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Thank you!

The graphing formula for a parabola is:  y - k  =  a(x - h)²  where (h, k) = (3, 2)

--->                                                          y - 2  =  a(x - 3)²

Since (1, 0) is on the parabola   --->       0 - 2  =  a(1 - 3)²

                                                                    -2  =  a(-2)²   

                                                                    -2  =  a(4)

                                                                    -½  =  a

--->         y - 2  =  -½(x - 3)²

--->    -2(y - 2)  =  (x - 3)² 

--->     -2y + 4  =  x² - 6x + 9

--->           -2y  =  x² - 6x + 5

--->               y  =  -½x² + 3x - 5/2

Also, the vertex is x=-b/2a, and a is -2... shouldn't it be -3, not 3?

Hint:

The shape is 6 sided, that means the sum of the angles is (6-2) * 180 = 4 * 180 = 720.

 - Now you create an equation and set it equal to 720.

The common difference is 2.

The formula for the n^th term of an arithmetic sequence:  t_n  =  t₁ + (n - 1)d

The 16^th term is 8   --->   n = 16   --->   8  =  t₁ + (16 -1)(2)

                                                              8  =  t₁ + (15)(2)

                                                               8  =  t₁ + 30

--->   t₁  =  -22

--->   t₂  =  -22 + 2  =  -20

cos^2 + sin^2 = 1

1/16   + sin^2 = 1

sin^2 = 15/16       sin =  sqrt15 /4

tan = sin / cos  =   sqrt15/4 /1/4  = sqrt 15

You can also use the theorem that says that  MA·AT  =  EA·AD

--->   9·9  =  4·AD

--->   AD  =  81/4   

--->   AD  =  20.25

Find the diameter and divide by 2.

2x^2 + 10x        + 2y^2-6y         = 18   divide by 2

x^2 + 5x          + y^2 -3y            = 9     complete the squares

(x+2.5)^2          + (y-1.5)^2      = 9 + 6.25 + 2.25

                                                  = 17.5         = r^2               area = pi r^2 = 17.5 pi

Call BE = x         then AC = x

Call DE = y

Call EC = z

Triangle(ACB) is similar to triangle(DEC).

--->   y / x  =  x / (x + z)

Right triangle   --->   y  =  sqrt(1 - x²)

x + y + z  =  2   --->   z  = 2 - x - y   --->   z  =  2 - x - sqrt(1 - x²)

y / x  =  x / (x + z)   --->   sqrt(1 - x²) / x  =  x / [ x + (2 - x - sqrt(1 - x²) ) ]

--->   sqrt(1 - x²) / x  =  x / [ 2 - sqrt(1 - x²) ]

Cross-multiplying:

--->   x²  =  2sqrt(1 - x²) - (1 - x²)

--->   x²  =  2sqrt(1 - x²) - 1 + x²

--->     0  =  2sqrt(1 - x²) - 1

--->    1  =  2sqrt(1 - x²)

--->   ½  =  sqrt(1 - x²)

--->   ¼  =  1 - x²

--->   x²  =  3/4

--->     x  =  sqrt(3)/2       [the negative answer can be ignored]

cos(ABC)  =  [ sqrt(3)/2  ] / 1

angle(ABC)  =  cos^-1[ sqrt(3)/2 ]

angle(ABC)  =  30^o 

Hint: AT = AM because ED is a perpendicular bisector. Whenever a chord intersects and forms a right angle, then one of them is a perpendicular bisector.

(3 - 3i)(-5 - 4) =

(3-3i)(-9)=

-27+27i

If the question is asking for the vertex, does that mean 'x' is 3, and we have to subsitute x for 3, to find out y?

Is that your way of saying thank you?

If cos θ= 1/4and θ is between 0 and 90, find tan θ

84 / 7 =12 mph - his speed against the wind.

84 / 6 =14 mph - his speed with the wind.

[12 + 14] / 2 = 13 mph - his speed in still air.

[14 - 12 ] / 2 = 1 mph - the speed of the wind.

what is -c^-2

Hello Guest!

-c^-2 \(=\large -\frac{1}{c^2}\)

  !

Recognize that the two roots are in the form x+y and x–y.  When this is the case, their product is always x² – y². 

_.

If I choose four cards from a standard 52-card deck, with replacement, what is the probability that I will end up with one card from each suit? 

Since you replaced each card after it was chosen, you end up with no cards, because you put them all back.  So, literally, the probability is zero.  If this isn't a trick question, then a better wording of the question would have been "If I choose four cards from a standard 52-card deck, with replacement, what is the probability that I will end up with will have drawn one card from each suit?" 

_.

Do you need help with the question or the answer ?!? 

a=3; b=2;c=1;d=0;p=1;m=0;n=frac(2#(a)-2#(b)+2#(c)-d);m=if(round(n*1E10)==round(tan(7.5)*1E10), goto loop, goto next);loop: printn,a,b,c,d;next:a++;if(a<35, goto5, 0);a=3;b++;if(b<35, goto5, 0);a=3;b=2;c++;if(c<35, goto5,0);a=3;b=3;c=1;d++;if(d<35, goto5, discard=0;

OUTPUT:  a = 6,   b = 3,   c = 2,   and   d = 2

Sqrt(6) - sqrt(3) + sqrt(2) - 2  =  tan(7.5 degrees).

The time 7:30 represents 7 hours and 30 minutes.

To this, we need to add:  2 hours, 20 minutes, 2 hours, 45 minutes, and 3 hours.

Hours: 5 mi 2 + 2 + 3  =  7 hours.

Minutes:  20 + 45  =  65 minutes.

      65 minutes = 1 hour, 5 minues.

We will need to add 7 hours + 1 hour + 5 minutes  =  8 hours 5 minutes

To 7:30, which is 7 hours and 30 minutes, we add 8 hours and 5 minutes, to get 15 hours and 35 minutes.

15 hours is 3 in the afternoon, so Randy leaves at 3:35

7:30  + 2 hr + 1/3 hr + 2 hr + 3/4 hr +3 hr = 15 :35       3:35 pm

Agree ....except final units will be  cm