geno3141

[ 1/x² + 1/y² ] / [ 1/x + 1/y ]

Look at all the denominators; their common denominator is x²y².

Multiply both the numerator and the denominator of the fraction by x²y²:

Numerator:  [ 1/x² + 1/y² ] · x²y²  =  y² + x²  =  x² + y²

Denominator:  [ 1/x + 1/y ] · x²y²  =  xy² + x²y  =  xy(x + y)

Answer:  [  x² + y² ] / [ xy(x + y) ]

(You can't simplify any farther.)

This problem is so much easier on a digital clock ... but ...

There are 360° in a circle.

Between any two numbers on the clock, there will be 360° ÷ 12  =  30°.  (This means that the hour hand moves 30° when going from 4:00 to 5:00.)

I'm going to measure all the degree from 12:00 going in a clockwise direction.

First, let's just consider the hour hand.

At exactly 4:00, the hour hand will be 4 x 30° = 120° from 12:00.

At 4:09, the hour hand will go another 9/60th of the distance from 4:00 to 5:00.  (9/60) x 30° = 4.5°.

So the hour hard will be 120° + 4.5° = 124.5° from 12:00.

Now, let's consider the minute hand. After 9 minutes, it will be 9/60th of the way around the dial, so it will be (9/60) x 360° = 54° from 12:00.

The distance between the two hands is:  124.5° - 54°  =  70.5°.

Did you mean 2/5 or 2.5?

a - 3.5 < 2.5                                     a - 3.5 < 2/5           

Add 3.5 to both sides:

a < 6.0                                                a   < 3.9

First draw the picture on a graph.

Then, there's a couple of things that you can do:

   Since it says add 5 to each x-value and subtract 2 from each y-value;

    ---   For each corner point, find a new corner point 5 spaces to the right and 2 spaces down, then                                    connect these points to get the new picture.

    or you can:

    ---   For each corner point, take the x-value and add 5, take the y-value and subtract 2, then graph these                         points and draw the new picture.

Either way, you should get the same new picture (this new picture is the image).

(x - 3)²  =  64

Find the square root of both sides:          (don't forget to use the ± sign)

x - 3  =  ± 8

So, either  x - 3  =  8          or          x - 3  =  -8              (now add 3 to both sides)

                    x  =  11         or               x  =  -5

Where did the 2 come from?

x²  =  45

x  =  √45

x  =  √9·√5

x  =  3√5

If your original function is  y  =  x²

and you want to translate it 3 units to the right, replace  x  with  x - 3:  y  =  (x - 3)².

If you want ot translate it 5 units to the left, replace  x  with  x + 5:  y  =  (x + 3)².

Notice, if you want to move it to the right, use a - sign; to the left, use a + sign.

If you want to translate it 4 units up, replace  y  with  y - 4:  y - 4  =  x²

                (or y = x² + 4).

If you wnat to translate it 7 units down, replace  y  with  y + 7:  y + 7  =  x²  

                (or y = x² - 7).

A translation of the vertex from (0, 0) to (a, b) results in the equation:  y - b  =  (x - a)².

The volume of the driveway, in cubic feet is:    V  = length x width x height

    V  =  162 x 6 x (1/3)  =  324 cubic feet

(since 4 inches = 1/3 foot)