Saturday, July 24th, 2010

### Solution:

1. 3x + 4y=25

2. 2x – 5y=9

We could rewrite these as follows by multiplying the first equation by 5 and the second by 4:

1. 15x + 20y = 125

2. 8x – 20y = 36

If we add the above two equations, we can eliminate y:

23x = 161

So x =3D 7, and plugging this into the first equation we can figure out

y: **21 + 4y =3D 25**,

so **y = 1**

Friday, July 23rd, 2010

### Solution:

First write down the two equations and then pick several values of x and use those values to calculate the corresponding values of y. You can use the x,y pairs to then plot each line. You will see that the two lines intersect at 2,8 =i.e. x=2 and y=8).

Friday, July 23rd, 2010

### Solution:

First, let’s plot f(x) =

Here’s what the graph looks like:

Now, the definition of “domain of a function” as follows: The domain of a given function is the set of “input” values for which the function is defined.” For instance, the domain of cosine would be all real numbers, while the domain of the square root would be only numbers greater than or equal to 0 (ignoring complex numbers in both bases).

As you can see from the above graph, the function is valid for all “real” values of x, except for 0. The set of “real numbers”, as you may know, can be thought of as points on an infinitely long number line. The shorthand way of saying “all real numbers except for x” is as follows:

Monday, July 19th, 2010

### Solution:

First recognize that this is in the form of (x^{2}-a^{2}), which can always be factored as (x+a)(x-a). If you multiply these two terms, you get x^{2}-ax+ax-a^{2}, which is equal to x^{2}-a^{2}.

So in this case, we can see that **a=3**,

so x^{2}-9

= x^{2}-3^{2}

= **(x+3)(x-3)**

Monday, July 19th, 2010

### Solution:

You can simply 12 – ( x + 3 ) +10 by rearranging the terms:

- 12 –x -3 +10
- 19-x

Saturday, July 17th, 2010

### Solution:

1. Let’s call the number of cookies Cara made “x”

2. First she sold three fifths of x(.6x)

3. The remaining amount is two fifths of x(.4x)

4. Then she one fourth of x;two fifths of “x” (.25*.4x = .1x)

5. .6x=.1x+200

6. .5x=200

7. x= 400

Saturday, July 17th, 2010

### Solution:

- 2(x – 5) = -11
- 2x – 10 = -11
- 2x = -1
- x = -0.5

Friday, July 16th, 2010

### Solution:

To calculate 2 times the square root of 45 (2sqrt(45)), you just need to calculate the square root of 45 and then multiply it by two:

**Step1: 2 x sqrt (45)**

**Step 2: 2 x 6.708**

**Step 3: 13.416**

We used a calculator to get obtain the square root of 45. Are you allowed to use a calculator? If not, we can show you how to calculate this manually.

Friday, July 16th, 2010

### Solution:

X is the smallest number

y=x+2

z=x+4

z+2x=25

x+4+2x=25

3x=21

X=7

Y=9

Z=11

The equation that we used to solve the problem is x+4+2x=25, which can be simplified to = x=21.