still. same answer! 

An 8-inch pizza has a radius of 4 inches.

A 12-inch pizza has a radius of 6 inches.

Area of first pizza: \(\pi r^2\)\(= 16\pi\)

Area of second pizza: \(\pi r^2=36\pi\)

Calculation of percentage: \(\frac{36-16}{16} \times 100 = 125%\)%

Therefore, the area is increased by \(125\)%

guest.

The points are R and T.

yes

uuuum. random question, but are you just a guest, or a member logged out.

https://web2.0calc.com/questions/polynomial_99864

Original pizza: \(4 ^2 \pi = 16 \pi\)

New pizza: \(6^2 \pi = 36 \pi\)

So, \(36 \div 16 = 2.25 = 225\text{%}\). But, recall that we are looking for the increase, so we subtract 100, to find that it is a \(\color{brown}\boxed{125 \text{%}} \) increase. 

yeah

BuilderBoi's right.

Try it for yourself, and see what you get 

By the Binomial Theorem, we have the system:

\(a \times n = -20\)

\({n \choose 2} \times a^2 = 180\)

Squaring the first equation gives us \(a^2n^2 = 400\), meaning \({n^2 \over {n \choose 2}} = {20 \over 9}\). Using trial and error, we find \(n = 10\), meaning \(a = -2\)

Now, we have \(c = {10 \choose 3} \times 1 \times -2x^3 = \color{brown}\boxed{-960}\)

nerdiest: Did YOU check the answer given as 142 to be correct? Why don't try it and list the 142 numbers.

Nah, It's ok to make mistakes, the important thing is to learn! :) 

look at BuilderBoi's answer.

\(\color{brown}\boxed{99}\)

We can position the letters in 7!/7  = 720 ways because you have to divide by 7 to eliminate the rotations.
To deal with the restriction, we do complementary counting. If you think of O and N as one letter, meaning they are together, then there are only 6 "letters" so 120 ways however, we have to multiply by two because the O can be to the right of N or the left. This gives 240 cases we do not want. 720-240=480.

oh no... i answered the question wroooong! NOOOOOO. You in fact might be correct. I'm the one who is dummmmmb. dang it.

your answer was pretty logical, but the answer was 2/3...

but I will give you credit for your hard work.