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thanks so much!

Draw a picture depicted in the problem

tan 20.5   =   height / d

tan 20.5   = 1020 / d                   solve for 'd' the distance from the airport

Nope, the answer isn't 20 or 28 (what I got)

I realized after it wasn't right

This is because the friends are distinguishable

Steve wins.

Integers    x     and    x-5

x^2    + ( x-5)^2 = 157

x^2    + x^2-10x+25 = 157

2x^2 -10x -132 =0               Quadratic FOrmula   x = 11   and   -6  so the other integer is  6  or  -11

11 and  6            -6   and -11

Be careful with this method....  you may miss the peak between data points!!!

take 1/2 of the   'x' coefficient and add it to the equation

1/2 * 4/5   = 4/10       squared =     16/100        or      8/50    or    4/25

@guest who just answered the question, thats wrong.. :)

The first equation gives you the definition of y....sub this into the second equation:

3 (8x-6)       +        2x    = -7      now you should be easily able to solve for 'x'  

                                                     then sustitute this 'x' into one of the equtions to find 'y'

1) Try x = 0.

2) Try x = y

3) Try y = 0

4) Try x = 1

5) Try y = 1

6) Try f(x) = c

Conclusion: There are no functions that work

Completing the square: \(\displaystyle \left( x + \frac{4}{5} \right)^2 = x^2 + \frac{4}{5} x + \frac{16}{25}\)

Constant = 16/25

What formula? Whatever formula you used is wrong

From the formula, the area of the parallelogram is 1/2*10*14 = 70.

As "CentsLord" calculated, there are 7 nPr 4 =840 permutations.

Each permutation begins with one of the 7 letters this many times =840 / 7 = 120 permutations for each letter. So, letter "L" will begin with 120 permutations. Each of other 6 remaining letters is equally represented in this many ways:120 / 6 =20 ways.

So, 120 permutations beginning with the letter "L" will have 20 of them that end in "P". Since we don't want "P" at the end, then will  drop the permutations that end in "P" and we have left: 

120 - 20 = 100 permutaions that begin with "L" and NOT end in "P".

The possible values of sin 2x are 1/3 and -1/4.

We can write -4 in exponential notation as 4e^(pi*i), so the equation is z^4 = 4e^(pi*i).

By Hamilton's Theorem, the solutions are z = 4^{1/4}*e^(pi*i/4), 4^{1/4}*e^(pi*i/4 + pi/4), 4^{1/4}*e^(pi*i/4 + 2*pi/4), and 4^{1/4}*e^(pi*i/4 + 3*pi/4).  Since 4^{1/4} = sqrt(2) and e^(pi*i/4) = (1 + i)/sqrt(2), the first solution is 1 + i.  Then the other roots work out as

4^{1/4}*e^(pi*i/4 + pi/4) = 1 - i,

4^{1/4}*e^(pi*i/4 + 2*pi/4) = -1 - i, and

4^{1/4}*e^(pi*i/4 + 3*pi/4) = -1 + i.

ab = 6*6/7 = 36/7.

Thanks, that makes sense! But why would you divide 23 by 2??

Answer:

m∠A = 25.5 degrees

m∠B = 116.5 degrees

b = 14.5 

Explanation:

Use law of sines:

a/sinA = b/sinB = c/sinC

10/sin38 = 7/sinA

7sin38 = 10sinA

4.3 = 10 sin A

0.430 = sin A

sin^-1(0.430) = A

m∠A = 25.5

same thing for m∠B and b

A perpendicular slope is the negative reciprocal. So for -2, it becomes 1/2 (multiply by -1, and take the reciprocal). The slope is 1/2, and it passes through (-3, 9). Can you solve from here? (Extra hint: Write out point slope form, then fill in what you know.)

This is probably not the most efficient way, but it works.

Let O = (0, 0), D = (0, -8). Then B = (-12, -8) because OD = 8 and OB = 4sqrt(13), so by the Pythagorean Theorem, BD = 12

Then, since AB is a line segment passing through O, we have that A = (12, 8). Use the distance formula from (0, -8) to (12, 8) and get sqrt((12-0)^2+(8-(-8))^2) = sqrt(12^2+16^2) = 20, so AD = 20.

You are very welcome!

:P

The asymptotes will intersect at the center of the hyperbola.

The center of the hyperbola is (1,2).

The slope of the asymptotes will be found by the square roots of the denominators, so the

slopes are  8/6  and  -8/6.

Equations:  y - 2  =  (4/3)(x - 1)     and     y - 2  =  (-4/3)(x - 1)

Let's assume that four of the players are in the left bracket and the other four players are in the

right bracket.

The number one ranked player always makes it to the finals. The other players, depending upon

the draw, that could make it to the finals are players number two, three, four, and five.

Let's assume that player number one is in the left bracket (the analysis is the same if this 

player is in the right bracket) ...

Where is player number two? 

If this player is in the right bracket, this person will make it into the finals; if not, this player will

be defeated by player number one.

After player number one is put into the left bracket, there are seven slots open for player number

two; four of them in the right bracket (and makes it into the finals and three in the left bracket and

loses to player number one).

The probability that this player is in the right bracket is 4/7.

We need to multiply this probability by the rank:  (4/7) x (2)  =  8/7  =  1.143.

If both player number one and player number two are in the left bracket, where is player number three?

There are six slots left and four are in the right bracket, so the probability that this player is in the right

bracket is 4/6.

The probability is (3/7) x (4/6)  =  12/42  =  2/7

[We need to include 3/7 because we have to have player number two in the left bracket.]

Multiplying this probability by the rank:  (2/7) x (3)  = 6/7  =  0.857

If player numbers one, two, and three are all in the left bracket, where is player number four? 

The probability that players one, two, and three are all in the left bracket and player number four

is in the right bracket is (3/7) x (2/6) x (4/5)  =  4/35.

Multiplying this probability by the rank:  (4/35) x 4  =  0.457

If players number one, two, three and four are all in the left bracket, player number five will be

in the right bracket:  (3/7) x (2/6) x (1/5) x (4/4)  =  1/35

Multiplying this probabiliy by the rank:  (1/35) x 5  =  0.143

Adding these answers together:  1.143 + 0.857 + 0.457 + 0.143  =  2.6