NotThatSmart

First, let's add up all 3 of the numbers. 

We get \(248 + 113 + 2870 = 3231\)

Now, we have to factor 3231. Notice that \(3+2+3+1=9\), so 3231 is divisble by 3. 

We get \(3231/3=1077 \). Notice that \(1+7+7=15\), so 1077 is also divisble by 3. 

\(1077/3 = 359\)

359 is prime. 

So now, we have 2 factors, 3 and 359. 

\(3+359=362\)

So our final answer is 362. 

Thanks! :)

In order to do this, we can set some variables.

Let's set \(x=0.\overline{2123}\)

If x is equal to that, then notice that \(10000 x = 2123.\overline{2123}\)

This is very important to the problem. 

Subtracting x from 10000x, we get

\(\eqalign{10000 X &= &\hfill2123.2123...\cr X &= &\hfill0.2123...\cr \hline 9999X &= &2123\cr}\)

Notice that the repeating decimal cancels out. 

Now, we solve for x. We get

\(X = \frac{2123}{9999}\\X = \frac{193}{909}\)

So our final answer is \(\frac{193}{909}\)

Thanks! :)

First, let's add all three numbers up. We get

\(333+183+401=917\)

Now, we must find factors of 917. 

There's actually only 4 of them, two of them which are 917 and 1. 

The other two are 7 and 131. 

\(7*131=917\)

So our two prime factors are 7 and 131. 

We have \(7+131=138\)

So 138 is our final answer. 

Thanks! :)

First, we put \(0.11012 \) in fraction form not reduced or simplified. 

To do this, we multiply the decimal by \(100000/100000\)

We get \(\frac{0.11012}{1}\times \frac{100000}{100000}= \frac{11012}{100000}\)

Now, we search for common factors. 4 is one. 

\(\frac{11012 \div 4}{100000 \div 4}= \frac{2753}{25000}\)

Unfortuantely, there are no more common factors after this, so we have

\(0.11012 = \frac{2753}{25000}\)

So our final answer is \(0.11012 = \frac{2753}{25000}\)

Thanks! :)

Let's first factor each number to the smallest it can be. We get

\(3 \cdot 41 + 3 \cdot 2^3 \cdot 19+ 3 \cdot 263\)

Notice that every number is a factor of 3. We get

\(3(41+152+263)\)

Adding every number inside the parenthesis, we get

\(3(456)\\ 3^2 \cdot 2^3 \cdot 19 \)

So 3, 2, and 19 are our numbers. 

\(3+2+19=24\)

So 24 is our answer. 

Thanks! :)

We can use variables and equations to solve this problem. 

First, let's let \(x=2.\overline{57}\)

If we have that for the value of x, we have \(100x = 257.\overline{57}\)

This is extremely important for our solution. 

Now, we subtract x from 100x. We have

\(100x-x=257.\overline{57}-2.\overline{57}\)

Notice the repeating decimal cancels out. We get

\(99x=255\\ x=255/99\\ x=\frac{85}{33}\\ x=2\frac{19}{33}\\\)

So our final answer is \(x=2\frac{19}{33}\)

Thanks! :)

We can keep couting up and up until we get prime numbers. 

First, we have \(101\). Notice it's only divisble by 1 and itself, so there's the first prime. 

All the even numbers obviously don't work, so we skip them. 

Next, we have \(103\). It also is only divisble by 1 and itself, so that's the second prime. 

Third, we have 105. It's divisble by 5, so it doesn't work. 

Then, we have \(107\), which is also a prime number. 

\(109\) is also prime, so we count that as our fourth prime number

111 is divisble by 3 and 37, so it doesn't work.

However, \(113\) is prime, so that's the smallest. 

So 113 is our answer. 

Thanks! :)

A prime number is only divisble by 1 and itself. 

First, let's look at 1. 

Even though it is divisible by 1, it only has one true factor, meaning it is not prime. 

Next, we have 2. Two is only divisble by 1 and itself, so it qualifies. 

Following this pattern, \(3=(3*1), 5=(5*1), 7=(7*1)\) are all prime. 

However, \(4 = 2*2, 6=2*3, 8=2*4, 9=3*3, 10=2*5\)are all what we call composite. 

Thus, we have \(2,3,5,7\) as our prime numbers. 

Thanks! :)

If a polygon has 3 sides, then it has to be a triangle. 

We can solve this problem by setting some variables. Let's set the smallest angle degrees as n. 

Now, since the angles from an arithmetic sequence, each angle is increasing an equal amount. 

This means if the first and last angle are 56 degrees apart, then the middle angle is \(56/2=23\) degrees bigger than n. 

Thus, we can write the equation \(n+(n+23)+(n+56)=180\)

Solving this equation, we get

\(3n+79=180\\ 3n=101\\ n=101/3\)

So our final answer is 101/3

This is not a whole number, but it does work. 

Thanks! :)

First, we need to combine all like terms to see what we area dealing with. We have

\(x^{2}+18x+3\). 

Now, completing the square for x by adding and subtracting 81, we get 

\((x+9)^2-78\)

Thus, we can easily fill in the blanks now. 

The first blank is 1

The second blank is 9

The third blank is -78. 

Thanks! :)