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Slope  =  (  -2 - 3)   / (8 - 2)  =  -5/6

Equation  of line   

y  = (-5/6) ( x  - 2)  +  3

y = (-5/6)x  +  5/3  +  3

y = (-5/6)x  +  14/3

Q =   (0,14/3)

To find P  

0  =  (-5/6)x  + 14/3

-14/3 =  (-5/6)x

(-14/3) ( -6/5)  = x =   28/5

The  area of  the triangle   =   (1/2) (28/5) ( 14/3)    =  196/15  units^2  ≈   13.07 units^2

Hint  :   the  product will only     = 0   if    one  (or more)  of the  digits   =   0

Using the Law of Sines

sin  22  /  5   =   sin x /  13

sin x   =    (13/5) sin 22                       take the inverse sine

arcsin   [  (13/5) sin 22  ]  =  x  ≈   76.9°

N - (5/8)N   =  15

(3/8)N   =  15

N =  15  ( 8/3)  =    40   before sharing

The  function  is

h =   21sin [  (4/5)pi *  t)   +  21

The  tire makes  1 rotation  every   60 /24  =  2.5 seconds

The  scale on  the  y  axis  is 3 cm   for every tick mark

The scale on  the  y axis =   2.5 /5   = .5 sec for each  tick  mark

At 

0 sec           h  = 21  cm

.625 sec     h =  42  cm

1.25 sec     h  =  21 cm

1.875 sec    h  = 0 cm

2.5 sec         h =  21

Here's a graph in Desmos  :  https://www.desmos.com/calculator/xdweyepyi7

In △ABC and △DCB, 

∵ AB = DC,  AC = BD and BC = BC 

         \({AB\over DC}={AC\over BD}={BC\over BC}=1\)

∴ By SSS (side-side-side) rule of similarity 

                      △ABC ~ △DCB 

If △ABC ~ △DCB  then they're also congruent. 

As a result by cpct (corresponding-part-of-congruent-triangle) we can prove that 

                      ∠ABC = ∠DCB 

Since AB‖CD and BC‖AD and opposite sides are also equal therefore, ABCD can be classified as a parallelogram.

As ABCD is a parallelogram the opposite angles are equal... hence ∠ABC = ∠ADC and ∠DCB = ∠DAB 

I hope I made it clear enough. 

You're welcome :) 

President = 10 options

Secretary = 9 options (can't be the person who was chosen for president)

Treasurer = 8 options (can't be president or secretary)

Morale officer = 7 options (can't be president, treasurer, or secretary)

Dog catcher = 6 options (can't be president secretary, treasurer, or morale officer)

10*9*8*7*6

=^._.^=

Hint: the remainder has degree less than 3.

Let n(P) play piano, n(T) take taekwondo and n(M) take lessons then

n(U) = 35         [Universal set]

n(T) = 11

n(P) = 11

n(M) = 20

n(P∩M) = 4

n(T∩P) = 3 

n(M∩T) = 5

n(P∪T∪M)' = 3 

⇒n(P∪T∪M) = 35 - 3 = 32 

Now subsittute all these values in the formula 

       n(P∪T∪M) = n(P) + n(T) + n(M) - n(P∩M) - n(T∩P) - n(M∩T) + n(P∩T∩M)

Then you'll get n(P∩T∩M). 

I hope its clear. 

2.6279807e+18
 

They're vertically opposite angles so, 

             5x - 10 = 60    ⇒ x = 14°

1 + 2 + 3 + 4 = 10

1 + 2 + 3 - 4 = 2

1 + 2 - 3 + 4 = 4

1 - 2 + 3 + 4 = 6

1 + 2 - 3 - 4 = -4

1 - 2 - 3 + 4 = 0 

1 - 2 - 3 - 4 = -8

So yeah! I think that's it 

2x - 7 + x + 4= = 90

3x - 3 = 90   ⇒ 3x = 93

x = 31°

🥱

20 is even. 

10 is even. 

5 is odd.

16 is even. 

8 is even. 

4 is even. 

2 is even. 

1 is odd. 

4 is even... and it starts to repeat. 

Can you take it from here?

=^._.^=

x_0 = 160/2

x_0 = 80 

=^._.^=

Thanks

\(1985*2113\)

The sum of the ages of the three Romano brothers is 63.
If their ages can be represented as consecutive integers,
what is the age of the middle brother?

\(\begin{array}{|rcll|} \hline (r_2-1) + r_2 +(r_2+1) &=& 63 \\ 3r_2 &=& 63 \quad | \quad : 3 \\ \mathbf{r_2} &=& \mathbf{21} \\ \hline \end{array}\)

The age of the middle brother is 21

As follows:

In the prime factorization of 12! + 15! + 18! + 21! + 24!, what is the exponent of 3?

(5-4i)-2(3+6i)  = 5 - 4i - 6 - 6i

Combine all real parts together and all imaginary parts together, s0:  (5-4i)-2(3+6i) =  -1 -10i

I was going to say that there are 4 choices for one end then 3 for the other end then 4! for the rest (assuming all the books are different)

So that is 4*3*4! = 12*24 = 288

Just as EP found  

GP:  \(1, {1\over8}, {1\over 8^2},...\)

a = 1, r = 1/8 

\({S}_{∞} ={a\over 1-r}\)

       \(={1\over 1-{1\over 8}}\)

       \(={8\over 7}\)