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See https://web2.0calc.com/questions/help_91968.

Let a be the angle betwen the line y = 1/3*x and the x-axis, and let b be the angle betwen the line y = 13/9*x and the x-axis.  Then tan(a) = 1/3 and tan(b) = 13/9, so a = arctan(1/3) and b = tan(13/9).

The angle for the angle bisector is (a+ b)/2, and tan((a + b)/2) = (13/9 + 1/3)/(1 + 13/9*1/3) = 6/5.

So, the slope of the angle bisector is 6/5.

Alright, I was assuming that when it said "these users are composing answers", they were actively typing away.

Your answer makes far more sense, I was just confused as he answered far more difficult questions in a few minutes lol.

answer is not -1238

Lowest common multiple of 6 and 7 is 42   

so 42 years from 1997 =.......

say the box is a cube

larger box

x * x * x   = x^3  = 5400 in³

                 x= 17.54 in

so the smaller box is  5.84  * 5.84 *  5.84 = 200 in³

..... or   5400 /(3 *3*3)   = 200 in³

Ahha! I see, but you should use the class mesage board for these questions.

I have to admit, I am stumped too.

You must know these 3 relationships:

1 - Distance  = Time x rate(speed)

2 - Time =Distance / rate(speed)

3 - Rate(speed) =Distance / time.

Now, let us see if you can solve your own problem, preferably, by posting it here!.

Distance between home and store L = 6mph*(5/6)h = 5m

Total distance travelled = 10m

Time for return trip =  5m/(12mph) = 5/12h

Total time = (5/6)h + (5/12)h = 15/12h = 5/4h

Average speed = Total distance/Total time = 10m/(5/4h) = 40/5mph = 8mph

I think you are about 72 y/o.

son = 42 y/o

grandson=6 y/o       

Here is an alternative approach:

It was False

That's not an ordered pair though.

it was A 

A formula for a parabola is:  y - k  =  a(x - h)²

where (h, k) are the coordinates of the vertex.

Since the vertex is at (2,-1),  h = 2   and  k = -1.

Putting those values into the formula:  y - -1  =  a(x - 2)²  or  y + 1  =  a(x - 2)²

To find the value of a, substitute these values:  y = 0  and  x = 5  into the equation.

     0 + 1  =  a(5 - 2)²

            1  =  a(3)²

            1  =  9a

            a  =  1/9

The equation is:  y + 1  =  (1/9)(x - 2)²

1/Ashley   + 1/amanda  + 1/ addison =  1/6

1/addison  + 1/amanda = 1/10

1/10 + 1/ashley = 1/6

1/ashley    = 2/30

ashley = 30/2 = 15 hours   

The probability is 2/9.

The probability is 1/4.

The correct value of a is 4.

Let  n  =  number of nickels.  The value of these nickels is  0.05n.

Let  q  =  number of quarters.  The value of these quarters is 0.25q.

The number of nickels is 24 less than twice the number of quarters.   --->   n  =  2q - 24

The total value of the nickels and quarters is $10.00.   --->   0.05n + 0.25q  =  10.00

Substituting:  0.05(2q - 24) + 0.25q  =  10.00

                       0.10q - 1.20 + 0.25q  =  10.00

                                 - 1.20 + 0.35q  =  10.00

                                              0.35q  =  11.20

                                                     q  =  32                      <---  number of quarters

Since  n  =  2q - 24   --->   n  = 2(32) - 24  =  40            <---  number of nickels

There are 5 even digits and 5 odd digits, so the probability that any digit is even is 5/10 = 1/2 = 0.50.

Similarly, the probability that any digit is odd is 0.50.

This is a binomial distribution. The appropriate formula is:  _nC_r·p^r·q^n-r

To get exactly 5 even digits:

  n = total number of chances = 7

  r = total number of successes (getting an even digit) = 5

  p = probability of success (getting an even digit) = 0.50

  q = probability of failure (getting an odd digit) = 0.50

_nC_r·p^r·q^n-r  =  ₇C₅·(0.50)⁵·(0.50)^7-5  =  0.0410

To get at least 5 digits, we must find the probability of getting exactly 5, of getting exactly 6, and of getting exactly 7, and adding together these three answers.

We have the answer for exactly 5, we now need the answer for exactly 6, so we need to re-do the above with r being 6, and we also need the answer for exactly 7, so we will also need to re-do the avove with r being 7, and then add these three answers together.

Let  x  =  price of one senior citizen ticket.

Let  y =   price of one student ticket.

8x + 9y  =  169     --->   (multiply by 8)    --->    64x + 72y  =  1352

7x + 8y  =  149     --->   (multiply by -9)   --->   -63x - 72y  =  -1341

(adding down the columns)                     --->        x            =      11    <---   cost of one senior citizen ticket.

Since  x = 11    --->     8x + 9y  =  169     --->     8(11) + 9y  =  169     --->     88 + 9y  =  169

(subtracting 88 from both sides)                                                                             9y  =  81

                                                                               cost of one student ticket   --->   y  =  9