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This doesn't have any real solutions....

Here are the non-real ones

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{19}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{15}}}}{\mathtt{\,\times\,}}{i}\\
{\mathtt{x}} = {\sqrt{{\mathtt{15}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,-\,}}{\mathtt{3.872\: \!983\: \!346\: \!207\: \!416\: \!9}}{i}\\
{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3.872\: \!983\: \!346\: \!207\: \!416\: \!9}}{i}\\
\end{array} \right\}$$

First, compute the parentheses. 

Then, multiply and divide.

19 is a prime number so you will have to use the quadratic formula to solve this one. 

42/65

Find the GCF (greatest common factor):

42: 1, 2, 3, 6, 7, 14, 21, 42

65: 1, 5, 13, 65

Are there any factors found in both numbers?

42 = 2 x 3 x 7

65 = 5 x 13

Notice that these two numbers have no common factors....thus nothing would "cancel".....so the fraction is in lowest terms......!!!

it becomes 2 equations

6x-3=9 or 6x-3=-9

you have to solve each of these.  There will be 2 answers. 

5445 mm = 0.005445 km.

1000 mm = 1 m.

1 km = 1000 m.

Basically, you are moving the decimal place 6 times to the left.

Thanks Aziz. :)

First, compute the parentheses.

Next, do the exponents.

Then, do the multiplication.

Finally, subtract.

Call x the number of campers on the low trail and y the number of campers on the high trail.

So we have

x + y  ≤ 30

x ≥10

y ≥ 5

This has many solutions....(10, 20) (11, 19) (12, 18) ( 13, 17).....etc.......(24,6)  (25, 5)

We can graph this...but there will be many "solution" points that aren't whole numbers - and thus - aren't really a part of the solution set because we can't have "part" of a person !!!

l = # of low terrain campers

h = # of high trail campers

$$l + h \le 30.$$

$$l \ge 10.$$

$$h \ge 5.$$

Yes, most likely.

Example: (2^2)^2 = 2^4 = 16.

Note, you just multiply the two powers together --> 2^(2*2) = 2^4 = 16.

Same for 3^(1/2)^(1/4) --> 3^(1/2*1/4) = 3^(1/8).

Are we suppose to solve for x?

The total cost of the 3 computers is $900*3 = $2700. 

If the principal pays $98 per month for each computer, she will be paying $98*3 = $294 per month.

It won't take her 12 months to pay because $294*12 = $3528. 

If we round up $294 to $300 --> $2700 / $ 300 per month = 9 months. However, this is an overestimation, so she will need 10 months to pay.

Thanks Chris  

Thanks chill and I understand. For word problems I pretty much just need the set up and then i should be able to figure it out from there. Can you please "set-up" the other word problem i Posted?

Hang in there DS.......tomorrow....you might be at the top of the board......the "point" totals seem to fluctuate more than the Dow Jones Industrials !!!!!

I'm gong to do the "set-up" but I want YOU to do the solving trQ !!!  You have to learn how to do this and I did one earlier for you......

Let x be the price of each orange and y be the price of each grapefruit.  So we have....

8x + 1y =   4.60

6x + 3y =   4.80

Hint....think about multiplying the top equation by -3 and adding it to the second equation to "eliminate" y.....!!!

This system has a solution.....don't ask me how I know....I just do !!!!

Let me know if you get stuck and I'll talk you through it...this might seem painful....but you won't learn just by being an "observer"

First, multiply 8 by 2. Then add 16 and 1.

$${\frac{{\mathtt{17}}}{{\mathtt{8}}}}$$

Now, turn it in a decimal.

$${\frac{{\mathtt{17}}}{{\mathtt{8}}}} = {\mathtt{2.125}}$$

That is your answer

$${\frac{{\mathtt{4}}}{{\mathtt{33}}}} = {\mathtt{0.121\: \!212\: \!121\: \!212\: \!121\: \!2}}$$

Okay and no problem. Thanks.

I think that this is it!

Add the prices together.

then, add the oranges only.

Do the same thing with the grapefruit.

Then, divide the number if grapefruits and oranges separately.

i am not sure because I have to log out now! Sorry if it's wrong.

Here's my two cents worth about this one:

This is a discontinuous function - and it passes the vetical line test because any vertical line would only cut the "graph" in one place. The graph would have an infinite number of disconnected "peaks" and "valleys" because the x values along the number line are continuous. In other words, all the rationals would have y values of 1 and all the irrationals would have values of 0. The graph is definitely non-continuous because there aren't any "intermediate"  y values - i.e., "y" is either 0 or 1 - and nothing in between !!   Basically, the graph would be just  "dots" at either y= 0 or at y =1. In a strange way though, this is an "even" function, because the negative of any positive rational would have a corresponding y value of 1 and the negative of any positive irrational would have a corresponding y value of 0. Thus, f(x) = f(-x). The y intercept would be  the "dot" at (0, 1) - because 0 is rational. The "x" intercepts would just be the "dots" where the irrational numbers are located on the number line because "f(x)" would be 0 at those points!!!  The domain is all real numbers, but there are onl two values for the "range" .....0 and 1 !!!

That's my "take" on this one !!!