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Let the Width=W

The Length=W+15

W x [W+15]=100

Solve for W:
W (W+15) = 100

Expand out terms of the left hand side:
W^2+15 W = 100

Add 225/4 to both sides:
W^2+15 W+225/4 = 625/4

Write the left hand side as a square:
(W+15/2)^2 = 625/4

Take the square root of both sides:
W+15/2 = 25/2 or W+15/2 = -25/2

Subtract 15/2 from both sides:
W = 5 or W+15/2 = -25/2

Subtract 15/2 from both sides:
Answer: |  W = 5 or W = -20 , So the Width=5 feet    The Length=5+15 =20 feet

we know that y-y1=m(x-x1)

Assuming (2, 5) = (x1, y1) and m = 3 and substituting the values, we get: y-5=3(x-2)

3x-y-1=0 ( this is the equation )

Part B : replace x by 7

3*7-1=y 

y=20

so the path doesn't pass through the point (7;22)

but (7:20)

Part C 

the second equation can be written as y=(-1/3) x + 2

so the multiple of their m is -1

so the equations are perpendicular  to each other

"A geosynchronous satellite is stationary over a point on the equator (zero degrees latitude) at the same longitude as Seattle, Washington. Seattle's latitude is 47.6°. If you want to communicate with the satellite, at what angle above the horizon must you point your communication device? The Earth's radius is 6.38×106 m. The orbital radius of a geosynchronous satellite was found in a previous problem (you can also calculate it using the mass of the Earth: 5.97×1024 kg)"

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Slope of line joining A and B is (4 - (-2))/(6 - 2) = 3/2  Hence slope of perpendicular line is -2/3

Midpoint of A and B is ( (2+6)/2, (-2+4)/2 )  or (4, 1)  

Equation of perpendicular bisector is  y - 1 = -(2/3)(x - 4)  or  y = -(2/3)x + 11/3

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"How can you do an XY Table with an imperfect fraction? Ex: y=4/3x+2 where x is -12, 0, and 15."

X             Y=(4/3)*X + 2

-12           (4/3)*(-12)+2 → -4*4+2 → -14

0               (4/3)*0+2 → 2

15            (4/3)*15+2 → 4*5+2 → 22

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Like so:

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52.1429

Press "2nd" key in the top left hand corner. You should see "acos", which is the same as inverse cosine.

The two factors are:

a*b=-9600, a+b=-290, solve for a,b

a= -320, b=30 or,

b=-320, a=30.

1 - 1/2% means .50/100 =.005

.005 x 100,000 =500 number of families with income of over $80,000.

2 - Solve the following system:
{x+2 y = -1 |     (equation 1)
3 y-x = -19 |     (equation 2)
Add equation 1 to equation 2:
{x+2 y = -1 |     (equation 1)
0 x+5 y = -20 |     (equation 2)
Divide equation 2 by 5:
{x+2 y = -1 |     (equation 1)
0 x+y = -4 |     (equation 2)
Subtract 2 × (equation 2) from equation 1:
{x+0 y = 7 |     (equation 1)
0 x+y = -4 |     (equation 2)
Collect results:
Answer: |  x = 7    and        y = -4

You can go online and try this very good graphing calculator and see if it can help you:

https://www.desmos.com/calculator

1 inch =25.4 mm

5 / 25.4 =0.196850 of an inch.

There are a variety of tests that you can do on large numbers, such as yours, such as Lucas-Lehmer test and Fermat's little theorem....etc. I tested your number and it is NOT a prime number. It has numerous factors.

Express the values of x that satisfy the inequality -3 ≤ x < 7 as an interval.

[-3, 7)

Find all values of s (s + 4)(s - 3) ≤ 0   Give your answer as an interval.

Let's solve this

s(s + 4)(s -3)  = 0      the three solutions are s =0, s = -4 and s = 3

Then, the solutions to this inequality  will occur on one or more of these possible intervals (-infinity, -4] , [-4, 0], [0,3] or [3, ifinity)

The intervals  (-infinity, -4]   and [0, 3]  will satify the inequality.....here's a graph : 

True, Now it works.

Well we were not hard to find.  :)

We didn't go anywhere  LOL

Anyway it is good to see you back again :)

Ello Melody!

God I missed you guys xD

1/5 + 4 + 4/5     we can arrange this as :

1/5 + 4/5 + 4  =

5/5 + 4   =

1 + 4   = 

5

Thx

Hi Jillybean :)

Hey, JillyBean....try downloading GoogleChrome.......it does the same thing to me at my local library until I download Chrome......then....it seems to work fine........

Melody -- I have little confidence that I know what I'm talking about, but I thought it was fun to think of the problem this way (I had to rewrite a little):

Let R be a relation on A={2,3,4,6.9) defined by "x is relatively prime to y"; that is the only positive divisor of x and y is 1.

a) Write R as a set of ordered pairs:

     {  (2,3), (2,9), (3,2), (3,4), (4,3), (4,9), (9,2), (9,4) }

     Notice that 6 is not a member of any of the ordered pairs.

b) Draw a digraph representing R:

    On a piece of paper, draw 5 dots and label them '2', '3', '4', '6', and '9'.

    Then, to represent (2,3), draw an arrow from dot '2' to dot '3' (the tail of the arrow is at '2' and the head points to '3').

    Draw all the other arrows: from 2 to 9, from 3 to 2, from 3 to 4, from 4 to 3, from 4 to 9, from 9 to 2 and from 9 to 4.

    The dot at '6' has no arrows that either point from it or point to it.

c)  Find the in-degree and the out-degree of each vertex (dot).

    The in-degree of a vertex is the number of arrows that point to that vertex.

         Since there are two arrows to dot '2', one from '3' and the other from '9', the in-degree of '2' is 2.

         Similarly, the in-degrees of '3', '4', and '9', are each 2; the in-degree of '6' is 0.

    The out-degree of a vertex is the number of arrows that start at that vertex and point to another vertex..

         Since there are two arrows from dot '2', one to '3' and the other to '9', the out-degree of '2' is 2.

         Similarly, the out-degrees of '3', '4', and '9', are each 2; the out-degree of '6' is 0.

d) List all paths of length 4 starting from vertex 3.

    1)  3 ► 4 ► 9 ► 2 ► 3

    2)  3 ► 4 ► 9 ► 2 ► 9

    3)  3 ► 4 ► 9 ► 4 ► 3

    4)  3 ► 4 ► 3 ► 2 ► 9

    5)  3 ► 4 ► 3 ► 2 ► 3

    6)  3 ► 4 ► 3 ► 4 ► 3

    7)  3 ► 4 ► 3 ► 4 ► 9

    8)  3 ► 2 ► 9 ► 4 ► 3

                  etc,

7)  Compute R²:

     From  {  (2,3), (2,9), (3,2), (3,4), (4,3), (4,9), (9,2), (9,4) }:

     (2,3) x (3,2) = (2,2)

     (2,9) x (9,4) = (2,4)

     (3,2) x (2,3) = (3,3)

     (3,2) x (2,9) = (3,9)

     (4,3) x (3,2) = (4,2)

     (4,9) x (9,4) = (4,4)

     (9,2) x (2,3) = (9,3)

     (9,4) x (4,9) = (9,9)

     --->     { (2,2), (2,4), (3,3), (4,2), (4,4), (9,3), (9,9) } 

     [It's interesting that these are either identical values or squares or square roots.]

    This digraph would contain the same five dots, but the arrow would be determined by these final ordered pairs.

Accept this answer at your own risk!